# DNV Wadam Wave analysis User Manual

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SESAM Wadam is a general analysis program for calculation of wave-structure interaction for fixed and floating structures of arbitrary shape, e.g. semi-submersible platforms, tension-leg platforms, gravity-base structures and ship hulls.

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SESAM

U

# SER

M

# ANUAL

# Wadam

# Wave Analysis by Diffraction and Morison Theory

D

# ET

N

# ORSKE

V

# ERITAS

SESAM

U

# SER

M

# ANUAL

D

# ET

N

# ORSKE

V

# ERITAS

# SESAM

# User Manual

# Wadam

# Wave Analysis by Diffraction and Morison Theory

# January 2, 2010

# Valid from program version 8.1

# Developed and Marketed by

# D ET N ORSKE V ERITAS

### DNV Software Report No.: 94-7100 / Revision8, January 22, 2010

Copyright © 2010 Det Norske Veritas

All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher.

Published by:

Det Norske Veritas

Veritasveien 1

N-1322 Høvik

Norway

Telephone:

Facsimile:

+47 67 57 99 00

+47 67 57 72 72

E-mail, sales: [email protected]

E-mail, support: [email protected]

Website: www.dnv.com

If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD

2 millions. In this provision “Det Norske Veritas” shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalf of Det Norske

Veritas.

**1 INTRODUCTION ............................................................................................................1-1**

**2 FEATURES OF WADAM ...............................................................................................2-1**

Calculation of Wave Loads from Second Order Potential Theory.................................. 2-47

**3 USER’S GUIDE TO WADAM........................................................................................ 3-1**

**4 EXECUTION OF WADAM............................................................................................ 4-1**

Reading a Command Input File into Prewad and Running Wadam ................................. 4-3

**5 PREWAD COMMAND DESCRIPTION.......................................................................5-1**

DEFINE ENVIRONMENT FREQUENCY-HEADING-PAIRS.................................................. 5-10

DEFINE ENVIRONMENT LINEARISING-WAVE-HEIGHT ................................................... 5-11

DEFINE GENERAL EXECUTION-DIRECTIVES ANALYSIS-TYPE..................................... 5-20

DEFINE GENERAL EXECUTION-DIRECTIVES DETERMINISTIC-MORISON.................. 5-21

DEFINE GENERAL EXECUTION-DIRECTIVES DRAG-LINEARISATION......................... 5-22

DEFINE GENERAL EXECUTION-DIRECTIVES DRIFT-FORCES ........................................ 5-23

DEFINE GENERAL EXECUTION-DIRECTIVES FIXED-FLOATING................................... 5-24

DEFINE GENERAL EXECUTION-DIRECTIVES HORISONTAL-DRIFT.............................. 5-25

DEFINE GENERAL EXECUTION-DIRECTIVES MORISON-EQUATION............................ 5-26

DEFINE GENERAL EXECUTION-DIRECTIVES OUTPUT-FORMAT .................................. 5-27

DEFINE GENERAL EXECUTION-DIRECTIVES POTENTIAL-THEORY ............................ 5-28

DEFINE GENERAL EXECUTION-DIRECTIVES PRINT-SWITCH........................................ 5-30

DEFINE GENERAL EXECUTION-DIRECTIVES RESULT-FILES......................................... 5-31

DEFINE GENERAL EXECUTION-DIRECTIVES SAVE-RESTART ...................................... 5-35

DEFINE GENERAL EXECUTION-DIRECTIVES SECOND-ORDER-RESULTS .................. 5-36

DEFINE GENERAL EXECUTION-DIRECTIVES TOLERANCES .......................................... 5-38

DEFINE GENERAL EXECUTION-DIRECTIVES WAVE-DRIFT-DAMPING ....................... 5-39

DEFINE GENERAL MULTI-BODY STRUCTURE-IDENTIFICATION.................................. 5-46

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 2D-MORISON-ELEMENT ............ 5-59

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 3D-MORISON-ELEMENT ............ 5-60

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref ANCHOR-ELEMENT .................... 5-61

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref DRY-ELEMENT ............................ 5-62

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref POINT-MASS................................. 5-63

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref PRESSURE-AREA-ELEMENT..... 5-64

DEFINE HYDRODYNAMIC-PROPERTY SECTION ref TLP-MOORING-ELEMENT ......... 5-65

**APPENDIX A TUTORIAL EXAMPLES............................................................................ A-1**

**REFERENCES.................................................................................................. REFERENCES-1**

**APPENDIX B THEORY....................................................................................................... B-1**

The Mapping of Loads from Panel Models to Finite Element Models.............................B-9

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**1-1**

**1 INTRODUCTION**

**1.1**

**Wadam — Wave Analysis by Diffraction and Morison Theory**

Wadam is a general analysis program for calculation of wave-structure interaction for fixed and floating structures of arbitrary shape, e.g. semi-submersible platforms, tension-leg platforms, gravity-base structures and ship hulls.

The analysis capabilities in Wadam comprise:

• Calculation of hydrostatic data and inertia properties

• Calculation of global responses including:

— First and second order wave exciting forces and moments

— Hydrodynamic added mass and damping

— First and second order rigid body motions

— Sectional forces and moments

— Steady drift forces and moments

— Wave drift damping coefficients

— Internal tank pressures

• Calculation of selected global responses of a multi-body system

• Automatic load transfer to a finite element model for subsequent structural analysis including:

— Inertia loads

— Line loads for structural beam element analysis

— Pressure loads for structural shell/solid element analysis

— Pressure loads up to the free surface

Wadam calculates loads using:

**Wadam**

**1-2**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

• Morison’s equation for slender structures

• First and second order 3D potential theory for large volume structures

• Morison’s equation and potential theory when the structure comprises of both slender and large volume parts. The forces at the slender part may optionally be calculated using the diffracted wave kinematics calculated from the presence of the large volume part of the structure.

The Wadam results may be presented directly as complex transfer functions or converted to time domain results for a specified sequence of phase angles of the incident wave. For fixed structures Morison’s equation may also be used with a time domain output option to calculate drag forces due to time independent current.

The same analysis model may be applied to both the calculation of global responses in Wadam and the subsequent structural analysis. For shell and solid element models Wadam also provides automatic mapping of pressure loads from a panel model to a differently meshed structural finite element model.

The 3D potential theory in Wadam is based directly on the Wamit program developed by Massachusetts

Institute of Technology Ref. /1/ and Ref. /2/.

**1.2**

**Wadam in the SESAM System**

Wadam is an integrated part of the SESAM suite of programs. It is tailored to calculate wave loads on models created by the SESAM preprocessors Patran-Pre, Prefem, Genie and Presel. The models are read by

Wadam from the Input Interface File (T-file). The Wadam analysis control data is generated by the Hydrodynamic design tool HydroD or by the Wadam preprocessor Prewad.

The results from the Wadam global response analysis may be stored on a Hydrodynamic Results Interface

File (G-file) for statistical postprocessing in Postresp. The loads mapped to structural finite elements may be stored on the Loads Interface File (L-file) for a subsequent structural analysis in Sestra.

**SESAM**

**Program version 8.1**

1.1

**22-JAN-2010**

**Wadam**

**1-3**

**Figure 1.1 SESAM overview**

**Wadam**

**1-4**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**1.3**

**How to read this Manual**

Chapter 2 FEATURES OF WADAM describes the problems Wadam can solve. Descriptions of models,

environment and results produced by Wadam are included.

Chapter 3 USER’S GUIDE TO WADAM presents tutorial examples. Each example includes a discussion of

the modelling, execution and results interpretation phases. Both simple examples and engineering applications are included.

Chapter 4 EXECUTION OF WADAM describes the input and output files of Wadam. The memory and disk

storage requirements are discussed together with some rules of thumb on execution time for different types of analysis. Finally, the chapter lists the problem size limitations in Wadam.

Chapter 5 PREWAD COMMAND DESCRIPTION contains a detailed description of the input commands

available in Prewad for establishing the Wadam analysis control data.

Appendix A contains input and output for tutorial examples of Chapter 3.

Appendix B includes additional theory description for Wadam.

**1.4**

**Terminology and Notation**

Composite model

Dual model

FE

HydroD

Hydrodynamic Results Interface File

Hydro model

Hydro property

Input Interface File

A hydro model consisting of a panel model and Morison model

representing separate parts of the structure. See Section 2.1.5.

A hydro model consisting of a panel model and Morison model

representing the *same* part of the structure. See Section 2.1.4.

Abbreviation for ‘finite element’ like in FE model

The hydrodynamic design tool. This is a modern graphical tool for modelling the input data to Wadam. Wadam is started directly from within this application.

A file containing results from a global response analysis. This file is termed G-file for short. The postprocessor Postresp per-

forms statistical postprocessing of these results. See Section 2.2

Hydrodynamic model. A model used for calculating hydrodynamic loads from potential theory and Morison’s equation. See

Hydrodynamic properties including added mass, drag coefficients, element diameters and anchor characteristics required for calculating hydrodynamic loads.

A file containing geometrical information of the structure (FE model plus hydro model). This file is termed T-file for short.

**SESAM**

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**Wadam**

**1-5**

Loads Interface File

Prewad

RSQ File

S-file swl

A file containing loads for a subsequent structural analysis.

This file is termed L-file for short. See Section 4.1.4.

Wadam’s interactive preprocessor

Wadam’s save-restart file named WADAM.RSQ; see Section

A file containing information on the relation between load cas-

es and wave frequencies. See Section 2.3.

Abbreviation for still water level.

**1.5**

**Status List**

There exists for Wadam (as for all other SESAM programs) a Status List providing additional information.

This may be:

• Reasons for update (new version)

• New features

• Errors found and corrected

• Etc.

The most recently updated status lists can be accessed over the internet. Go to www.dnv.com/software and select the Support tab. Then click on the "SESAM Status lists" entry. A user name and password is required to access this site. These can be obtained from Software Support ([email protected]).

Alternatively you may use the program Status for looking up information in the Status List: In Manager click . Then give File | Read Status List and select Wadam. In the Status List Browser window narrow the number of entries listed:

• Entries relevant to a specific version only

• Entries of a specific type, e.g. Reasons-for-Update

• Entries containing a given text string

Click the appropriate entry and read the information in a Print window.

**1.6**

**Wadam Extensions**

Wadam has the following extensions which require separate passwords:

2ORD Calculation of second order sum- and difference- frequency transfer functions for bodies in monochromatic and bi-chromatic incident waves.

NBOD Calculation of first-order hydrodynamic analysis of multiple bodies.

**Wadam**

**1-6**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

STRU

WDD

Transfer of hydrodynamic loads to structural finite element models with beam, shell and solid elements.

Computation of Wave Drift damping coefficients.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**2-1**

**2 FEATURES OF WADAM**

This chapter describes the features of the Wadam program. The chapter is organised with Section 2.1

two main analysis capabilities:

• Global response analysis for calculating rigid body type of results

• Detailed load calculation for transfers of finite element type of loads to a structural model

described in Section 2.6. Additional information on calculation methods is included in Appendix B.

**2.1**

**Definition of Model Types in Wadam**

The definition of models in Wadam includes three main model types: (1) the hydro model which is used to calculate hydrodynamic forces, (2) the structural model where hydrodynamic and hydrostatic loads are represented as finite element loads and (3) the mass model. The mass model is relevant for floating structures only and may be defined either as finite elements with mass properties or as a global mass matrix. The dif-

Interface Files generated by e.g. the SESAM preprocessors Patran-Pre, Prefem, Genie and Presel.

2.1

**Figure 2.1 Overview of model types in Wadam**

**Wadam**

**2-2**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

The hydro model may, see Figure 2.1, consist of either:

• A *panel model* for calculation of hydrodynamic results from potential theory

• A *Morison model* for calculation of hydrodynamic loads from Morison’s equation

• A combination of a panel- and a Morison model — called a *composite model*. The composite model is used when potential theory and Morison’s equation are applied to *different parts* of the hydro model.

• A combination of a panel- and a Morison model — called a *dual model*. The dual model is used when both potential theory and Morison’s equation shall be applied to the *same part* of the hydro model. The dual model must be used when pressure distribution from potential theory shall be transferred to a beam structural model.

The legal combinations of panel and Morison models are shown in Figure 2.2.

2.2

**Figure 2.2 Hydro model combinations**

Wadam models will be neglected.

**Table 2.1 Overview of SESAM element types interpreted in the various Wadam models**

**Type of element**

**Number of nodes**

**Panel model**

**Morison model**

**Mass model**

**Structural model**

**Beam elements**

Beam

Curved beam

**Shell elements**

2

3

√ √

√

√

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**2-3**

**Table 2.1 Overview of SESAM element types interpreted in the various Wadam models**

**Type of element**

Triangular flat thin shell

Quadrilateral flat thin shell

Subparametric curved triangular thick shell

Subparametric curved quadrilateral thick shell

Multilayered curved triangular shell

Multilayered curved quadrilateral shell

**Solid elements**

Triangular prism

Linear hexahedron

Tetrahedron

Isoparametric triangular prism

Isoparametric hexahedron

Isoparametric tetrahedron

**Mass elements**

One node mass element

**Number of nodes**

3

8

6

4

6

8

6

8

4

15

20

10

1

**Panel model**

√

√

√

√

√

√

√

√

√

√

√

√

**Morison model**

**Mass model**

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

√

**Structural model**

√

√

√

√

√

√

√

**2.1.1**

**The Coordinate Systems**

Wadam uses three different coordinate systems for single-body hydro models:

• A global coordinate system

• An input coordinate system

• Local finite element coordinate systems

The global coordinate system, denoted (X glo

, Y glo

, Z glo

), is right handed with the origin in the still water level. The Z-axis is normal to the still water level and the positive Z-axis is pointing upwards as shown in

the Figure 2.3 and Figure 2.4.

**Note: The results refer to the global coordinate system. The origin is termed the result reference point or the motion reference point.**

**Wadam**

**2-4**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

The input coordinate system, denoted (x inp

, y inp

, z inp

), is the coordinate system in which the hydro model and the structural model are defined. Wadam imposes the restriction that all input models, i.e. the panel,

Morison, mass and FE models must be modelled with the same input coordinate system. The coordinates of the off-body points are given in the global coordinate system. The relation between the global coordinate system and the input coordinate system is defined as follows:

• The origin of the input coordinate system must lie along the positive or negative Z-axis of the global coordinate system. It may also coincide with the origin of the global coordinate system.

• A parameter is used to define the position of the origin of the input coordinate system relative to the origin of the global coordinate system. If the origin of the input coordinate system is below the still water level then this parameter, called ZLOC, shall have a negative value.

• The x- and y-axes of the input coordinate system must be parallel with the x- and y-axes of the global coordinate system and point in the same direction.

If the Hydrodynamic preprocessor HydroD is used, there are no constraints on the position or orientation of the input coordinate system. The input coordinate system is then specified in relation to the global coordinate system by 3 translations and 3 Euler angles.

2.3

**Figure 2.3 2D representation of a TLP hull with input coordinate system below the swl, ZLOC=-h**

**SESAM**

**Program version 8.1**

2.4

**22-JAN-2010**

**Wadam**

**2-5**

**Figure 2.4 2D representation of a semi-submersible with centre of gravity along the global z-axis, **

**ZLOC=-h**

Local finite element coordinate systems are also used in the hydro model when this includes a Morison model. These local coordinate systems are discussed in the sections where they are referred to.

**2.1.2**

**The Panel Model**

The panel model is used to calculate the hydrodynamic loads and responses from potential theory.

The panel model may be a single superelement or a hierarchy of superelements. It may describe either the entire wet surface or it may take advantage of either one or two planes of symmetry of the wet surface. With symmetry planes employed the computational effort to solve the potential problem is reduced both with

2.1.7, there is the restriction that no planes of symmetry can be exploited.

The symmetry plane option requires that the basic part, i.e. the actually modelled part, is modelled on the

sion Leg Platform (TLP) panel model.

**Note: No panels are allowed in the symmetry plane(s).**

2.5

**Figure 2.5 Symmetry plane definitions**

**Wadam**

**2-6**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

The basic part of a panel model consists of quadrilateral or triangular panels representing the wet surfaces of a body. The panel model is modelled in the Patran-Pre or Prefem preprocessor using standard finite elements. If more than one superelement is modelled the superelements must be assembled in Presel. The ele-

ments accepted in the panel model are defined in Table 2.1.

Note that panels are constructed by drawing straight line segments between the corner nodes of the finite element sides. Therefore twisted panels are forced to be planar by projecting element corner nodes onto panel vertices in the plane defined by the line segment midpoints.

The wet surface of a panel model is identified by defining a dummy load on the panel model in Patran-Pre or Prefem. In Prefem this is achieved by applying a so-called HYDRO-PRESSURE load with load case number one to all wet surfaces of the model. Panels will be generated for all element sides below the still water level and above the sea bed where HYDRO-PRESSURE load is defined. The model may be verified in Prefem by displaying the mesh on the wet surface and adding the HYDRO-PRESSURE load. The load is illustrated by arrows pointing from the fluid onto the wet element sides. In Patran-Pre the corresponding option is the Hydro, Element Uniform load.

Wadam will automatically adjust the wet element sides extending above the still water level into panels with its uppermost edge and vertices in the still water level. Depending on the shape and orientation of the wet element sides this may actually lead to either an adjustment or a division of a wet element side into new pan-

below the sea-bed.

2.6

**Figure 2.6 Panel adjustments at the still water level**

The Wadam data check reports all the panels extracted from the input panel model noting specifically those panels which have been adjusted or divided into two separate panels.

The modelling of a panel model with thick shell elements, which often is the case when the panel model is defined as the wet surface of a structural model, may introduce significant deviations in the representation of volume and area exposed to wave forces. It may be required to establish a separate panel model with nodes on the outer surface of the thick shell structural model.

**SESAM**

**Program version 8.1**

2.7

**22-JAN-2010**

**Wadam**

**2-7**

**Figure 2.7 The basic part of a TLP panel model**

**2.1.3**

**The Morison Model**

The Morison model is used to calculate hydrodynamic loads based on Morison’s equation. In addition to representing the complete or parts of the structure the Morison model is used to include external forces from mooring lines and tethers in a hydro model. Furthermore, if hydrodynamic loads from potential theory, i.e. pressure loads calculated on panels, shall be transferred to a beam structural model then the Morison model

The Morison model is put together from a set of Morison elements. The Morison elements are based on 2 node beam elements and single nodes in a first level superelement generated by Patran-Pre, Prefem or

Genie. The Morison elements are actually defined by assigning hydrodynamic properties to nodes and beam elements in HydroD or Prewad.

The different types of Morison elements available for calculation of hydrostatic and hydrodynamic effects are:

• 2D Morison elements for calculation of hydrostatic and hydrodynamic loads on wet 2 node beam elements

• 3D Morison elements for calculation of hydrostatic and hydrodynamic loads in three directions in specific nodes

• Pressure area elements for calculation of hydrostatic and hydrodynamic loads at the ends of 2D Morison elements

• Dry Morison elements for transfer of hydrostatic and hydrodynamic loads from potential theory to 2 node beam elements

• Point mass elements for modelling of additional nodal mass in specific nodes

**Wadam**

**2-8**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

• Mooring and tether elements for calculation of additional restoring contributions in specific nodes

The inertia loads due to the mass of Morison elements may also be calculated. This option is available for all elements except the mooring and tether elements.

**Note: The Morison model must be modelled as one single first level superelement. No symmetry plane options are available for the Morison model.**

Figure 2.8 shows a beam model and Figure 2.9 the corresponding Morison model representation with 2D

Morison elements and pressure area elements. The modelling principles for establishing different types of

Morison elements are discussed in the following subsections.

2.8

**Figure 2.8 2 node beam element model of a semi-submersible platform**

**SESAM**

**Program version 8.1**

2.9

**22-JAN-2010**

**Wadam**

**2-9**

**Figure 2.9 Morison model representation of a semi-submersible platform with 2D Morison elements and pressure area elements**

**2D Morison Elements**

A 2D Morison element is most conveniently defined as a 2 node beam element in a preprocessor and assigned a section number to be matched by a hydro property section specified in HydroD or Prewad.

A 2D Morison element is used to include added mass and drag forces according to Morison’s equation; see

Section 2.6.4. It is also used to include hydrostatic restoring contributions.

The hydro property description for a 2D Morison element include added mass and viscous drag coefficients in the two directions perpendicular to the longitudinal element axis. The hydrodynamic coefficients are

per unit length and the diameter of the element is specified. The length and diameter may either be taken from the preprocessor generated beam model or specified by HydroD or Prewad.

The section numbers play an important role in the analysis of a Morison model. The use of section numbers to include different hydrodynamic effects in the Morison model should therefore be carefully planned before section numbers are assigned to 2D beam elements in the preprocessor. E.g. if different drag and inertia coefficients shall be used in different locations this should be reflected by the section definitions.

The hydrodynamic coefficients specified for a 2D Morison element apply to circular cross sections. For elements with non-circular cross-sections the hydrodynamic coefficients in the ξ and ζ directions are directly related to an equivalent cross-sectional diameter. Wadam calculates this equivalent diameter as the circum-

scribing diameter shown for the examples in Figure 2.10.

**Wadam**

**2-10**

2.10

**22-JAN-2010**

**SESAM**

**Program version 8.1**

Equivalent diameter

**Figure 2.10 Equivalent diameters for non-circular cross sections**

The 2D Morison elements may be divided into sub-elements each of which may be assigned different hydro property sections. The sub-elements may have equal or varying lengths.

figure illustrates how Wadam automatically performs the subdivision of elements depending on whether they intersect the still water level or not.

on each side of the still water level. This element is first divided into five sub-elements. The sub-element intersecting the still water level is further divided into two new sub-elements such that a sub-element border lies in the still water level. The result is actually six sub-elements of which the first five receives hydro loads and optionally inertia forces. The last sub-element will only receive inertia forces.

ment numbering starts at the deepest node irrespective of which is the first and which is the second node when defining the Morison element. This forced ordering of sub-element numbers is performed for all elements with one node below and the other either at or above the still water level. For completely submerged or dry elements the sub-element division is straight forward, i.e. increasing sub-element numbers from the

first to the second node; see Figure 2.11 (c).

**SESAM**

**Program version 8.1**

2.11

**22-JAN-2010**

**Wadam**

**2-11**

**Figure 2.11 The sub-element division of 2D Morison elements**

The local coordinate system for a 2D Morison element ( ξ, η, ζ) is defined as follows:

• The ξ-axis is normal to the element and parallel with the xy-plane of the input coordinate system.

• The η-axis points along the element from node N

1

Morison element as shown in Figure 2.12 (a).

to node N

2

where N

1

is the first node defining the 2D

• The ζ-axis is the third axis in the right handed cartesian coordinate system defined by ξ and η.

• The ξ-axis is parallel with the x inp

-axis if the η-axis is parallel with the z inp

In addition to the 2D Morison elements connected to 2 node beam elements defined by preprocessors 2D

Morison elements may also be defined directly by HydroD or Prewad. Such additional Morison elements must however be related to existing nodes in the Morison model defined in a preprocessor. Additional Morison elements may be used to include specific load contributions in a global response analysis.

**Note: The loads from additional 2D Morison elements will, however, not be transferred to loads in a subsequent structural analysis thus resulting in load imbalances in the structural analysis.**

**Wadam**

**2-12**

2.12

**22-JAN-2010**

**SESAM**

**Program version 8.1**

**Figure 2.12 Local coordinate system of 2D and 3D Morison elements**

**3D Morison Elements**

A 3D Morison element is defined in HydroD or Prewad and can only be connected to nodes in the Morison model.

A 3D Morison element may be used to include loads which cannot be represented with a 2D Morison element in a hydro model. Drag forces and added mass forces in the longitudinal direction of a 2D Morison element are examples of forces that can be included with a 3D Morison element.

A 3D Morison element may be viewed as a submerged sphere which can receive both hydrostatic and hydrodynamic loads. It will not contribute to the restoring matrix.

The hydro property description for a 3D Morison element includes added mass and viscous drag coefficients in three directions together with a diameter of the submerged sphere.

The local coordinate system for a 3D Morison element ( ξ, η, ζ) will by default coincide with the coordinate system of the Morison model (x inp

, y inp

, z inp

). If the local coordinate system shall be different from that of the Morison model a guiding point defining the local

η-axis must be specified. Figure 2.12 shows this with

node N

1

being the 3D Morison element and node N as described above for 2D Morison elements.

2

being the guiding point. The ξ- and ζ-axes are defined

The forces on a 3D Morison element is acting at the node to which the 3D Morison element is connected.

**Pressure Area Elements**

A pressure area element is defined in HydroD or Prewad and connected to a node in the Morison model. The node represents the centre of the circular pressure area element. The direction of the element is defined by a

guiding point and the area with diameter *d* as shown in Figure 2.13.

**SESAM**

**Program version 8.1**

2.13

**22-JAN-2010**

**Wadam**

**2-13**

**Figure 2.13 The pressure area element definition**

The pressure area element includes the hydrostatic and Froude-Krylov pressure force. (The Froude-Krylov force is the force due to the undisturbed incoming wave.) The force is applied in node N1 in the direction of the element normal, i.e. from N1 to the guiding point. The Froude-Krylov pressure force represents a simplified approximation to the correct pressure. Therefore 3D Morison elements must be used to include the end effects of added mass and viscous damping.

The pressure area element has three main application areas. These are:

• Include normal pressure at submerged ends of a cylinder; see Figure 2.14 (a)

• Adjust (subtract) the pressure at intersection between cylinders; see Figure 2.14 (b)

• Include longitudinal forces due to varying cylinder diameters; see Figure 2.14 (c)

2.14

**Figure 2.14 Application areas for the pressure area element**

The use of pressure area elements in the dual and composite hydro model types requires some special atten-

tion. This is described in more detail in Section 2.1.4 and Section 2.1.5.

**Dry Morison Elements**

A dry Morison element is defined as a 2 node beam element with no assigned hydro properties. This is most conveniently achieved by defining a beam element in the preprocessor with a section number not matching any hydro property section number specified in HydroD or Prewad.

**Wadam**

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A dry Morison element may be used to transfer panel pressures directly to 2 node beam elements in a struc-

formed on a dry Morison element.

A dry Morison element includes only the mass per unit length and the diameter of the element. A dry Morison element may alternatively be defined directly in HydroD or Prewad. The end nodes of the dry Morison element must in this case be connected to nodes existing in the Morison model.

A dry Morison element specified directly in HydroD or Prewad is not part of a structural model. Therefore, when the loads on a structural model are calculated, panel pressures connected to dry Morison elements defined directly in HydroD or Prewad will not be mapped onto the structural model and load imbalance will occur.

**Point Mass Elements**

A point mass element is defined in HydroD or Prewad and can only be connected to existing nodes in the

Morison model.

A point mass element may be used to include nodal masses in a Morison model whereby point masses defined by the preprocessors are created as point mass elements in Wadam. (The point mass element numbers are generated automatically starting at element number 400,000.) The point mass section numbers are generated in the range 1001 to 1999. Note that no other element or section numbers may coincide with those automatically generated for the point mass elements.

The property description for a point mass element includes the mass of the node. The point mass elements may alternatively be defined directly in HydroD or Prewad.

**Note: Contrary to some of the other element types specified directly in HydroD or Prewad the nodal loads from point mass elements will be mapped onto the structural model.**

**Mooring Elements**

A mooring element is defined in HydroD or Prewad and can only be connected to nodes in the Morison

element is also termed anchor element.

A mooring element may be used to include external restoring forces from weightless mooring lines with linear stiffness characteristics.

The mooring elements are connected to nodes in the Morison model. The first connection node for the mooring element is the guiding point, also termed the fairlead. The second connection point may be at a

windlass as shown in Figure 2.15 (a). The two mooring element connections may optionally be the same

node. The hydro properties of a mooring element include the element orientation, the pre-tension and the restoring characteristics.

The element orientation includes two different angles; The angle mooring line and the angle

Note that the angle α inc

α

α inc

between the still water level and the x

between the positive x-axis and the mooring line as shown in Figure 2.15 (b).

≤ π/2 with respect to the negative x-axis for nodes with x < 0.

The restoring contributions from the mooring elements are assembled into the body restoring matrix and hence contribute to the rigid body motion. The rigid body motion computed yields dynamic restoring forces

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2-15 acting in the mooring element nodes. They are mapped onto the structural model as nodal loads. No nodal moment loads are transferred to the structural model.

**Note: Spring elements on the Input Interface File are neglected.**

2.15

**Figure 2.15 Mooring element definitions**

**TLP Mooring Elements**

A TLP mooring element is defined in HydroD or Prewad and connected to nodes in the Morison model. It is

TLP mooring element formulation.

A TLP mooring element may be used to include external restoring forces from a weightless tether with linear tether characteristics.

The hydro properties of a TLP mooring element include the length L of the tether, the pre-tension and the elastic stiffness parameter λ. A horizontal offset position x offset

, y offset

may also be specified as shown in

Figure 2.16. Note that the tether length shall be the actual length at the offset position.

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**Figure 2.16 The TLP mooring element**

The restoring contributions from the TLP mooring elements are assembled into the body restoring matrix and hence contribute to the rigid body motion. The rigid body motion computed yields dynamic restoring forces acting in the mooring element nodes. They are mapped onto the structural model as nodal loads.

**Note: No nodal moment loads are transferred to the structural model.**

**2.1.4**

**The Dual Model**

The dual model is a hydro model where a panel model and a Morison model represents the *same* part of a

used to include the forces related to added mass and potential damping whereas the Morison model is used to include the viscous drag forces.

2.17

**Figure 2.17 A dual model with both a panel model and a Morison model representing a structure**

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The dual model is mandatory when hydrodynamic loads from potential theory shall be used in the structural analysis of a beam model.

In a dual model the hydrodynamic loads are always transferred from a panel model to a Morison model. The viscous drag forces are calculated from Morison’s equation on the Morison model while the contributions from potential theory are represented as loads on Morison sub-elements according to a panel-to-Morison element correspondence defined by the user. Panel pressures may be transferred to loads on 2D Morison elements, 3D Morison elements, pressure area elements and dry Morison elements. For 2D Morison elements

the panel pressures are transferred specifically to each sub-element as shown in Figure 2.18.

The loads on Morison elements are transferred to a beam model as line loads for 2D Morison elements and dry Morison elements. For the 3D Morison element and the pressure area element the loads are transferred as nodal loads.

The hydrostatic load transferred to the structural model is computed from the Morison model including the pressure area elements.

2.18

**Figure 2.18 The correspondence between panels and a 2D Morison element**

In a dual model all the panels must be connected to Morison elements. There may, however, be Morison ele-

ments in a dual model without connections to panels as shown in Figure 2.2.

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Note that no moment loads will be transferred to a Morison element from integration of panel pressures.

That is, the transfer of panel pressures will only be correct if the pressures integrated gives no resulting moment with respect to the Morison element.

Pressure area elements must always be used to include end effects of Morison elements which are not part of a dual model.

The panel model included in a dual model may utilise the standard symmetry plane options for panel models. In this case Wadam will map the panel pressures to the symmetric parts of the Morison model although

of a dual model which includes a two-plane symmetric panel model and a Morison model.

**Note: It is not possible to have a correspondence from a panel to a beam which lies in a plane of symmetry.**

2.19

**Figure 2.19 Dual model with a two-plane symmetric panel model**

**2.1.5**

**The Composite Model**

The composite model is a hydro model suitable for structures consisting of both slender and large volume parts. The slender parts are represented with a Morison model and the large volume parts with a panel model.

The hydrodynamic forces on a composite model are computed from potential theory for the panel model and from Morison’s equation for the Morison model. The hydrodynamic exciting forces and matrices from both theories are accumulated in the system of equation of motions for the composite model.

The wave kinematics applied in Morison’s equation may either be taken from the incident wave field. or it may be specified to depend on the diffracted wave field generated from solving the diffraction problem for

with 2D Morison elements, may optionally be exposed to loads from a diffracted wave field caused by the shaft of the large volume structure.

With a composite model the pressure area element shall normally be included in the Morison model for all wave lengths.

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**Figure 2.20 Example of a composite model with a panel model and a non-overlapping Morison model**

**2.1.6**

**Single Super element Composite model**

From version 8.1-09 of Wadam, the beams receiving loads from the Morison model and the shells or solids receiving loads from the panel model may be modelled in the same 1. level super element. The panel model may then be defined separately, whereas the Morison model is the same super element as the structural model. It is also possible to have the panel model, the Morison model and the structural model all in the same super element.

**2.1.7**

**Multi-Body Modelling**

The hydrodynamic and mechanical interaction between a number of structures can be analysed with the multi-body option. The hydrodynamic interaction is computed from the potential theory as applied for a single structure with the principal extension that the number of degrees of freedom is increased from 6 to 6N where N is the number of structures. A stiffness coupling between structures cannot be described directly in

Wadam.

Each of the bodies may be represented with a hydro model and optionally a structural model and a mass model. The bodies may be either fixed or floating.

A hierarchical set of coordinate systems is introduced in which the individual structures and their input models are specified. The coordinate systems applied in a multi-body analysis are therefore different from

those of a single-body analysis; see Figure 2.21. The coordinate systems are defined as follows:

• The global coordinate system (X glo

, Y glo

, Z glo

) is a right handed cartesian coordinate system with its origin at the still water level and with the z-axis normal to the still water level and the positive z-axis pointing upwards.

• The individual body coordinate systems (x

B coordinate system.

, y

B

, z

B

) of each structure are specified relative to the global

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• The input coordinate system (x inp

, y inp

, z inp

) of each input model included in a body is specified relative to the body coordinate system of that body.

The body independent coordinates are described in the global coordinate system, e.g. the fluid kinematics evaluation points.

The coordinates related to a particular body are described in the corresponding body coordinate systems, e.g. the result reference coordinate system.

The coordinates related to the individual input models are described in the input coordinate systems, e.g. nodal coordinates of the input models.

2.21

**Figure 2.21 The hierarchical coordinate system definition**

**2.1.8**

**Mass Modelling**

Global mass information is required in Wadam for analysis of floating structures. The mass is used both in the hydrostatic calculations to report imbalances between weight and buoyancy of the structure and in the equation of motion.

Wadam provides two methods to establish global mass matrices:

• Direct input specification of a global mass matrix

• Assembling of a global mass matrix from a mass model (no utilisation of symmetry planes)

Wadam transfers accelerations to Loads Interface Files for subsequent structural analysis. A consistent calculation of inertia loads from these accelerations is ensured in Wadam and Sestra by access to the same module for finite element mass generation.

For beam element models there is the alternative option to calculating inertia loads in Wadam and transferring the loads to the Loads Interface Files.

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The remaining part of this section describes the two methods for establishing global mass information.

**Direct Input Specification of Global Mass Matrix**

The direct input specification of a global mass matrix comprises giving the total mass of the structure together with the centre of gravity, the gyration radii and the products of inertia. The centre of gravity is specified with respect to the input coordinate system. The gyration radii and the products of inertia are specified with respect to the global coordinate system.

The direct input specification of a global mass matrix cannot be used together with the option to integrate forces on sectional planes in the hydro model. This is because the global mass matrix does not include any information of the mass distribution on the particular elements and hence the inertia force contributions from these elements cannot be computed. As described below the option to generate the mass from a mass model must be used to obtain these sectional forces.

**Assembling of Global Mass Matrix from Mass Model**

The mass model used in the assembling of a global mass matrix may be defined using one of two options:

• It may be defined using the global generate option which interprets a finite element model built from an arbitrary superelement hierarchy. With this option mass contributions are assembled from the element

• It may be generated with the distributed mass option which only works with the Morison model. This implies that the entire mass description must be represented in the Morison model. With the distributed mass options contributions are assembled from the following types of Morison elements:

— 2D Morison elements

— 3D Morison elements

— Dry Morison elements

— Point mass elements

The assembling of a global mass matrix from a mass model must be used together with the option to integrate forces on sectional planes in the hydro model.

The mass model must be defined in the same coordinate system as used for the other input models. This is

described in more detail in Section 2.1.1.

The mass model may be identical to the structural model or it may be a completely different superelement hierarchy.

**2.1.9**

**Structural Modelling**

The structural model may be built from an arbitrary large superelement hierarchy. It may include any of the

receive hydrostatic and hydrodynamic loads.

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The finite elements which shall receive hydrostatic and hydrodynamic loads must be identified in the modelling phase. The technique to identify elements differs between beam elements and element types with surfaces (shells and volumes) as described in the two subsections below.

Nodal accelerations from rigid body motion will be calculated for all the nodes in a structural model.

If the structural model consists of more than one superelement a combination of loads from different superelements is required in the superelement assembling performed in Presel. The combination of loads is

**Loads on Superelements with Beams**

The beam elements and nodes which shall receive hydrostatic and hydrodynamic loads from Wadam must be included in a Morison model. The loads are transferred to the beam elements and nodes which are con-

nected to Morison elements in HydroD or Prewad: see Section 2.3.5.

Note that both hydrostatic and hydrodynamic load contributions on free ends of beam elements require the

element ends to be closed with Morison pressure area elements as described in Section 2.1.3.

Note also that additional 2D Morison elements defined in HydroD or Prewad do not correspond to beam elements in the structural model and hence cannot contribute to the structural loads. The additional Morison elements should be used with care; They are a source to imbalances between the loads calculated in a global response analysis and the element and nodal forces transferred to a structural model.

**Loads on Superelements with Shell and Solid Elements**

For shell and solid elements loads are transferred to the finite element sides which are identified as wet. The so-called HYDRO-PRESSURE load option in Prefem (or Hydro, Element uniform load in Patran-Pre) is used to identify the wet element sides. The definition of wet sides of the structural model is equivalent to the

superelements of a structural model.

Wadam transfers pressure loads to both the external wet surface of a structural model and to the wet surfaces of internal tanks. The dummy load case number of the HYDRO-PRESSURE load must be used to identify which of the wet elements shall receive external and which shall receive internal HYDRO-PRESSURE loads. The rules for this dummy load case numbering is the following:

External wet surface: The HYDRO-PRESSURE load case number must be equal to one.

Internal wet surface: The HYDRO-PRESSURE load case for the first internal wet surface (tank) must be equal to two. Additional internal tanks are numbered consecutively with load case number three assigned to tank number two and so on.

It is important in the definition of wet element sides that the direction of the pressure load is pointing from the fluid towards the element side. For this purpose both Patran-Pre and Prefem provides an option to visu-

of the normal vectors pointing towards wet element sides. This load can also be visualized and verified in

HydroD.

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**Figure 2.22 Idealised view of hydro pressures on structural element sides**

The dummy HYDRO-PRESSURE load cases used to identify wet structural elements will not be in conflict with load cases generated by Wadam or other load cases defined by the preprocessors.

**2.1.10 Free Surface Modelling**

The free surface model used in the second order sum- and difference- frequency force calculation in Wadam may be generated by Patran-Pre or Prefem. It may optionally also be interpreted directly from the Wamit

version 5.3S free surface format, Ref. /2/.

The part of the free surface actually modelled by surface panels is defined by the radius of a circle as shown

according to the decaying rate of local waves. An appropriate approximation is *R* ~ O(*h*) for shallow water and *R* ~ O( λ) for deep water. Here h is the water depth and λ>>*h* is the longest wave length involved. The ratio *h*/

λ may have to be substantially larger than 1 to achieve accuracy in deep water, Ref. /3/.

2.23

**Figure 2.23 Free surface mesh**

The free surface must be meshed with 4 node shell elements (no 3 node elements). The HYDRO-PRES-

SURE load case must point in the negative z-direction.

The free surface model shall have the same symmetry properties as the panel model.

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**2.1.11 Load Case Numbering and Load Case Combinations**

The default load case numbers LC generated by Wadam on the Loads Interface Files are given from the following equation.

LC = ( ( ( + ( ) (2.1) where:

MM

NOK

LL

NPHA

IPHA

I

NSEL is the actual heading number is the total number of frequencies is the actual frequency number is the number of phase angles if the time output option is specified, NPHA = 1 if complex loads are generated is the actual phase angle number, IPHA = 1 if complex loads are generated is zero for static load cases and one for dynamic load cases is the number of occurrences of the first level superelement in question

ISEL is the actual occurrence number of the first level superelement in question

through NSEL as static load cases and load cases number NSEL+1 through NOK· NOH · (NSEL+1) as

frequency and heading angle.

The relation between superelement occurrence numbers in Wadam and the superelement index numbers in

For loads transferred to a structure modelled with shell or solid elements Wadam includes some options to manipulate the generation of loads on the Loads Interface Files and the numbering of load cases. More specifically, for floating structures Wadam by default generates four different types of loads represented as static and dynamic loads respectively. These are:

• Hydrostatic pressure and gravity summed together in the first global load case.

• Hydrodynamic pressure loads and nodal accelerations summed together for each combination of incident wave frequency and heading angle into global load cases starting with load case number two.

For the case of load transfer from a panel model to a shell/solid model each of the four load types above may optionally be either suppressed or divided into separate load cases. This is controlled from HydroD or Prewad.

For structural models consisting of one superelement only Wadam will by default generate a hydrostatic load case for the still water condition and a sequence of hydrodynamic load cases, one for each specified combination of wave frequency and wave direction. If deterministic load calculation is specified separate

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2-25 load cases are also created for each specified phase angle. The load cases generated by Wadam will be the global load cases for single superelement structural models.

For structural models defined from a hierarchy of superelements the hydrostatic and hydrodynamic load cases for each superelement will include the load cases for all the occurrences of each particular superele-

Furthermore, for structural models defined from a hierarchy of superelements the load cases created by

Wadam for first level superelements are combined into new higher level load cases in Presel. The load case combination is performed recursively, i.e. repeated for each new higher level superelement created in Presel.

At the structure level the load case combinations coincides with the global load cases. See also the SESAM

System Manual for a description of the assembling of superelement hierarchies and load combinations.

The term superelement occurrence number defines the actual location of a superelement in a superelement hierarchy. The number is found by counting the occurrences of a superelement from left to right in a superelement hierarchy (or from top and down in hierarchy as printed by Presel).

Two simple examples are included to describe the relation between global load case numbers and the load case numbers generated by Wadam. In both examples the set of global loads include one static load case and

6 dynamic load cases defined as the combinations of three incident wave frequencies and two heading angles.

**Example 2.1**

**Load case numbering for a single superelement model**

This example consists of a structural model built from one single superelement. Here the load case numbers

ence between the global load case numbers and the wave frequency and heading combinations.

**Table 2.2 Load case numbering for a single superelement structural models**

**Load case number (global = Wadam) Load case description**

1

2

3

4

5

6

7

Hydrostatic

β = 0°, ω = 0.0

β = 0°, ω = 0.1

β = 0°, ω = 0.2

β = 90°, ω = 0.0

β = 90°, ω = 0.1

β = 90°, ω = 0.2

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**Example 2.2**

**Load case numbering for a model assembled in a superelement hierarchy**

This example is a model consisting of a first level superelement, superelement number 10, used in two different positions in a two level superelement hierarchy. The top level superelement number is 100. Adopting

2.24 shows the superelement hierarchy.

2.24

**Figure 2.24 Two-level superelement hierarchy with occurrence 1 and 2 of superelement 10 included in superelement 100**

also includes the superelement occurrence numbers, a description of the separate load cases and the Presel generated superelement index numbers.

**Table 2.3 Load case numbering for a model assembled in a superelement hierarchy**

7

7

6

6

5

5

4

4

**Global load case number**

1

1

3

3

2

2

**Wadam load case number**

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Load case description static static

β = 0°, ω = 0.0

β = 0°, ω = 0.0

β = 0°, ω = 0.1

β = 0°, ω = 0.1

β = 0°, ω = 0.2

β = 0°, ω = 0.2

β = 90°, ω = 0.0

β = 90°, ω = 0.0

β = 90°, ω = 0.1

β = 90°, ω = 0.1

β = 90°, ω = 0.2

β = 90°, ω = 0.2

**Occurrence of superelement 10**

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

**Presel index**

1

2

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In this very simple example there is a one-to-one correspondence between occurrence numbers and Presel index numbers. This one-to-one correspondence is not required. However, when the occurrence numbers and the Presel indices do not match the load combination in Presel should be carefully performed to ensure that the indices correspond to the correct occurrence numbers.

The one-to-one correspondence may be violated for particular choices of using the same first level superelement in several sub-hierarchies of a multi level superelement model.

**2.2**

**Global Response Analysis**

**2.2.1**

**General**

The global response feature in Wadam computes the response of fixed and floating structures due to wave loads. Results computed are forces and response transfer functions assuming rigid bodies. Also global matrix results data, sectional loads and off-body kinematics results may be produced. The results can be transferred to the statistical postprocessor Postresp for graphics presentation and further results processing through a Results Interface File.

The statistical postprocessing in Postresp consists of statistical analysis of transfer functions including calculation of response spectra and short and long term statistics. Postresp also includes the option to calculate the equation of motion from the global matrices and exciting forces transferred from Wadam.

The global response analysis is performed for a system consisting of a hydro model and a mass model. The latter is only required if the system is specified to be floating. Additional mooring and tether stiffness characteristics may also be provided for floating systems.

The hydro model may consist of either a panel model, a Morison model built from beam elements or a combination of these two model types. The hydro model represents different types of hydrostatic and hydrody-

namic loads. The hydro model concept is described in detail in Section 2.1.

A mass model is required when the global response analysis includes calculation of motions. A mass model may either be defined as a FE model where the mass of each finite element contributes to a 6 by 6 body mass matrix, also termed the global mass matrix. Alternatively the mass model may be specified directly as

an input global mass matrix. The mass model is described in more detail in Section 2.1.8.

**2.2.2**

**Computation of Wave Loads**

Wadam calculates wave induced forces for a specified set of wave frequencies and heading angles by one of the following three calculation methods:

• Morison’s equation applied to a Morison model

• The MacCamy-Fuchs formula applied to a Morison model

• The potential theory applied to a panel model

• A method in which Morison’s equation and the potential theory both are applied to compute hydrodynamic loads on the same hydro model. This calculation method restricts the hydro model to be built from either:

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— Non-coupled Morison and panel models

posite model the wave kinematics applied in Morison’s equation may optionally be modified to take into account the diffracted wave field due to the presence of a panel part in the hydro model.

— A Morison model partly or completely coupled to a panel model

This type of hydro model is termed a dual model and is described in Section 2.1.4. The dual model

serves two purposes. It provides a mechanism to add viscous drag forces from Morison’s equation to the damping terms calculated from potential theory. It also provides a mechanism to calculate hydrodynamic pressure loads on a panel model and to subsequently represent these loads as line loads on beam elements in a structural model.

The motion responses for a hydro model is obtained by solving the equations of motion for a set of wave frequencies and heading angles. The rigid body added mass, damping and restoring matrices used in the equations of motion may be calculated by applying Morison’s equation, the potential theory or the composite method as described above. Except for frequency dependent added mass matrices these matrices may alternatively be specified directly by the user.

**2.2.3**

**The Global Response Results**

The wave induced forces and moments and the motion responses calculated by Wadam are reported with respect to a motion reference point which is located at the intersection between the still water level and a vertical line through the common origin of the models used in the analysis. The coordinate systems in

Wadam are described in Section 2.1.1.

The results available from a global response analysis of a hydro model include transfer functions for:

• Wave exciting forces and moments

• Motion responses

• Sectional loads

• Rigid body matrices

• Off-body kinematics

• Surface elevations

Section 2.5 describes all these results types in more detail.

**2.3**

**The Calculation of Detailed Loads on a Structural Model**

**2.3.1**

**General**

The detailed load calculation feature provides a tool for automatically transferring wave loads from a hydrodynamic analysis into finite element loads for a structural analysis.

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Both hydrostatic and hydrodynamic loads on a structural model may be calculated. The results, which may be both FE pressure loads and nodal loads, will be transferred to Loads Interface Files for subsequent linear static or dynamic analysis in Sestra. Wadam also transfers environmental information and load case numbering information to Sestra on a separate file (the S-file). The latter is specifically required for a subsequent stochastic fatigue analysis using Framework.

**2.3.2**

**The Structural Load Types**

Three different load types may be generated by Wadam and transferred to a structural model. These are:

• Hydrostatic loads with contributions from forces in the still water condition and pre-tension from mooring and tether systems

• Gravity load representing the weight of the structure

• Hydrodynamic loads with contributions from exciting forces from incident waves, forces from wave induced motion and rigid body accelerations

Detailed descriptions of distributed loads are included in Section 2.5.15 and Section 2.5.16.

Wadam generates separate load case numbers for the hydrostatic load and for each of the hydrodynamic loads, i.e. for each wave frequency and heading. These loads may be combined into new load cases with

Presel. The new combined load cases will be used during subsequent structural analysis and postprocessing.

SESAM.

**2.3.3**

**Deterministic Loads**

Wadam also provides the option to report transfer functions for FE loads as deterministic loads (time domain). That is loads represented for specified phase angles of incident waves with given wave amplitudes.

The deterministic results presentation may also be used together with the option to calculate the following types of loads:

• Non-linear viscous drag forces from Morison’s equation for fixed structures.

• Pressure loads up to the instantaneous free surface, see Section 2.6.7.

• Time invariant current profiles added to the incident wave field in the calculation of forces by Morison’s

equation. See Section 2.4.2 for the description of current profiles in Wadam.

**Note: Deterministic loads cannot be computed for a dual model.**

**2.3.4**

**Detailed Loads Transfer to a Model with Shell or Solid Elements**

The transfer of detailed loads to a large volume structure modelled with shell or solid elements is performed as follows:

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• The hydrostatic load at still water condition is calculated as normal pressures directly on the shell and solid element surfaces defined as wet sides.

• The hydrodynamic pressure loads on shell or solid elements can only be obtained from a potential theory calculation based on a panel model. The actual mapping of panel pressures into normal pressure loads in

a structural model is automatically performed by the algorithm described in Appendix B 3.3.

• Independent nodal loads require a Morison model to be used together with the panel model. More specifically, if loads from mooring lines and tethers shall be included in a structural system a Morison model consisting of the connection nodes must be created.

**2.3.5**

**Detailed Loads Transfer to a Model with Beam Elements**

The transfer of loads to a slender structure, for example a jacket or a jackup, modelled with beam elements is performed as follows:

• The hydrostatic load at the still water condition is represented as loads on beam elements and nodes in the structural model.

• The hydrodynamic loads are calculated for the beam elements and nodes corresponding to the Morison elements. The method of load calculation depends on the connection between the hydro model and the structural model:

— If the hydro model is a Morison model then the hydrodynamic pressure loads obtained by Morison’s equation are represented directly as line loads and nodal loads on the beam element model.

— If the hydro model is a panel model then the hydrodynamic loads are first calculated as panel pressures and then transferred to a Morison model according to a panel-to-Morison element correspondence. The Morison element loads are subsequently represented as line loads and nodal loads on the beam element model.

**2.4**

**Environmental Description**

**2.4.1**

**Surface Waves**

The models in Wadam may when first order potential theory and Morison’s equation are applied be exposed to planar and linear harmonic waves, i.e. waves described by the Airy wave theory. For the second order

The incident waves may be specified by either wave lengths, wave angular frequencies or wave periods. The direction of the incident waves are specified by the angle β between the positive x-axis and the propagating

direction as shown in Figure 2.25 (a).

The incident wave used in Wadam is defined as

η = Re *Ae* i ( – ( cos + sin β ) )

]

(2.2) which alternatively may be written as

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η = A cos ( – ( cos β + y sin β ) )

This represents a wave with its crest at the origin for *t* = 0 as shown in Figure 2.25 (b).

2.25

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**Figure 2.25 Surface wave definitions**

*The fluid velocity v = v x*

**i** + *v* y

**j** + *v* z

**k** and acceleration **a** = *a* x

**i** + *a* y

**j** + *a* z

**k** for the incident waves are: k z

β

*A x k*

*ω where d v h*

= v x y j = A --cosh kz kd sinh

*) cos ( v z*

= – A ω sinh ( kz kd sinh ( kd )

) sin ( – ⋅ )

*) a h*

= – a x i + a y j = A ω 2 k cosh ( kz kd sinh

*) sin ( – ⋅ a z*

= – A ω 2 sinh kz kd ) sinh cos ( )

)

Depth

Absolute value of wave number

Wave angular frequency

Wave amplitude

= *x***i** + *y***j** — location in the x-y plane

= *k* (**i **cos β + **j **sinβ) — two dimensional wave number

Vertical coordinate with z-axis upward, *z *= 0.0 at still water level

Direction of wave propagation

(2.4)

(2.5)

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The finite depth dispersion relation used in the above expressions is

ω 2

= gk tanh

The wave period is given by

T =

2 π

ω and the wave length is

λ =

*2 ω k*

For a more detailed description of linear wave theory see Ref. /8/.

The fluid kinematics above the still water level is obtained by constant extrapolation in Wadam.

(2.6)

(2.7)

(2.8)

**2.4.2**

**Current Profiles**

Wadam provides the option to specify time invariant current profiles for the calculation of deterministic

Morison element forces.

**Note: The current can only be used for fixed structures.**

The current profile may be specified at a set of positions along the z-axis of the global coordinate system.

Current values at intermediate z-positions are obtained by linear interpolation. The direction of the current in the horizontal plane is specified at each positions.

2.26

**Figure 2.26 Current profile definition**

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**2.4.3**

**Water Depth**

Wadam provides the option to specify a water depth. The water depth is used in two different calculation phases in the program:

• It is used in the processing of the panel model to remove all panels below the sea-bed.

• It is used in the calculation of Green’s functions for finite water depth.

**2.5**

**Results Types Reported from Wadam**

**2.5.1**

**Units**

When performing an analysis with SESAM the user must apply a set of consistent units. The same units must be used in all programs throughout the analysis from modelling to results presentation.

The basis for determining a set of consistent units is the fundamental equation: f = *m***a**

In terms of the fundamental units of mass [M], length [L] and time [T] this equation may be written:

(2.9)

F =

*T*

2

(2.10)

Force, stress, density, etc. are not fundamental units and must be derived in terms of the units of mass, length and time. Whenever possible it is simplest to use S.I. units:

[L]

[M]

Length in meters (m)

Mass in kilograms (kg)

[T] Time in seconds (s)

Force will then be in Newton (N):

*1 N = 1 s*

2

(2.11)

The units used in Wadam is controlled by the acceleration of gravity [L/T 2 other input data must be expressed in terms of these units. For example:

] and the fluid density [M/L 3 ]. All

• Fluid kinematic viscosity: [L 2 /T]

• Fluid velocity: [L/T]

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**2.5.2**

**Result Reference Point**

For single-body structures the results from Wadam are reported with respect to a result reference point

**2.5.3**

**Dimensioning of Results**

Wadam reports results on dimensionalised and non-dimensionalised form as follows:

• The Hydrodynamic Results Interface File contains dimensionalised results.

• The Loads Interface Files contain dimensionalised results.

• The Wadam print file contains both forms as follows:

— Chapters 2 and 5 contain dimensionalised results.

— Chapter 4 contains non-dimensionalised results.

*The non-dimensionalising factor D n ised results F d*

from the formula:

specified in Table 2.4 and Table 2.5 may be used to obtain dimensional-

*F d*

*= D n*

*F n*

(2.12)

*L*

*V*

*A where F n*

is a non-dimensionalised result reported in chapter 4 in the Wadam print file. The factors used in the tables are:

ρ Density of the fluid g Acceleration of gravity

Characteristic length

Displaced volume of the body

Amplitude of the incoming wave, equal to one for harmonic results

**Table 2.4 Dimensionalising factors for matrices**

**Result type**

Inertia matrix

Added mass matrix

*i*=1-3, *j*=1-3

ρ*V*

ρ*V*

*D n entry i,j*

*i*=1-3, *j*=4-6

*i*=4-6, *j*=1-3

ρ*VL*

ρ*VL*

*i*=4-6, *j*=4-6

ρ*VL*

ρ*VL*

2

2

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**Result type**

Damping matrix

Restoring matrix

**Table 2.4 Dimensionalising factors for matrices**

*i*=1-3, *j*=1-3

ρ*V*sqrt(*g*/*L*)

ρ*Vg*/*L*

*D n entry i,j*

*i*=1-3, *j*=4-6

*i*=4-6, *j*=1-3

ρ*V*sqrt(*gL*)

ρ*Vg*

*i*=4-6, *j*=4-6

ρ*VL*sqrt(*gL*)

ρ*VgL*

**Table 2.5 Dimensionalising factors for results**

*D n mode i*

**Result type**

Exciting forces

Motion

Drift forces

Sectional loads

Fluid pressures

Fluid velocities

Fluid accelerations

2nd order forces

2nd order motions

2nd order pressures

*i*=1-3

ρ*VgA*/*L*

*A*

ρ*gLA* 2

ρ*VgA*/*L*

ρ*gA*

*A*sqrt(*g*/*L*)

*Ag*/*L*

ρ*gLA* 2

*A*

2

/*L*

ρ*gA* 2 /*L*

*j*=4-6

ρ*VgA*

*A*/*L*

ρ*gL* 2

*A*

2

ρ*VgA*

ρ*gL* 2

*A*

2

*A*

/*L*

2

2

**2.5.4**

**Transfer Functions and Phase Definitions**

The transfer functions in Wadam describe responses for bodies in harmonic waves. The reported responses are normalised with respect to the incident wave amplitudes. With a transfer function *H*( ω,β) the corresponding time dependent response variable *R*( ω,β,*t*) can be expressed as

R ( , = [ ( ( ω β ) )*e* i ω*t*

] (2.13) where *A* is the amplitude of the incoming wave, ω is the frequency of the incoming wave, β describes the direction of the incoming wave and *t* denotes time. The phase angle φ between the incident wave and the time varying response is defined from

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R ( ω β *t *) = [ ( ω β ) *e* i ( ω*t *φ )

] (2.14) where |*H*| is the amplitude of the transfer function. The transfer function and the phase angle may be expressed as

*H = H*

Re

*+ iH*

Im and φ = atan ---------

Re

The time varying response can alternatively be expressed as

(2.15)

R ( ω β *t *) =

Re cos –

Im sin ω*t *] (2.16)

The phase lead φ of the response relative to an incident wave with the wave crest at the origin of the global

coordinate system is shown in Figure 2.27.

2.27

**Figure 2.27 Definition of phase between the response and the incident wave**

**2.5.5**

**Hydrostatic Restoring Results**

Wadam calculates the hydrostatic restoring results from the hydro model. It is given with dimensions and include:

• The sum of displaced volume of the panel and Morison part of the model

The total displaced volume is reported together with the separate contributions from the panel and Morison parts.

For the panel model the volume is reported from three different calculations, i.e. from summing up of control volumes in the three different directions. The reported total volume is taken as the median of the three volumes (not mean but middle value of three values).

**Note: If the separate control volumes are differing by a significant number this normally indicates that the wet surface of the model is not properly defined.**

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• The centre of buoyancy

• The water plane area

• The metacentric height

• The global hydrostatic restoring matrix assembled from both hull restoring and additional stiffness terms

The additional hydrostatic stiffness terms included in the hydro model may include contributions from:

• Risers, mooring lines or tethers represented with Morison mooring or tether elements

• Stiffness matrices specified directly on the analysis control data

For multi-body models the hydrostatic restoring matrix for each body is reported.

**Note: By definition, the global hydrostatic restoring matrix from the dual part of a hydro model is calculated from the panel model. The hydrostatic restoring from the Morison elements with no panels connected are also assembled to the global hydrostatic restoring data.**

**Note: The global hydrostatic restoring calculation differs from the calculation of the hydrostatic **

**load case in a subsequent detailed load calculation. As described in Section 2.5.15 the hydro-**

**static loads on a structural beam model is calculated directly from the beam elements irrespective of any dual model. This definition requires a high degree of hydrostatic similarity between a panel model and its dual beam model if consistency shall be preserved between Wadam and a structural analysis in Sestra.**

**Note: In the hydrostatic restoring contribution from the Morison elements the local waterplane moment for each Morison member is not included. This can cause errors if some of the beams have a large diameter. The fix to this problem is to include this restoring contribution as an additional restoring matrix.**

**2.5.6**

**Global Mass Matrix**

A 6 by 6 mass inertia coefficient matrix is reported for each body. It is generated according to the input definition and hence may be calculated from either:

• The hydro model

• The structural model

• A specific mass model

• The input definition of an inertia mass matrix based on:

— Specifying the centre of gravity and the radii of gyration together with the total mass

— Specifying the 6 by 6 global mass matrix

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**2.5.7**

**Added Mass Matrix**

The 6 by 6 added mass matrix is reported for each separate body. The added mass interaction matrices between any two bodies in a multi-body system are also reported. The added mass matrix is calculated according to the type of the hydro model as follows:

• Frequency dependent added mass from potential theory

• Frequency independent added mass from Morison’s equation

For the composite hydro model the added mass at a given frequency is reported with both frequency dependent and independent contributions.

**2.5.8**

**Damping Matrix**

The 6 by 6 damping matrix is reported for each separate body. The potential damping interaction matrices between any two bodies in a multi-body system are also reported. The damping matrix is calculated according to the type of the hydro model as follows:

• Frequency dependent damping from potential theory

• Frequency independent linearised viscous damping from Morison’s equation

• HydroD or Prewad specified frequency dependent or frequency independent 6 by 6 damping matrices

For the composite hydro model type the damping for a given frequency is reported as both frequency dependent and independent contributions.

**2.5.9**

**Exciting Forces and Moments**

The transfer functions for exciting forces and moments due to the incident waves are reported for each body at all the combinations of frequencies and wave headings. The transfer functions for rigid body forces and moments are calculated as follows:

• By integration of exciting forces from all types of Morison elements obtained from the linearised Morison’s equation

• By integration of pressures on all the panels obtained by solving the diffraction problem

• By applying the Haskind relation on the radiation potentials if no detailed panel pressures shall be calculated

For the dual and composite model types the exciting forces from the panel and Morison parts are reported both separately and as the combination used in the subsequent analysis, e.g. in the equation of motion.

By selecting time domain output the above results will be reported as deterministic forces and moments at specified phases of the incident waves with given wave amplitudes.

For fixed structures the deterministic Morison option may be used to include the following non-linear effects in Morison’s equation:

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• Non-linear viscous drag formulation

• Time invariant current may be superimposed on the fluid velocities.

• Forces and moments may be calculated up to the free surface by constant extrapolation of the linear wave profile.

**2.5.10 Rigid Body Motion**

The transfer functions for rigid body motion due to the incident waves are reported for each body for all the combinations of wave frequencies and heading angles. The roll, pitch and yaw motions are reported in radians.

The equation of motion is assembled from the calculated global matrices and transfer functions as described in the previous sections. The HydroD or Prewad specified damping and stiffness matrices will be added to the otherwise calculated matrices.

By specifying the time domain output format the motions will be reported as deterministic motions at specified phases of the incident waves with given wave amplitudes.

**2.5.11 Second Order Mean Drift Forces**

The second order mean drift forces due to the linear incident waves are reported both on the print file and in the Hydrodynamic Results Interface File. They are calculated by one of the following methods:

• Momentum conservation in the three horizontal degrees of freedom

• Pressure integration in all six degrees of freedom. This method will also give the mean drift forces on each individual body in a multi-body analysis.

**2.5.12 Second Order Sum and Difference Frequency Results**

The transfer functions for sum and difference frequencies are reported in the print file and on the Hydrodynamic Results Interface File. The following second order results are available:

• The quadratic second order force

• The second order forces on the body by an indirect calculation method

• The second order forces on the body by a direct calculation method

• The second order pressure distribution on the body (only available in the print file)

• The second order wave elevation at specified points (only available in the Wamit output file format)

**2.5.13 Fluid Kinematics**

The transfer functions for pressure and particle velocity in specified points in the fluid is reported both on the print file and in the Hydrodynamic Results Interface File. The fluid kinematics points are specified in the fluid domain outside the hydro model. The fluid kinematics depends on the type of hydro model:

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• It is obtained from the incident undisturbed wave field if only Morison’s equation is applied.

• It is obtained from the diffracted wave field if the potential theory is applied to a fixed structure.

• It is obtained from the radiated and diffracted wave field if the potential theory is applied to a floating structure.

By specifying the time domain output format the fluid kinematics will be reported as deterministic pressure and velocities at specified phases of the incident waves with given wave amplitudes.

The surface elevation η in a radiated and diffracted wave field is obtained from potential theory as

η = (2.17) where *p* is the non-dimensionalised pressure at the still water level.

**2.5.14 Wave Drift Damping**

The Wave Drift Damping describes the rate of change of the Mean Drift force with forward speed computed at zero speed. The sign of this rate of change is in most cases negative, meaning that this will represent a damping mechanism for the slow drift motion excited by the second-order difference frequency forces or due to the interaction of the waves with a current.

The 3x3 Wave Drift Damping matrix (surge, sway, yaw) is reported in the Hydrodynamic Results Interface

File. This matrix is computed according to the methods described in Ref. /9/.

The computation of the wave drift damping requires a free surface mesh which is defined as input exactly like the free surface mesh for second-order analysis. The mesh used in the Wave Drift Damping computations does, however, not need to have a circular outer boundary.

A Morison model can not be used if Wave Drift Damping is to be computed.

The iterative equation-solver for the potential-solution can not be applied if Wave Drift Damping is computed

**2.5.15 Distributed Hydrostatic Loads**

The hydrostatic loads on a structural model is calculated directly on the individual finite elements of the model. It is represented on the Loads Interface Files as a real load case.

**Structural Beam Models**

For wet beam structural superelements the hydrostatic load case is represented as line loads on the beam finite elements and as nodal loads on nodes receiving loads from 3D Morison elements and pressure area elements. In addition, the pre-tension from Morison anchor and TLP elements are included as nodal loads in the hydrostatic load case.

The gravity component of the static load is only included as direct loads if the mass model is specified as a distributed mass model. When using other types of mass models the gravity acceleration only will be written to the Loads Interface File.

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A general description of line loads on beam finite elements is included in Appendix B 3.2.

**Note: Pressure Area Elements should always be defined at the end of vertical members such as the legs on a semi-submersible. **

**Structural Shell or Solid Models**

For wet surfaces of shell and solid elements in a structural model the hydrostatic loads are represented as normal pressures. Because the hydrostatic pressure intensities are evaluated individually at the z-coordinate of each node the normal pressure on wet element sides will have a variation in the z-direction as opposed to the hydrodynamic loads which are constant over each element.

The gravity component of the static load is included by writing the acceleration of gravity to the Loads

Interface File.

**2.5.16 Distributed Hydrodynamic Loads**

The distributed hydrodynamic loads are calculated in a body fixed coordinate system and include the following contributions:

• Exciting forces from incident waves

• Forces from wave induced motion

• Fluctuating hydrostatic pressure forces due to the body motion

The distributed forces presented in the Wadam print file are:

• Transfer functions for pressures on the panels in the hydro model

1

• Transfer functions for forces acting at the centre of gravity for 2D Morison and dry Morison elements

• Transfer functions for nodal forces acting on nodes in the hydro model which are connected to the following Morison element types:

— 3D Morison elements

— Pressure area elements

— Mooring and TLP elements

— Point mass elements

The distributed loads transferred to the Loads Interface Files are:

• Transfer functions for normal pressures on the wet sides of shell and solid elements. The pressures are constant over the elements. These loads originate from pressures at the centroid of panels according to

the mapping algorithm described in Appendix B 3.3. They include fluctuating hydrostatic pressure.

1. Not including fluctuating hydrostatic pressure.

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• Transfer functions for line loads on beam elements. These loads originate from forces at the centre of gravity of 2D Morison sub-elements and dry Morison elements. The calculation of line loads on 2 node

beam elements is described in Appendix B 3.2.

• Transfer functions for loads at nodes which are connected to Morison elements

• An acceleration field acting on all the nodes in the structural model

• The inertia components are only included as loads if the mass model is specified as a distributed mass model.

Wadam and the structural analysis program Sestra both employ the standard SESAM finite element library to generate a mass representation. This implies that the connection between accelerations and inertia loads is consistently handled in the two programs.

**2.5.17 Load Sum Reports**

Load sums are important tools to verify both the correctness of input models to Wadam and of the consistency between Wadam and subsequent structural analyses.

Wadam reports load sums on both the structural model and the hydro model in chapter 5.1 in the print file.

Note that these load sums are reported with dimensions.

• Load sums for the loads transferred to the structural beam model:

— The sum of hydrostatic loads transferred to a beam model is reported in the print file as static loads. It includes the hydrostatic forces from each Morison type of element as follows:

• The buoyancy and pre-tension components from mooring and TLP elements are always included.

• The gravity components are only included if the mass model is specified as a distributed mass model.

— The sum of hydrodynamic loads acting on the beam model is reported in the print file for each incident wave frequency and wave heading. It includes the hydrodynamic forces from each Morison type of element as follows:

• The hydrodynamic pressure components acting on beams and nodes

• The inertia components are only included if the mass model is specified as a distributed mass model.

• Load sums for the loads transferred to the structural shell/solid model:

— The sum of hydrostatic loads transferred to a shell/solid model is reported in the print file as static loads. It includes the buoyancy of the structure.

— The sum of hydrodynamic pressure loads transferred to the shell and solid structural model is reported in the print file for each incident wave frequency and wave heading. It includes the part of the hydrodynamic loads actually transferred to normal pressure loads on shell and solid elements.

Note that this load sum does not include inertia loads.

— The sum of pressures and inertia loads acting on the structural model may be calculated from the Sestra data check where the accelerations transferred from Wadam are converted into inertia loads; see

• Load sums for the hydro model:

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— The sum of hydrodynamic forces acting on a panel model is reported in the print file for each incident wave frequency and heading. It includes the pressures acting at the centroid of each panel in the hydro model. Note that this load sum does not include inertia loads.

**2.5.18 Sectional Loads**

Wadam calculates sectional loads by integration of distributed forces on specified sides of given planes intersecting a hydro model. The frequency dependent exciting and inertia forces are included in the integration. The sectional planes are specified in the input coordinate system and must be normal to one of the main

plays a simple submerged beam model with a sectional plane x inp defined in the input coordinate system (x inp

, y inp

, z inp

).

= 0. The moment reference point is

2.28

**Figure 2.28 Sectional loads at a plane through x=0**

The sectional loads are reported in the Wadam print file and on the Hydrodynamic Results Interface File as complex transfer functions.

Still water sectional loads are reported on the Wadam print file.

The sectional loads are integrated with respect to a body fixed coordinate system. The sectional load on a cut comes from the integration of **F**-m**a** over that part of the structure which is on the positive or negative side of the cut. The components of the load are in the global system. This means that for the dynamic loads the load computed by integration over the positive side and the load computed by integration over the negative side will be equal in magnitude, but have a phase difference of 180 degrees.

As an example we consider a ship cut at x=0 normal to the x-axis:

If integration over the positive side is specified the sectional load will be the force acting on the part of the hull with x<0 from the part with x>0. This means that the static bouyancy force will give a positive vertical shear force and a negative vertical bending moment. We will also find that the phase angle of the vertical bending moment in a hogging situation is close to zero for long waves.

If integration over the negative side is specified the static bouyance force will give a positive vertical shear force and a positive vertical bending moment. The phase angle for the vertical bending moment in a long wave will be close to +/- 180 degrees.

The contributions to the sectional loads from different hydro models are computed as follows:

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• For Morison models the exciting and inertia forces, obtained at the centre of gravity of each Morison sub-element on the specified side of the sectional plane, are included.

• For panel models the exciting forces at the centroid of each panel are included. The inertia forces are included with respect to a centre of gravity calculated for the part of the model that is on the specified side of the sectional plane.

For panel models the sectional loads from integrating the hydrostatic pressure loads on the panel model are also reported in the print file (LIS-file).

• For dual models the forces represented at the centre of gravity of the Morison sub-elements are included.

This implies that the potential pressures transferred to the Morison sub-elements according to a correspondence list are included together with the viscous forces calculated directly on the Morison element.

**Note: Sectional loads calculation should be used with care when global matrices are specified directly as input to Wadam. This is because the global matrices do not provide the detailed information required to integrate distributed force contributions.**

In addition to the total sectional loads it is also possible to compute and write to the Global Results Interface

File (G-file) differnt parts of the sectional load. This includes sectional added mass matrix, sectional damping matrix, sectional body mass matrix and sectional excitation force. These quantities cannot be handled by

Postresp, but they may be read into DeepC.

To compute these sectional load details a modification of the Wadam*.FEM file must be done manually:

Open this file in an editor an find the card WADAMA1. (This is one of the first cards on the file.) Change the 19th number on this card from 0 to 1.

**2.5.19 Roll Damping Coefficients**

Wadam calculates the roll damping coefficient *B*

44 namic effects:

by including contributions from the following hydrody-

• Potential damping from surface wave radiation

• Linearised viscous damping from eddy-making of the bilge keel

• Linearised viscous damping from skin-friction of the hull

• Linearised viscous damping from bilge keel

The potential damping effect is included in the radiation potentials and is defined within the regular linear theory.

The linearised viscous roll damping effects from eddy-making due to the naked hull is computed based on

contributions are linearised in order to be included in the harmonic equations of motion.

The potential damping and the skin friction contributions are calculated from a strip model which is automatically generated from a panel model. The other two effects are calculated from information about the bilge keel.

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The viscous damping coefficient is generally defined as

*B*

*

44

= K η

*4 max*

In Wadam the coefficient *K* is calculated approximately as a function of the wave-frequency, the hull form and the bilge keel dimensions. The variable η

*4 max*

is the maximum expected roll angle.

When viscous roll damping is included in the equation of motion the roll angle amplitude is not known in advance rather it is a part of the solution. Therefore, the user has to estimate the maximum expected roll angle for each wave heading. The calculated transfer function for roll motion is compared with the maximum value specified for that heading. If the computed roll motion is ‘close’ to the specified angle then the roll transfer function for that value is assumed to be ‘correct’. If the difference is not acceptable then another

η estimate must be made and the roll motion re-computed. Note, however, that the potential solution is independent of η. Hence the potential should be saved during the first computation and the program should be submitted with a restart option during this iteration process. If the maximum roll angle is taken from short term statistics (only one sea state) then Wadam can perform the iteration process automatically. If the maximum roll angle is taken from long term statistics then the iteration must be carried out manually.

It should be kept in mind that these coefficients are only valid within the range of tests and models used in the experiments. Extrapolation outside this range should be performed with care.

The roll damping option in Wadam also includes a linearised roll restoring coefficient in the equation of

motion. The calculation of this coefficient is described in Appendix B 3.1.

**Note: The Roll damping model can only be used for ship-like structures with symmetry about the **

**XZ-plane.**

**Note: The computation of the bilge keel damping breaks down when the bilge keel is very small. The symptom is that the damping starts to increase when the width of the bilge keel decrease. The exact limit is case dependent, but as an indication the width of the bilge keel should not be smaller than 10cm. **

**2.5.20 Global drag-coefficient for roll-damping**

A global coefficient for quadratic damping of the roll-motion can be given as user-specified input. This makes it possible to use results from model-tests directly. The quadratic damping is linearized by stochastic linearization. This way, model tests performed independent of sea-states can be used in connection with any given sea-state valid for the actual location of the structure. The formulation of the method of stochastic linearization is explained in Appendix B 3.5.

**Note: This kind of damping should not be combined with any other types of damping effects, except the potential dampimg. In other words, the old roll-damping model, the Morison model or user-specified linear damping are not to be combined with the global tortional drag.**

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**2.6**

**Calculation Methods**

**2.6.1**

**Calculation of Wave Loads from Potential Theory**

and diffraction effects on large volume structures. The actual implementation is based on Wamit

1 which uses a 3D panel method to evaluate velocity potentials and hydrodynamic coefficients.

This implementation can be used for infinite and finite water depths and both single bodies and multiple interacting bodies can be analysed. The flow is assumed to be ideal and time-harmonic. The free surface condition is linearised for the first order potential theory while the non-linear free surface condition is imposed for the second order potential theory computation. The radiation and diffraction velocity potentials on the wet part of the body surface are determined from the solution of an integral equation obtained by using Green’s theorem with the free surface source potentials as the Green’s functions. The source strengths are evaluated based on the source distribution method using the same source potentials.

The integral equation is discretisised into a set of algebraic equations by approximating the body surface with a number of plane quadrilateral panels. The source strengths are assumed to be constant over each panel. Two, one or no planes of symmetry of the body geometry may be present. The solution of the algebraic equation system provides the strength of the sources on the panels. The equation system, which is complex and indefinite, may be solved by a direct LU factorisation method or by an iterative method.

**Boundary Value Problem Formulation**

The assumption of potential flow allows defining the velocity flow as the gradient of the velocity potential

Φ that satisfies the Laplace equation

∇

2

Φ = 0

(2.18) in the fluid domain. The harmonic time dependence allows defining a complex velocity potential φ related to Φ by

Φ = Re ( φ*e* i ω*t*

) (2.19) where ω is the frequency of the incident wave and *t* is time. The associated boundary-value problem will be expressed in terms of the complex velocity potential φ with the understanding that the product of all complex quantities with the factor *e* i ω*t*

applies. The linearised form of the free-surface condition is

*φ z*

– K φ = 0 z = 0 (2.20) where *K* = ω 2

/*g* and *g* is the acceleration of gravity. The velocity potential of the incident wave is defined by

φ

0

*= cosh kz H cosh kH*

)

– ( cos + sin β )

(2.21) where the wave number *k* is the real root of the dispersion relation and β is the angle between the direction of propagation of the incident wave and the positive x-axis.

1. Wamit is a computer program developed by Massachusetts Institute of Technology.

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Linearisation of the problem permits decomposition of the velocity potential φ into the radiation and diffraction components:

φ = φ

*R*

+ φ

*D*

φ

*R*

= i ω ∑ j = 1 6

*ξ j*

*φ j*

φ

*R*

= φ

0

+ φ

7

(2.22)

(2.23)

(2.24)

*The constants ξ j*

* denote the complex amplitudes of the body oscillatory motion in its six rigid-body degrees of freedom and φ j*

the corresponding unit-amplitude radiation potentials. The velocity potential φ

7

represents the disturbance of the incident wave by the body fixed at its undisturbed position. The total diffraction potential φ

*D*

denotes the sum of φ

7

and the incident wave potential.

On the undisturbed position of the body boundary the radiation and diffraction potentials are subject to the conditions

*φ jn*

*= n j*

(2.25)

φ

*Dn*

= 0 where (*n*

1

, *n*

2

, *n*

3

) = **n** and (*n*

4

, *n*

5

, *n*

6

*) = r × n, r = (x, y, z). The unit vector n is normal to the body boundary and points out of the fluid domain. The boundary value problem must be supplemented by a condition of outgoing waves applied to the velocity potentials φ j*

, *j*=1,...,7.

**2.6.2**

**Calculation of Wave Loads from Second Order Potential Theory**

difference-frequency components of the second order forces, moments and rigid body motions (Quadratic

Transfer Functions) in the presence of bi-chromatic and bi-directional waves.

**2.6.3**

**Removal of Irregular Frequencies**

Wadam provides an option to remove the irregular frequencies from the radiation-diffraction solution. This method is based on a modified integral equation obtained by including a panel model of the internal water plane. The panel model of the water plane is automatically created by Wadam.

**2.6.4**

**Morison’s Equation**

and to calculate the detailed forces **F** acting on 2D Morison elements and 3D Morison elements. The form of

included.

**F**

Where:

= ω 2 ( M + ρ*V*

*M*

*C a*

2 ρ*V*

*M*

*( C a*

*+ I + ( ) f c*

*+ f g*

*+ f b*

(2.26)

**Wadam**

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ω

**M**

*C a*

**I**

ρ

*V*

*M*

**B**

Incident wave frequency

3 by 3 diagonal mass inertia matrix

3 by 3 diagonal added mass coefficient matrix

3 by 3 identity matrix

Density of water

Displaced volume of the Morison element

Linearised viscous damping matrix expressed as

B =

1

2

ρσ**C**

*D*

⋅

**3 π max x**

ξ

**C**

*D*

*σ f c*

3 by 3 diagonal drag coefficient matrix

Projected area of the Morison element

Complex amplitude of the incident wave field

Complex amplitude of the motion

*Fluctuating hydrostatic restoring force representing the first order restoring contributions integrated in the equation of motion f g*

*Fluctuating gravity force representing the acceleration of gravity calculated in a coordinate system fixed with the Morison model f b*

Fluctuating buoyancy force calculated in a coordinate system fixed with the Morison model

sation of the general viscous drag force **F**

*D*

expressed as

**F**

*D*

=

1

2

ρσ**C**

*D*

( =

1

2

ρσ**C**

D 3

8

*π max*

( ) = ( – ) (2.27)

The term

3

8

*π max*

(2.28) is a standard result obtained by assuming equal work done at resonance by the non-linearised and the equivalent linear damping term. *V* and same *V* max incident wave frequencies.

*max*

is a linearising velocity amplitude specified as input to Wadam. The one

is applied in the linearised drag force calculation for all the motion modes and for all the

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For deterministic analysis of fixed structures Morison’s equation is expressed on the form

F = ρ*V*

*M*

*( + a*

+ ρσ**C**

D v v where time independent current may be included in **v**.

(2.29)

The contributions from Morison elements are calculated in the particular element local coordinate systems.

The contributions are transformed into the body coordinate system prior to the assembling of rigid body quantities.

calculated from potential theory.

**2.6.5**

**The Equation of Motion**

The equation of motion in Wadam is established for harmonic motion of rigid body systems expressed in the global coordinate system.

By applying Newtons law and including the added mass, damping and exciting force contributions acting on the panel and Morison parts of a hydro model the complex 6 by 1 motion vector X( ω,β) can be found from the equation of motion

*[ – ω 2 ( + ω ) + i ( p*

*+ B v e*

( ,

### β

) = F ( ω β ) (2.30) where

**M**

**A**( ω)

**B**( ω) p

*B v*

C represents the 6 by 6 body inertia matrix represents the 6 by 6 frequency dependent added mass matrix represents the 6 by 6 frequency dependent potential damping matrix represents the 6 by 6 linearised viscous damping matrix represents the 6 by 6 hydrostatic restoring matrix

*C e*

**F**( ω,β) represents the 6 by 6 external restoring matrix is the 6 by 1 complex exciting force vector for frequency ω and incident wave heading angle

β

The eigenvalues λ and eigenvectors Φ of the rigid body system is obtained for a given incident wave frequency by solving the eigenvalue problem

[ – ) + C ]Φ = 0 (2.31)

The natural periods of the rigid body system at a given incident wave frequency is expressed as

T =

2 π

λ

(2.32)

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**2.6.6**

**Calculation of Tank Pressures**

Wadam calculates by an approximate algorithm the harmonic pressure load on the wet finite element sides in internal tanks.

The loads are calculated by applying a hydrostatic pressure distribution in the accelerated reference frame fixed with respect to the tank. The pressure load is divided in a constant and an oscillating part and represented by separate load cases. The pressure gradient is given by

∇*p* = ( ) (2.33) where **g** is the acceleration due to gravity, **a** is the complex acceleration of the mid-point of the tank and ρ is the mass density of water. The gravity vector described in a coordinate system oscillating with the body has a constant and an oscillating part. Accordingly, the pressure gradient described in the body-fixed coordinate system has a constant part ρ**g** and an oscillating (dynamic) or fluctuating part:

*∇ p f*

*= f*

*– a ) (2.34) where g f*

is the fluctuating part of gravity. A detailed outlining of the tank pressure calculation is included in

The tanks are modelled by assigning the HYDRO-PRESSURE load to those surfaces which are the walls of the tanks. The number of the HYDRO-PRESSURE load will be the number of the tank. This numbering must start at 2 since the HYDRO-PRESSURE with load case 1 is the external pressure. All surfaces with the same HYDRO-PRESSURE number will be assumed by Wadam to be the same tank.

The filling of the tanks is controlled by assigning the hydro-pressure load only to the wet part of the tank walls. No sloshing effects are included, i.e. the fluid is assumed to move like a rigid body.

**Note: The mass of the tank fluid must be included in the mass model for Wadam. In the structural **

**(FE) model the inertia forces from the tank fluid are represented as pressure loads and should therefore not be included in the structural mass.**

**2.6.7**

**Pressure Loads up to Free Surface**

Wadam may be used to extrapolate to the free surface the panel pressures calculated by first order potential theory (up to the still water level). Note that this implies that the dry finite elements below the still water

constant extrapolation, also called stretching, of pressures above the still water level is applied. This pressure extrapolation option depends on the amplitudes of the waves and hence this option is only available when results in the time output format is specified.

Note that the pressures only will be received by the finite elements above the still water level defined as wet in the structural model.

For a panel model this option is available for both fixed and floating structures, but the intersection of the structure and the free surface must be vertical. If a Morison model is included the option is only available for fixed structures.

**SESAM**

**Program version 8.1**

2.29

**22-JAN-2010**

**Wadam**

**2-51**

**Figure 2.29 Constant extrapolation of panel pressures to the free surface**

**2.6.8**

**Reduced pressure up to the free surface**

One of the "stretching" methods is the approach referred to as reduced loads. This is a kind of “meanstretching” applied in frequency domain.

In this procedure, the loads are multiplied with a linearly attenuated reduction factor in a zone between some given distance below and above the still-water level. Below the still-water level, the reduction factor is applied directly. Above the still-water level, the reduction factor is applied to the loads extrapolated from just below (ideally at) the still-water level.

The loads are attenuated linearly down to zero as the level increases from still-water level and up to a given amplitude. This amplitude is typically an extreme-level of the waves (eg a 20 year level). For an amplitude

*A* the pressure load on a panel with centroid at level * z* c

* above the still-water level z w*

are then:

*P*

*R*

*= wP*

0

*; z w*

*≤ z c*

≤ A (2.35) where *P*

*0*

* is the pressure at the panel-centroid nearest to still-water level approximately vertically below the panel with centroid at z c*

and *w* is the linear attenuation factor defined by w =

*A – ( z*

2*A*

*– z w*

)

(2.36)

The reduction is continued down below the still-water level, but is then applied to the pressure at the panel centroid:

*P*

*R*

*= wP z c*

*; A ≤ ( z c*

*– z w*

*(2.37) where P(z c*

*) is the pressure at the panel-centroid at z c*

*. P(z c*

) and *P* from the boundary value problem bounded by the still-water level.

*0*

are the standard pressure-calculations

**Wadam**

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**Program version 8.1**

**22-JAN-2010**

**2.7**

**The Save-Restart System**

The save-restart option in Wadam provides a mechanism to store potentials from the solution of the radiation and diffraction problem from one Wadam run to the next. Hence, for a given model the radiation and diffraction potentials for combinations of incident wave frequencies and heading angles need only be calculated once.

The save-restart file may be viewed as a database for the calculated potentials. That is, potentials for different combinations of frequencies and heading angles may be appended to the save-restart file from a sequence of runs. Furthermore, Wadam may extract potentials for a subset of the frequencies and heading angles stored on the file.

If the model is changed the save-restart database (Wadam.RSQ) must be deleted. Otherwise Wadam will not run. Notice, however, that when Wadam is executed from HydroD this application allows for management of multiple restart databases.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**3-1**

**3 USER’S GUIDE TO WADAM**

This chapter describes how to use Wadam to analyse typical hydrodynamic problems involving fixed, floating and tethered structures. Simple tutorial examples as well as more real life engineering problems are presented. Some practical modelling guidance is also provided.

The examples cover the most common Wadam applications. They do not cover all program features or all ways in which the program may be used.

Section 3.1 describes the following two simple examples:

• Motion response analysis of a floating box

• Motion response analysis of a tethered floating box with transfer of loads to a shell finite element model of the box

for Prewad. The preprocessor inputs required for establishing the models are included in Appendix A.

Section 3.2 describes three engineering application examples:

• Motion response analysis of a TLP with transfer of loads to a shell finite element model of the TLP hull and deck

• Motion response analysis of a semi-submersible platform with transfer of loads to a 3D beam model of the pontoons, columns, braces and deck

• Motion response analysis of a ship hull

**Wadam**

**3-2**

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**Program version 8.1**

**22-JAN-2010**

**3.1**

**Simple Examples**

**3.1.1**

**Motion Response of Floating Box**

The panel model representing the box is shown in Figure 3.1 (see the input in Appendix A 1). The box

dimensions are 90 by 90 metres with a draft of 40 metres. The box is freely floating. Since the box is double-symmetric the panel model need only represent the part of the box in the first quadrant. The arrows in the figure pointing from the fluid onto the panel model defines the wet surface of the model. See also the

definition of wet surfaces in Section 2.1.2.

3.1

**Figure 3.1 Prefem plot of the panel model representing a quarter of the box. Notice the arrows showing the direction of the HYDRO-PRESSURE load.**

This example is a plain global analysis for a panel model. The Wizard for setting up the input for such an

with the HYDRO-PRESSURE load displayed. This picture shows a finer discretisation than the Prefem model.

The Prewad input for motion response analysis of the freely floating box is presented below. Bold font highlights the commands as opposed to comments. If this input is found in a file with name Prewad_in.jnl then

start Prewad *and* Wadam from Manager as illustrated in Figure 3.4.

**SESAM**

**Program version 8.1**

3.2

**22-JAN-2010**

**Wadam**

**3-3**

3.3

**Figure 3.2 HydroD wizard for the floating box example.**

**Figure 3.3 Display of HYDRO-PRESSURE load in HydroD.**

**Wadam**

**3-4**

3.4

**22-JAN-2010**

**SESAM**

**Program version 8.1**

Check here to create Wadam analysis control data

**Figure 3.4 Starting Prewad and Wadam from SESAM Manager.**

%

% Define general information about the model

%

** DEFINE**

**GENERAL**

%

% Specify the analysis models to be used for,

% 'mass model' - Global Mass Matrix

% 'panel model' - Superelement 1

% 'Morison model' - Not needed in this example

%

% For the 'user-specified' global mass matrix give

% - coordinates of c.g. in input coord. syst.

% - radii of gyration about global x- y- z-axes

% - products of inertia about global x- y- z-axes

% - total mass of box

**ANALYSIS-MODELS**

**MASS-MODEL GLOBAL-MASS-MATRIX**

**USER-SPECIFIED**

**0. 0. 29.38**

**33.04 32.09 32.92**

**0. 0. 0.**

**332.1E06**

**SINK-SOURCE 1**

**END**

%

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

% Specify the constants - characteristic length (90. metres)

% - mass density of water (1025. Kg * / m**3)

% - accn. due to gravity (9.81 m / sec**2)

% - linearising velocity (not relevant here)

% - z-location of input coord. system (-40.metres)

% - 3 dummy values = 0. or > 0.

%

**CONSTANTS**

**90. 1025. 9.81 0. -40. 0. 0. 0.**

%

% Specify the execution directives:

% - analysis type is global motion response

% - calculation of horizontal drift forces

% - the model is a floating structure with

% 2-planes of symmetry YZ-XZ

% yes, calculate eigenvalues for motions

% - for potential solution (panel model)

% use an iterative equation solution and

% do not remove the irregular frequencies

% - store motions results on file for further

% postprocessing in e.g. Postresp

%

**EXECUTION-DIRECTIVES**

**ANALYSIS-TYPE GLOBAL-RESPONSE**

**HORISONTAL-DRIFT YES**

**FIXED-FLOATING**

**FLOATING YZ-XZ-PLANE**

**YES**

**POTENTIAL-THEORY**

**EQUATION-SOLUTION**

**ITERATION**

**IRREGULAR-FREQUENCY**

**NO-REMOVAL**

**END**

**RESULT-FILES**

**GLOBAL-RESPONSE SIF**

**END**

**END**

%

% Give 3 lines of text to appear in output listing from Wadam

%

**TEXT**

**' WADAM USER MANUAL - EXAMPLE 3.1A'**

**' Floating Box 90 x 90 metres and Draft 40 metres'**

**' Global motions response analysis'**

**END**

%

% Define the environmental data to be used for the motions response

% - water depth (100 metres)

% - wave-directions (0. and 45. degrees)

% - wave periods (8. 10. 12. secs) with finite water depth

%

**3-5**

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**3-6**

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**Program version 8.1**

**22-JAN-2010**

**ENVIRONMENT**

**WATER-DEPTH 100.**

**WAVE-DIRECTION**

**0. **

** 45.**

**END**

**WAVE-PERIOD**

**8. FINITE**

**10. FINITE**

**12. FINITE**

**END**

**END**

**END**

%

% This file contains input data for Wadam.

**3.1.2**

**Motion Response of Floating Box Tethered to the Sea-Bed**

This section describe the motion response analysis of a tethered box with transfer of loads to a shell finite element model of the same box.

2.1. (Today this would be done in Patran-pre or Genie.)

The springs correspond to the tethers included in the hydro model. The Prefem and Presel inputs for creating

the structural model are given in Appendix A 2.2 and Appendix A 2.3 respectively.

The Prewad input for this analysis is presented below. Note that compared with the commands for the freely floating box this Prewad input includes a structural model definition and transfer of loads to a composite

Morison model. If this input is found in a file with name Prewad_in.jnl then start Prewad *and* Wadam from

Manager as illustrated in Figure 3.4.

we select ‘Composite model’ and we tick off for inclusion of TLP elements.

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**Program version 8.1**

3.5

**22-JAN-2010**

**Wadam**

**3-7**

**Figure 3.5 Structural model assembly of simple box model tethered to the sea-bed**

%

% Define general information about the model

%

**DEFINE**

**GENERAL**

%

% Specify the analysis models to be used for:

% 'mass model' - Global mass-matrix generated from 'structural model'

% 'panel model' - Superelement No. 1 (1/4 Box)

% 'Morison model' - Superelement No. 2 (Tethers)

% 'structural model' - Superelement No. 21 (Box (3) + Tethers (2))

%

% The 'Structural model' comprises:

%

% T21 T21 created by Presel

% ! T3 models 1/4 of Box

% ! T2 models the 4 Tethers

% _____________________________

% ! ! ! ! !

% T3 T3 T3 T3 T2

%

%

% Note : Structural model is also used as mass model

% No mass is generated for the Tethers

%

**ANALYSIS-MODELS**

**MASS-MODEL GLOBAL-MASS-MATRIX GENERATE 21**

**STRUCTURAL-MODEL 21**

**MORISON-MODEL 2**

**SINK-SOURCE 1**

**END**

%

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**Program version 8.1**

**22-JAN-2010**

% Specify the constants - characteristic length (metres)

% - mass density of water (kg/m**3)

% - accn. due to gravity (m/sec**2)

% - linearising velocity (not relevant here)

% - z-location of input coord. system (metres)

% - 3 dummy values = 0. or > 0.

%

**CONSTANTS**

**90. 1025. 9.81 0. -40. 0. 0. 0.**

%

% Specify the execution directives

% - computed tolerances

% - analysis type global motion response

% - calculation of drift forces

% - model is a floating structure with

% 2-planes of symmetry YZ-XZ

% and, YES, calculate eigenvalues for rigid body

% degrees of freedom

% - for potential solution (panel model)

% use an iterative solution

% - do not remove irregular frequencies from solution

% - normal amount of output in print file

% - store motions results on file and

% generate Loads interface file where

% structural model is composite i.e.

% shell + beam (in Morison superelement)

% and, YES, store hydrostatic loadcase as

% 1st loadcase

%

**EXECUTION-DIRECTIVES**

**TOLERANCES**

**COMPUTED-TOLERANCES 1.0 1.0 0.1 0.1**

**END**

**ANALYSIS-TYPE STRUCTURAL-LOADS**

**HORISONTAL-DRIFT YES**

**FIXED-FLOATING**

**FLOATING YZ-XZ-PLANE**

**YES**

**POTENTIAL-THEORY**

**EQUATION-SOLUTION ITERATION**

**IRREGULAR-FREQUENCY NO-REMOVAL**

**END**

**PRINT-SWITCH**

**NORMAL**

**RESULT-FILES**

**GLOBAL-RESPONSE SIF**

**STRUCTURAL-LOADS COMPOSITE-STR-MODEL YES**

**LOAD-TRANSFER-OPTION**

**FILE-FORMAT FORMATTED**

**OFFSET-IN-LOAD-CASE-NUMBERS AUTO**

**END**

**END**

**SESAM**

**Program version 8.1**

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**Wadam**

**END**

%

**TEXT**

**' WADAM USER MANUAL - EXAMPLE 3.1B'**

**' Tethered Floating Box 90 x 90 metres and Draft 40 metres'**

**' Global motions response analysis with transfer of loads'**

**END**

%

% Define the environmental data to be used for the motions response

% - water depth (metres)

% - wave-directions (degrees)

% - wave periods, finite or infinite water depth

%

**ENVIRONMENT**

**WATER-DEPTH 100.**

**WAVE-DIRECTION 0. 45. END**

**WAVE-PERIOD 8. FINITE 10. FINITE 12. FINITE END**

**END**

%

% Define the input data for the 4-tethers

% - element no.s and nodes no.s to which they attach

% el no.1 to node no. 1, el no.2 to node no.2, etc.

%

**ELEMENT**

**TLP-MOORING-ELEMENT 1 1 2 2 3 3 4 4**

**END**

**END**

%

% Define section types, one type for each different set of properties,

% in this case all tethers have the same properties

%

% - length (metres)

% - pre-tension (N)

% - elastic stiffness (N/metre)

% - platform offset in x-direction (metres)

% - platform offset in y-direction (metres)

%

**HYDRODYNAMIC-PROPERTY**

**SECTION 101**

**TLP-MOORING-ELEMENT 965. 9.59E7 2.0E7 20. 20.**

**END**

%

% Connect section type no.101 to each of the four tethers

%

**CONNECT**

**101 1 2 3 4 END**

**END**

**END**

**END**

%

% This file contains input data for Wadam.

**3-9**

**Wadam**

**3-10**

3.6

**22-JAN-2010**

**SESAM**

**Program version 8.1**

**Figure 3.6 HydroD wizard for the tethered box example (left) and the TLP example in Section 3.2 **

**(right).**

**3.2**

**Engineering Application Examples**

This section describes how Wadam may be applied for typical engineering problems. The examples have been selected to demonstrate the main features of Wadam. They do not cover all options in the program. The text for each example explains the options used in that specific example only.

The panel models shown in this section may be used as guidance during the modelling phase. It is however important to create a panel model suitable for the type of analysis to be performed. A panel model that is suitable for global response analysis is not necessarily acceptable for other types of analyses. This remark is equally important for the structural model.

type of structure and covers, in principle, all necessary analyses for calculation of first order wave loads on

and ships. An overview of the various analysis types discussed in this chapter is included below.

• **Global response calculations for a TLP; see Section 3.2.1**

This analysis covers several aspects that are important for a TLP:

— Rigid body motions are calculated for all six degrees of freedom. These motions may be used to calculate displacements, velocities and accelerations for specified points in the structure. Such calculations are performed with the statistical postprocessor Postresp.

— Constant drift forces are calculated. They may be used to find the maximum offset positions by external programs.

**SESAM**

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**Wadam**

**3-11**

— Sectional forces are calculated for four sections. There is one vertical section in the centre of the platform and one close to the columns. The other horizontal sections are just above the pontoons and below the topsides. The wave periods and headings that give maximum response in the structure are selected on basis of these forces. It may, however, be difficult to select the worst waves only on the basis of sectional forces. The use of simplified structural analysis may also be a valuable help for selection of waves for a more detailed global analysis.

— Wave kinematics is calculated for points around the columns. These are used for calculation of the wave up-welling around the columns and subsequent air gap calculations.

Potential theory is used for all the wave periods.

• **Load transfer to a TLP shell structural model; see Section 3.2.2**

This analysis shows how the loads calculated in Wadam are transferred to a structural shell model. The ultimate limit state (ULS) capacity of the hull is checked in a subsequent structural analysis. All wave pe-

load cases in the capacity check. The transferred loads include hydrodynamic pressure loads, inertia loads and tether reaction forces due to the rigid body motions. Hydrostatic loads are not transferred.

• **Load transfer to a TLP beam element model; see Section 3.2.3**

This is a typical fatigue analysis of the topsides where Wadam is used to calculate wave loads for many wave periods and headings. Due to the large number of load cases from waves a simplified model of the hull is used for the structural analysis. This model is calibrated against the shell structural model above.

The transferred loads include line loads from hydrodynamic pressures, inertia loads and tether reaction forces due to the rigid body motions. Hydrostatic loads are not transferred. Potential theory is used for all wave periods.

• **Global response calculations for a dual model of a semi submersible; see Section 3.2.4**

selection of wave periods and headings. These are used in a subsequent structural analysis. Four similar sections are used for sectional load calculation. One vertical section in the centre of the platform and one close to the columns. One horizontal section is just above the pontoons and the other below the topsides.

Potential theory is used for low wave periods while Morison’s equation is used for higher wave periods

(wavelengths longer than 600 m). Morison’s equation is used in order to include viscous damping for the heave eigenperiod of 21.5 seconds.

• **Global response calculations for a ship; see Section 3.2.5**

This analysis is used for two different purposes:

— Sectional forces are calculated for several sections along the ship. As the ship, in principle, is equal to a beam with loads sectional forces may be used directly for dimensioning purposes within certain limits. Combinations of the sectional force components are used to calculate stresses in various positions of the ship. It should however be remembered that this is a simplification. Structural analysis should be used for more detailed stress calculations. The sectional forces combination is performed in the statistical postprocessor Postresp.

— Based on the global responses acceleration components and combined accelerations in specified points may be calculated in Postresp. This is of less importance for the tanker used in this example but may be important for other types of ships or barges transporting heavy equipment.

For both alternatives the roll response is of major importance. Non-linear roll damping and restoring are therefore included according to a linearising procedure. Potential theory is used for all wave periods. Forward speed is not allowed in Wadam and is consequently not included.

**Wadam**

**3-12**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

The different steps in the analyses are described in the following sections. A short description of each analysis including examples of some analysis steps is presented. An extensive set of examples is enclosed in

**3.2.1**

**TLP Global Response Analysis**

This example shows the use of Wadam in a typical global response analysis of a TLP. The analysis is mainly

theory is used for all wave periods. The following calculations are performed in Wadam for this analysis.

The first two points are automatically calculated while the rest is chosen for this analysis.

• Hydrostatic calculation in which both the hydrostatic and inertial properties for the structure are calculated

• Calculation of hydrodynamic exciting forces, added mass, damping and global motion response for the

TLP

• Eigenvalue calculations for rigid body motions. One set of eigenvalues is calculated for each wave period.

• Sectional forces in specified sections. These are used for selection of waves to be used in a structural analysis.

• Calculation of constant drift forces and moments including the effect of motion. These are used in a succeeding analysis where the maximum offsets for the TLP are calculated.

• Calculation of fluid kinematics in specified points used for air gap and wave up welling analyses. The fluid kinematics include the effect of radiation and reflection of waves from the TLP.

Preparation for this analysis in Wadam consists of the following steps:

• Creation of the panel model in Patran-Pre or Prefem. Symmetry of the structure is used and only one quarter of the TLP is modelled.

• Creation of beam elements for the Morison model in Patran-Pre or Genie

• Transfer of Input Interface Files to the directory where the Wadam analysis is performed

• Definition of execution directives, additional elements, environmental properties, etc. in Prewad

A Morison model is used for inclusion of mass. The tether stiffness is, as required by Wadam, connected to elements in the Morison model.

The TLP considered is a typical double symmetric structure with rectangular pontoons and circular columns. All tethers, three in each column, are connected to the TLP in the column bottom. Tether pre-tension

is equal for all tethers. A sketch of the TLP is shown in Figure 3.7.

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**Figure 3.7 TLP geometry**

**Panel Model**

only one quarter of the panel model is modelled. The remaining parts of the model are generated in Wadam by the yz-xz symmetry option.

3.8

**Figure 3.8 Basic part of the TLP panel model from two view points**

The basic part of the panel model is modelled as one first level superelement in Patran-Pre or Prefem. It is required that it is modelled in quadrant one, that is with x, y ≥ 0. The input coordinate system is located at the water level in the centre of the TLP.

The wet sides of the panel model are identified in Prefem by:

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• An inside-outside definition

That is, Wadam must know which side to calculate pressures on.

DEFINE POINT INS1 x-val y-val z-val END END

SET INSIDE wet surfaces POINT INS1 END END

• Hydrodynamic load definition on outside surfaces

PROPERTY LOAD 1 HYDRO-PRESSURE wet surfaces OUTSIDE OUTSIDE-SURFACE END END

The mesh density of the structure is important for the hydrodynamic loads. It is of importance that the mesh density reflects the hydrodynamic pressure variation around the structure. In areas where the pressure variation is large element sizes should be small.

The following items should be remembered when modelling a panel model:

• The pressure variation as a function of draught is at a maximum close to the surface, i.e. small element heights should be used close to the surface.

• The pressure variation is large close to the edges in the structure, i.e. element sizes normal to the edge length should be small.

• The elements should be modelled as planar as possible. Elements which are too twisted should be divided into smaller elements.

• Large changes in element size for neighbouring elements should be avoided.

• The largest element diagonal should be smaller than one quarter of the wave length for all wave periods contributing significantly to the wave pressure at given locations.

It is also noted that the mesh refinement of a hydro model normally needs to be high if the mean drift forces by pressure integration shall be obtained. This compared to the calculation of rigid body responses where reliable results may be obtained with a considerably coarser mesh.

**Morison Model**

and spring elements representing the tethers. These spring elements are neglected by Wadam and may actually be omitted in the Morison model for this analysis. Node masses are used to include the mass above the still water level. Except for the mass distribution the same Morison model is used for all the analyses for the

TLP. This shows the similarity of the analyses. The same input coordinate system as for the panel model is used. This is required by Wadam.

The Morison model is used to connect the tether elements specified in HydroD or Prewad. All additional elements specified in Prewad must be connected to existing elements or nodes in the Morison model. The tether elements are consequently connected to appropriate nodes in the Morison model.

The mass distribution used in the sectional force calculations is taken from the Morison model. It is therefore important that the distribution is correct.

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**Figure 3.9 Morison model**

**Additional Elements**

For this analysis the following additional elements are defined in Prewad:

• TLP mooring elements

The TLP mooring elements are specified for inclusion of tether stiffness. One element is specified for each tether. The inclusion of stiffness for one tether in Prewad is defined as follows:

DEFINE ELEMENT TLP-MOORING-ELEMENT

% elno node1

11 131

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY SECTION

% ref len pre stiff xoff yoff

21 TLP-MOORING-ELEMENT 965.0 5.0E7 9.59E7 35.0 35.0

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY CONNECT

% ref elno

21 11

END END END

**Check of Results**

Several checks should be performed during a Wadam analysis. The following checks should as a minimum be made after a global response analysis:

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• Error and warning messages

Wadam will give error or warning messages if the Prewad input data and the input models contain inconsistencies.

• Hydrostatic properties calculated on the model

• Mass properties

A summary of the mass calculations is given in the Wadam listing.

• Rigid body eigenperiods for the structure

The eigenperiods show whether Wadam has interpreted the stiffness and mass properties as expected and is an extra check of these values.

• Transfer functions for exciting forces, added mass, damping and rigid body motions The transfer functions should generally not be too irregular. Large jumps in the transfer functions, especially for added mass and potential damping, may be caused by too large wave period steps, the presence of irregular frequencies or numerical problems in Wadam. The irregular frequencies may usually be removed by the removal of irregular frequency option. This option is specified in Prewad by the following command:

DEFINE GENERAL EXECUTION-DIRECTIVES POTENTIAL-THEORY

IRREGULAR-FREQUENCY REMOVE alpha

END END END

This feature should, however, be used with care as there is no alpha value that will remove the irregular frequencies for all geometries. The selection of alpha must be based on trial and error. A key point is to observe that the responses are not disturbed in a large frequency range for some ALPHA values. For most

geometries 0.2 has shown to be a good starting value. See Section 2.6.3 for further description.

**3.2.2**

**TLP Load Transfer to a Shell Structural Model**

are used in a subsequent structural analysis and are together with other load cases used to check the capacity of the hull.

description of the additional elements.

The following calculations are performed in Wadam for this analysis. The first two tasks are automatically calculated while the others are specified for this analysis.

• Hydrostatic calculation in which both the hydrostatic and inertial properties for the structure are calculated

• Calculation of hydrodynamic exciting forces, added mass, damping and global motion responses for the

TLP

• Eigenvalue calculations for rigid body motions. One set of eigenvalues is calculated for each wave period.

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• Detailed load calculations and load transfer to a structural model. This includes:

— Rigid body accelerations and fluctuating gravity

— Pressure loads caused by waves, damping and added mass

— Tether reaction forces caused by rigid body motions of the TLP

Preparations for this analysis in Wadam consist of the following steps:

• Creation of the panel model with Patran-Pre or Prefem. Symmetry of the structure is used and only one quarter of the TLP is modelled.

• Creation of beam elements for the Morison model with Patran-Pre or Genie.

• Creation of the structural model with Genie, Patran-Pre and Presel.

• Transfer of Input Interface Files to the directory where the Wadam analysis is performed.

• Definition of execution directives, additional elements, environmental properties, etc. in HydroD or Prewad.

Potential wave theory is used for all the wave periods and the panel model is thus used for calculation of all wave loads. A Morison model is used to include the tether reaction loads transferred to the structural model.

**Structural Model**

structural model is shown in Figure 3.11.

3.10

**Figure 3.10 The sub-sea part of the structural shell model**

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**SESAM**

**Program version 8.1**

**Figure 3.11 The geometry assembly for the structural shell model**

The model is built from first level superelements created in e.g. Patran-Pre and Genie and then built together

is built using Presel. The load case number description includes wave loads from Wadam and loads defined

in the preprocessors. See Section 2.1.11 for further description.

Wet surfaces on the structural model are identified in Patran-Pre or Prefem by use of the same modelling

steps as for the panel model. See Section 2.1.9 for further description.

The structural model could also have been used as the hydro model for calculation of hydrodynamic loads.

Separate models are normally used to optimise panel dimensions and shapes as well as to minimise the number of panels in the panel model.

Structural mass is distributed with a high degree of accuracy in the model. This is necessary in order to include the inertia forces, transferred as nodal accelerations, in a proper way in the structural analysis.

**Load Transfer**

The following loads are transferred to the structural model:

• Hydrodynamic wave pressures

Pressure distribution from exciting forces, added mass and potential damping are transferred to each wet element in the structural model.

• Inertia loads

Rigid body accelerations are transferred to all nodes in the structural model.

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**Program version 8.1**

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• Tether reaction forces

The rigid body tether reaction forces are transferred to the nodes in the Morison model where the tether elements are connected.

Loads are automatically transferred to the structural model in Wadam. Tether loads may, however, only be transferred to nodes in a beam structural model corresponding to a Morison model. Such loads are consequently written to a composite structural model.

Wave exciting forces, added mass and damping are transferred to the structural model as pressure loads on the elements with specified hydro-pressure. Inertia forces due to rigid body motions are transferred as nodal accelerations to all the nodes in the structural model.

Tether reaction forces are transferred to the appropriate nodes in the Morison model. The Morison model corresponds to a superelement in the structural model such that the tether reaction forces are transferred to the structural model.

This load transfer is defined by the following commands:

DEFINE GENERAL EXECUTION-DIRECTIVES

% stalo

STRUCTURAL-LOADS COMPOSITE-STR-MODEL NO

END END END

%--------------------------------------------------------------

DEFINE GENERAL ANALYSIS-MODELS

MORISON-MODEL 100

STRUCTURAL-MODEL 301

END END END

The structural model contains several static load cases to be used in the dimensioning of the TLP. These load cases are numbered in increasing order, starting at one, in the different first level superelements included in the structural model. Subsequently, the wave load numbers start at the first idle load case number for each first level superelement. Unformatted Loads Interface Files are used in the load transfer to the structural analysis. This is specified in Prewad as follows:

DEFINE GENERAL EXECUTION-DIRECTIVES RESULT-FILES LOAD-TRANSFER-OPTION

OFFSET-IN-LOAD-CASE-NUMBER AUTOMATIC

FILE-FORMAT UNFORMATTED END END END END END

Local load cases for all first level superelements are created. There are 40 global load cases in the analysis

(8 wave headings and 5 wave periods) but the number of local load cases is larger for superelements that are repeated. For superelement 111 the total number of local load cases is 320 (8 occurrences each with 40 load cases).

The loading on the elements and nodes in the structural model is written to Loads Interface Files used in the structural analysis. One file containing all local wave load cases is written for each first level superelement.

In addition, an S-file is created containing input to Sestra about wave periods, headings and load cases. This file, S301.FEM, must be located in the same physical directory as the Input Interface Files when the structural analysis is performed. The S-file is mandatory for the structural analysis only if information about wave periods and headings is used in the postprocessing and could be omitted for this analysis.

• L100.FEM — Tether reaction forces due to rigid body motions for superelement 100 (Morison model)

• L111.FEM — Pressure loads and nodal accelerations for superelement 111 (Pontoon)

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• L112.FEM — Pressure loads and nodal accelerations for superelement 112 (Intersection area)

• L113.FEM — Pressure loads and nodal accelerations for superelement 113 (Lower part of the column)

• L114.FEM — Pressure loads and nodal accelerations for superelement 114 (Middle part of the column)

• L12*.FEM — Nodal accelerations for all other first level superelements

• S301.FEM — Input file for subsequent Sestra analysis

**Check of Results**

analysis to make sure that the results are reliable:

• Information about matching between elements in the panel model and the structural model

All wet elements in the structural model should receive wave pressure loads from the analysis. If the distance from one element in the structural model to the nearest element in the panel model or the difference in orientation of the element normals is too large then Wadam will not transfer any loads to the element.

Prewad, i.e. distol and angtol, should be increased. It is, however, important to be aware of the possible problems when the tolerances are increased. The transferred pressures may not be correct for these elements and the load sums for the structural model and the panel model may not be satisfactory.

• Difference between calculated loads on the panel model and loads transferred to the structural model

The total pressure loads transferred from the panel model to the structural model are printed in the Wadam listing. These load sums should be checked against the sum of calculated pressures on the panel model. A large difference indicates that a new analysis should be performed changing either the tolerance, the panel model or the structural model. The transfer of pressure loads from the panel model to the structural model

is described in detail in Appendix B 3.3.

• Load sums for the wave loads in the structural analysis

The sum of loads printed in the Wadam listing contains pressure loads on wet elements only. Inertia forces are not included and thus the total load sums cannot be checked. The total load sums must therefore be checked in the structural analysis. Since all loads are transferred from Wadam — including the tether restoring loads — the load sums for wave load cases should be close to zero in the structural analysis. Large forces in the load sums indicate errors either in the load transfer or in the load combinations in Presel.

**3.2.3**

**TLP Load Transfer to Beam Element Model**

loads are used in a subsequent structural analysis where fatigue damage is calculated for parts of the topside structure. The beam element model is used to reduce CPU consumption and disk requirements.

of the panel model and to Section 2.1.3 for a description of the additional elements.

The following calculations are performed in Wadam for this analysis. The first two tasks are automatically calculated while the others are specified for this analysis.

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• Hydrostatic calculation in which both the hydrostatic and inertial properties for the structure are calculated

• Calculation of hydrodynamic exciting forces, added mass, damping and global motion response for the

TLP

• Eigenvalue calculations for rigid body motions. One set of eigenvalues is calculated for each wave period.

• Detailed load calculations and load transfer to structural model. This includes:

— Nodal accelerations for all nodes in the structure

— Line loads on the beams corresponding to Morison elements. The loads are obtained from integration

of panel pressures in a dual model; see Section 2.1.4.

— Tether reaction forces caused by rigid body motions of the TLP

Preparations for this analysis in Wadam consist of the following steps:

• Creation of the panel model in Patran-Pre or Prefem. Symmetry of the structure is used and only one quarter of the TLP is modelled.

• Creation of beam elements in Genie or Patran-Pre for the Morison and structural models

• Creation of the remaining part of the structural model in Genie and/or Patran-Pre and Presel

• Transfer of Input Interface Files to the directory where the Wadam analysis is performed

• Definition of execution directives, additional elements, environmental properties, etc. in HydroD or Prewad

• Definition of correspondence between panels in the panel model and elements in the Morison model for transfer of integrated pressure loads

Potential wave theory is used for all wave periods and the panel model is thus used for calculation of all wave loads. The mass from the structural model is used in the calculation of motions in Wadam.

**Structural Model**

except that the sub-sea part of the structure is substituted by the Morison model. One extra superelement is also used to connect the Morison model to the rest of the structural model. This extra superelement is shown

in Figure 3.12. Figure 3.13 shows the geometry assembly for the structural model.

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**SESAM**

**Program version 8.1**

**Figure 3.12 (a) Extra superelement for connection of Morison model to the rest of the structural model and (b) Example of use of the extra superelement**

3.13

**Figure 3.13 Geometry assembly for the TLP structural model**

The model is built up from first level superelements created in Patran-Pre and Genie and then built together

bers is built up using Presel. As this is a fatigue analysis only wave loads from Wadam are included in the

load combinations. See Section 2.1.11 for further description.

Structural mass is distributed with a high degree of accuracy in the model. This is necessary in order to include the inertia forces, transferred as nodal accelerations, in a proper way in the structural analysis.

In this analysis the same superelement represents the Morison model in the Wadam analysis and is a part of the structural model. The structural spring stiffness defined in the tether attachment points are used as support conditions in the structural analysis. Such spring stiffness is disregarded by Wadam. Tether elements are defined in Prewad to include the tether stiffness in the Wadam analysis.

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**Morison Model**

mass above the still water level is removed. This mass is now included in the structural model.

model is now very important. This stiffness is modelled with 2 node beam and bar elements for columns and

correct stiffness.

**Load Transfer**

The following loads are transferred to the structural model:

• Hydrodynamic wave pressures

Pressure forces are summed up from exciting forces, added mass and potential damping. It is transferred as line load to each element specified in the correspondence command in Prewad.

• Inertia loads

Accelerations from rigid body motions are calculated for all nodes in the structural model.

• Tether reaction loads

The rigid body tether reaction forces are calculated on the Morison model. This means that the reactions forces are written to the nodes specified in Prewad.

All wave induced loads are written to the structural model. The line loads are written to the Morison model.

The Morison model is now a part of the structural model defined in Presel and the load transfer is defined through the following commands in Prewad:

DEFINE GENERAL EXECUTION-DIRECTIVES

% anc addmass stalo

STRUCTURAL-LOADS BEAM-STR-MODEL YES NO NO

END END END

%--------------------------------------------------------------

DEFINE GENERAL ANALYSIS-MODELS STRUCTURAL-MODEL 302 END END END

The transfer of pressure loads from the panel model to the Morison model is not automatic. Correspondence between panel model and Morison model must be defined through the following command in Prewad:

DEFINE CORRESPOND

% elno selno seltyp index ssno1 ssno2 ssinc

114 1 99 1 GROUP 713 897 8 END

115 1 99 1 GROUP 714 898 8 END

END END

Pressure loads on the panel model are summed up and applied as line loads on the corresponding elements in the Morison model, i.e. no moments are transferred. It is thus important to specify load transfer to the correct elements in the Morison model.

Inertia loads are included as rigid body accelerations.

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**Program version 8.1**

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Local load cases for all first level superelements are created starting on load case 1 (since no static load cases are included). There are 160 global load cases in the analysis (8 wave headings and 20 wave periods).

The loading on the elements and nodes in the structural model is written to Loads Interface Files used in the structural analysis. One file containing all local load cases is written for each superelement. In addition, the

S-file, S302.FEM, is created containing input to Sestra about wave periods, headings and load cases. This file must be located in the same physical directory as the Input Interface Files when the structural analysis is performed. If this file is not included in the structural analysis fatigue postprocessing cannot be performed.

• L100.FEM — Tether reaction loads due to rigid body motions, line loads from hydro pressure and nodal accelerations for superelement 100 (Morison model)

• L101.FEM — Nodal accelerations for superelement 101 (‘Connection’ superelement)

• L12*.FEM — Nodal accelerations for all other first level superelements

• S302.FEM — Input file for subsequent Sestra analysis

**3.2.4**

**Global Response of a Semi-Submersible using Dual Model**

This example shows the use of Wadam in a typical global response calculation of a semi submersible. The analysis is mainly used for selection of wave periods and headings to be used in analyses similar to the one

of 21.5 seconds.

The following calculations are performed in Wadam for this analysis. The first two tasks are automatically calculated while the others are specified for this analysis.

• Calculation of hydrodynamic exciting forces, added mass, damping and global motion response for the semi-submersible

• Sectional forces and moments in specified sections

Preparations for the analysis in Wadam include the following steps:

• Creation of a panel model in Patran-Pre/Prefem and Presel. Symmetry of the structure is used and only one quarter of the semi-submersible is modelled.

• Creation of beam elements for the Morison model in Genie or Patran-Pre.

• Transfer of Input Interface Files to the directory where the Wadam analysis is performed

• Definition of execution directives, additional elements, environmental properties, etc. in Prewad

• Definition of correspondence between panels and Morison elements

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**Program version 8.1**

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The mass is included as distributed mass on the Morison model.

The semi-submersible considered in this example is a typical double symmetric twin pontoon structure with the connection between the pontoons and the deck consisting of four columns, two transverse braces and four diagonal braces. The upper part of the structure consists of an upper and a lower deck and a derrick in

the middle of the upper deck. The geometry of the semi-submersible is shown in Figure 3.14.

A symmetrical mooring system is used with mooring lines connected at the fairlead and windlass of the platform.

3.14

**Figure 3.14 Geometry of the semi-submersible**

**Panel Model**

The basic part of the panel model for the semi-submersible is modelled as two first level superelements in

Prefem and combined into a second level assembly in Presel. The superelements and the assembly are

is modelled. The remaining parts of the model are generated in Wadam by reflection (mirroring) of the basic part.

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**SESAM**

**Program version 8.1**

**Figure 3.15 Quarter of a double symmetric panel model for the semi-submersible**

The element sizes for this model may seem very large at first glance. However, no waves with periods below six seconds are assumed to give dimensioning stresses. Hence only higher periods are included in the analysis. Thus the element size is acceptable for this analysis.

The mesh density of the structure is of major importance for the hydrodynamic loads. It is important that the mesh density reflects the hydrodynamic pressure variation around the structure. In areas where the pressure

ples of panel models.

**Morison Model**

Pre would have been used). The model consists of 2 node beam elements and point masses. Additional elements are defined in Prewad in order to include correct hydrostatic and hydrodynamic behaviour. The inclu-

sion of these elements is described in Section 2.1.3.

The input coordinate system used is the same as for the panel model as required by Wadam.

Dry Morison elements are included to model the structural properties and weight of parts of the structure above the still water level as well as other internal parts of the structure, e.g. the inside of the junction between the columns and pontoons. No hydro properties will be defined for these elements. This means that the section numbers used for dry and 2D Morison elements modelled in Genie or Patran-Pre, both represented by beam elements, must be different. This is the case even if the beam elements have identical structural properties.

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**Program version 8.1**

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**Figure 3.16 Beam elements of the Morison model**

**Additional Elements**

Hydrodynamic properties for 2D Morison elements are together with the consecutive additional elements defined in Prewad:

• The 2D Morison element

All beam elements in the Morison model that receive hydrodynamic loads are identified in Prewad. The reference number (11 below) is the same as a section number specified in the Morison model. All the loads are automatically transferred to the correct elements. Retained mass, termed dm below, means that the mass defined on the Input Interface File will be used.

DEFINE HYDRODYNAMIC-PROPERTY SECTION

% ref stot dia dm cksi czeta aksi azeta

11 2D-MORISON-ELEMENT 1 7.4035 RETAINED 0.7 0.7 1.0 1.0

END END END

Retained mass means that the distributed mass on the Input Interface File will be used.

• The 3D Morison element

One 3D Morison element is defined at all ends of the pontoons. In this way the effect of added mass in the longitudinal direction of the pontoons is included. The commands for inclusion of one 3D Morison element are shown below:

DEFINE ELEMENT 3D-MORISON-ELEMENT

% elno node1

201 1

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY SECTION

% ref dia dm drag addmass x2 y2 z2

201 3D-MORISON-ELEMENT HYDRODYNAMIC 12.3608 0.0 0 0 0 0.7 0 0 0 0 0

END END END

%---------------------------------------------------

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DEFINE HYDRODYNAMIC-PROPERTY CONNECT

% ref elno

201 201

END END END

• The pressure area element

A total of 72 pressure area elements are included to account for free ends, diameter changes and junctions between beam elements. Since each pressure area element must have a unique point specifying the direction of the force there must be a separate set of hydro-properties for each element.

The Prewad definition for one element is shown below:

DEFINE ELEMENT PRESSURE-AREA-ELEMENT

% elno node1 node2

601 1 1

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY SECTION

% ref dia x2 y2 z2

601 PRESSURE-AREA-ELEMENT WAVE-LENGTH-DEPENDENT 9.885 27.36 27.36 0.0

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY CONNECT

% ref elno

601 601

END END END

• Anchor element

The mooring system consists of four anchor elements, one for each column. The fairlead is defined at the bottom of the columns and windlass at the third node from the top of the column. The Prewad definition for the element in the first quadrant is shown below:

DEFINE ELEMENT ANCHOR-ELEMENT

% elno node1 node2

101 2 5

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY SECTION

% ref angin angx force skh skv

101 ANCHOR-ELEMENT 30.0 45.0 0.0 265.2 0.0

END END END

%---------------------------------------------------

DEFINE HYDRODYNAMIC-PROPERTY CONNECT

% ref elno

101 101

END END END

**3.2.5**

**Global Response for a Ship**

This example illustrates how Wadam may be used in a typical global response analysis for a ship with no forward speed. This calculation is in principle equal to global response analysis for other types of structures.

**SESAM**

**Program version 8.1**

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The two significant differences are the non-linear viscous roll damping and the corrections in restoring forces due to the non-linear GZ-curve. Both effects are introduced in a linearised form.

• Calculation of hydrodynamic exciting forces, added mass, damping and global motion response for the ship

• Eigenvalue calculations for rigid body motions. Added mass for the first wave period is used in the calculations.

• Calculation of sectional forces in specified sections

• Calculation of linearised viscous roll damping and restoring terms

Preparations for the analysis in Wadam consist of the following steps:

• Creation of the panel model in Patran-Pre/Prefem and Presel. Symmetry of the structure is exploited and only one half of the ship is modelled.

• Creation of beam elements for the mass model in Genie or Patran-Pre.

• Transfer of Input Interface Files to the directory where the Wadam analysis is performed

• Definition of execution directives, damping models, environmental properties, etc. in HydroD or Prewad

The ship used in this example is a typical Aframax tanker with a 62.4 metre long bilge keel on each side.

**Panel Model**

half only. The total model is generated in Wadam through reflection (mirroring) of the basic part.

3.17

**Figure 3.17 Total panel model of the ship including reflected part**

The basic part of the panel model is modelled as one first level superelement in Prefem. The coordinate system for the model is located at the water level above the centre of gravity of the ship. Modelling advice for

the panel model is given in Section 2.1.2.

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**SESAM**

**Program version 8.1**

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**Mass Model**

mass distribution is modelled in a manner adequate for the sectional force calculations. The mass is simply modelled as transverse beams representing the mass of each section thereby ensuring that the roll radius of gyration and metacentric heights are correct. Large additional masses are modelled with point masses.

3.18

**Figure 3.18 Mass model for the ship**

**Roll Damping Model**

For a ship or barge the roll motions will generally be much larger than for floating offshore structures. These large roll motions increase the viscous damping significantly. The non-linear damping contributions are

description.

The following non-linear contributions are included in the model:

• Viscous damping from skin friction and eddy-making for the naked hull

This part of the viscous damping is included for all sections of the ship model as follows:

DEFINE GENERAL ROLL-DAMPING-MODEL

% nos xoff xbow

STRIP-MODEL 25 -113.412 -112.112 FP-TO-AP

% bst bilgr sect

2.6 0.0 BOW-SECTION

. . ...

12.0 1.8 MID-SECTION (repeated for all 25 sections)

. . ...

5.6 0.0 STERN-SECTION

END END END

• Viscous damping and eddy making from the bilge keel.

The effect of the bilge keel is included in the following way:

DEFINE GENERAL ROLL-DAMPING-MODEL

% xfr bilgl bilgb

BILGE-KEEL -29.862 62.4 0.38

% y z phi

19.85 13.67 0.0

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**3-31**

. . . (repeated for all sections with bilge keel)

END END END

• Roll restoring from the GZ-curve

The roll restoring coefficient is modified on basis of the given GZ-curve as shown below:

DEFINE GENERAL ROLL-DAMPING-MODEL

%

GZ-CURVE

% hang gz

0.0 0.0

5.0 0.212 (repeated for all angles on the curve)

. . END

END END END

The non-linear contributions above are linearised according to the maximum expected roll angle for each wave heading in the sea state considered. These roll angles are found from a sequence of analyses performed until convergence between input roll angles and computed extreme roll angles is achieved. Satisfactory convergence is analysis dependent but should at least be achieved when the error in the angle is less than 0.1 degrees.

**Check of Results**

response analysis of a ship:

• Roll angles

The computed roll angles should be transferred to Postresp for statistical postprocessing. For the given sea state considered the maximum roll angles should be equal to the roll angles given in the Prewad input.

**Wadam**

**3-32 22-JAN-2010**

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**4-1**

**4 EXECUTION OF WADAM**

**4.1**

**Program Environment**

Wadam is a batch program. It may be started from Manager, from a command-window or from HydroD.

The input to Wadam is prepared by the Prewad or HydroD. Both these programs creates the Wadam analysis

control data file WADAMn.FEM as shown in Figure 4.1.

4.1

**Figure 4.1 HydroD (or Prewad) -Wadam communication**

**Wadam**

**4-2**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

As depicted in Figure 4.1 the entire set of permanent files associated with a Wadam run is:

Analysis control data

Input Interface File

Print file mandatory mandatory mandatory

Loads Interface File

Hydrodynamic Results Interface File optional optional

Additional analysis control data for Sestra (S-file) optional

Save-restart file for velocity and source potentials optional input input output output output output input/output

In addition to the permanent files Wadam will generate a set of temporary files during the execution. These files will be opened on the directory where the process is located unless specific assignments are provided in the command procedures.

HydroD is normally started directly from a shortcut on the desktop. HydroD can also read Prewad-jnl files.

4.2

**Figure 4.2 The HydroD GUI and the command for executing Wadam.**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**4-3**

**4.1.1**

**Starting Prewad from Manager**

Prewad is started from Manager by **Model | Hydro Modelling Prewad**. The Prewad window opens up in which the interactive commands may be clicked in the column at the right or typed in the area at the bottom.

Commands may be abbreviated as long as they are unique.

The most practical way of using Prewad is often to edit a previously created Prewad input file and use this

as a command input file. This is described in Section 4.1.2.

**4.1.2**

**Reading a Command Input File into Prewad and Running Wadam**

In the Hydro Modelling window opening up when giving **Model | Hydro Modelling Prewad** in Manager

this to File name a new box appears in which you may specify a Command input file that will be automatically read into Prewad once the program is started by clicking OK.

If the box **Run interactively after command input file processing** is checked Prewad will after processing the input await interactive user input. You may then add more Prewad commands. Use the EXIT command to leave Prewad. If your Command input file contains all input required there is no need to check this box.

Check the box **Write dataset on exit** if you want Prewad to create the Wadam analysis control data file.

This is normally what you want to do. The **Dataset** number may be used to distinguish separate Wadam runs. If you only intend to perform a single Wadam analysis let it be 1.

Check the box **Run wave load analysis after Prewad** if you want to automatically start Wadam once Prewad has finished and written the Wadam analysis control data file. If you are uncertain as to whether your

Prewad input is correct you may leave this box unchecked. If you thereafter decide to run Wadam then give

**Load | Wave Loading Wadam**, select the proper **Dataset** and start the execution.

**Note: If your Command input file constitutes the complete input then make sure the Database status is set to New. You need to change Old to New if you previously have run Prewad in which case there will exist a Prewad database causing the Database status to come up as Old.**

**Note: You may also read a Command input file from inside Prewad by using the SET COMMAND-**

**INPUT FILE command followed by the # command; see these.**

**Wadam**

**4-4**

4.3

**22-JAN-2010**

**SESAM**

**Program version 8.1**

**Figure 4.3 Manager and the Hydro Modelling window with Command input file specification**

**4.1.3**

**The Input Files**

**Analysis Control Data**

The file WADAMn.FEM contains all the input data controlling the analysis to be performed by Wadam. The file is generated by HydroD or Prewad. The input data are established based on the Prewad commands in

Chapter 5 of this manual or by HydroD.

**Input Interface Files**

The Input Interface Files contain the model to analyse. The files are established by the preprocessors. A detailed description of the Input Interface File format may be found in the Input Interface File Description.

The Input Interface Files are formatted files.

There is one Input Interface File for each separate superelement. Wadam imposes the naming convention that the Input Interface Files must exist in the default directory for the analysis and that there must be no prefix for the Input Interface Files. That is, the Input Interface File names must be of the form

Tn.FEM

where the T identifies the file as an Input Interface File and n is the superelement number.

With the multi-body option there is no restriction on the file prefix. Hence, with the multi-body option the

Input Interface Files may be of the form prefixTn.FEM

where the prefix is specified in Prewad.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**4-5**

**4.1.4**

**Output Files**

**Loads Interface File**

Loads Interface Files are generated for the first level superelements only. The Loads Interface Files constitute a subset of the Input Interface File data types. The naming convention for Loads Interface Files is similar to that of the Input Interface Files except that the identifying letter T is replaced by an L. That is:

Ln.FEM

The Loads Interface Files are by default unformatted. They may optionally be specified as formatted. In addition the utility program Waloco may convert between formatted and unformatted Loads Interface Files.

If the Loads Interface Files contain dynamic load cases in the frequency domain format an additional analysis control data file for the subsequent Sestra analysis is created. This is the S-file containing standard analysis control data for the Sestra analysis. The naming convention for the S-file is

Sn.FEM

where n is the superelement number of the top level superelement in the structural model.

**Hydrodynamic Results Interface File**

The Hydrodynamic Results Interface File is created if a global response analysis is performed in Wadam. It contains transfer functions for rigid body responses together with transfer functions for off-body kinematics and the rigid body matrices. The naming convention for the Hydrodynamic Results Interface File is

G1.SIF

G1.SIU

G1.SIN

for formatted sequential file for unformatted sequential file for Norsam direct access format

**Print File**

The print file contains major results information from a Wadam analysis. The full description of the result

types in the print file is included in Section 2.5 in this manual.

**4.1.5**

**The Save-Restart File**

The save-restart file contains the velocity and source potentials obtained from solving the radiation and diffraction problems. The save-restart file also contains hydro model data used in consistency checking when the potentials are used in a restart run. The naming convention for the save-restart file is

Wadam.RSQ

The file is formatted.

**Wadam**

**4-6**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**4.2**

**Program Requirements**

The disk space requirements in Wadam depend on the type of analysis and of the input models. The execution time is dominated by the solution of the radiation and diffraction problems that is performed for each incident wave frequency.

**4.3**

**Program Limitations**

Wadam imposes restrictions on the size of the hydro model analysis. The size of the structural model used in the detailed load calculation is virtually unlimited.

The size dependent limitations are listed below. Note however that the limits may vary between different installations. The actual list of limitations is printed in the status list and in section 1.2 in the Wadam print file.

The limit values specified in the list below applies to the standard installation:

Geometry limitations:

Maximum number of panels (for the basic part of the model)

Maximum number of free surface panels (for the basic part of the model)

Maximum number of off-body points

Maximum number of nodes in the Morison model

Maximum number of elements in the Morison model

Maximum number of sub-elements in the Morison model when diffracted wave kinematics is used in Morison’s equation

Maximum number of sub-elements in one Morison element

Maximum number of superelements in the Morison model

Maximum number of panels corresponding to one Morison sub-element

Maximum number of sections for sectional loads

Maximum number of bodies

15000

3000

2000

5000

5000

2000

99

25

5

1

15

Analysis limitations:

Maximum number of wave frequencies

Maximum number of wave headings

Maximum number of wave headings using Haskin’s relation

Maximum number of phase angles with the time output format

Maximum number of current profiles

Maximum number of levels in one current profile

60

36

36

14

1

30

**4.4**

**Warnings and Error Messages**

Warning and error messages may occur in the print file or on the job log file. Error messages will halt the execution. Warnings are less serious and the execution will continue. However, the warnings may be a

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

4-7 symptom of a more serious problem. Henceforth the program may abort with an error message at a later stage in the program execution. In any case, warning messages should be carefully interpreted.

**Warnings and Error Messages in the Print File**

Problems and errors discovered during the check of analysis control data and the input models are reported on the print file. The input data check includes:

• Check of analysis control data

• Check of input models including the balance between buoyancy and weight of the hydro model

Execution errors due to malfunctioning of a program procedure will result in a short message and a trace back of all the calling procedures.

**Wadam**

**4-8 22-JAN-2010**

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-1**

**5 PREWAD COMMAND DESCRIPTION**

The Wadam analysis is controlled by the analysis control data file WADAMn.FEM; see Section 4.1. This

fixed format file is created by the interactive program Prewad or by HydroD. This chapter describes the Prewad commands.

The hierarchical structure of the commands and numerical data is documented by use of tables. How to interpret these tables is explained below. Examples are used to illustrate how the command structure may diverge into multiple choices and converge to a single choice.

In the example below command A is followed by either of the commands B and C. Thereafter command D is given. Legal alternatives are, therefore, A B D and A C D.

A

B

C

D

In the example below the three dots in the left-most column indicate that the command sequence is a continuation of a preceding command sequence. A block with any number of rows (in this case two) concluded by the command END signifies that the rows may be repeated any number of times. The sequence is concluded by END. Legal alternatives are for example A B C D E END and A D E B C B C END. The three dots in the right-most column indicate that the command sequence is to be continued by another command sequence.

B C

... A D E ...

END

The characters A, B, C and D in the examples above represent parameters being COMMANDS (written in upper case) and numbers (written in lower case). All numbers may be entered as real or integer values.

**Note: The command END is generally used to end repetitive entering of data. Using double dot (..) rather than END to terminate a command will, depending on at which level in the command it is given, save or discard the data entered. Generally, if the data entered up to the double dot is complete and self-contained the double dot will save the data. If in doubt it is always safest to leave a command by entering the required number of END commands.**

**Note: Command alternatives in Prewad not documented here are obsolete.**

**Wadam**

**5-2**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**CHANGE**

CHANGE

CORRESPONDANCE

ELEMENT

ENVIRONMENT

GENERAL

HYDRODYNAMIC-PROPERTY

END

...

**PURPOSE:**

The command changes previously given input.

For explanation of the parameters of this command see the corresponding alternatives in the DEFINE command.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-3**

**DEFINE**

DEFINE

CORRESPONDANCE

ELEMENT

ENVIRONMENT

GENERAL

HYDRODYNAMIC-PROPERTY

END

...

**PURPOSE:**

The command specifies all Wadam analysis control data such as environmental properties, hydrodynamic elements, hydrodynamic properties, connection between Morison elements defined by Prewad and hydrodynamic properties and correspondence between Morison and panel models.

**Wadam**

**5-4**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE CORRESPONDANCE**

... CORRESPONDANCE elno selno seltyp index ssno

GROUP ssno1 ssno2 ssno3 ssinc

END

END

**PURPOSE:**

The command defines correspondence between elements in the Morison model and panels in the basic panel model (correspondence for mirror images of panel model is handled automatically). This correspondence will define a ‘dual’ part of the Morison model used when Morison and radiation-diffraction theory is combined and/or when radiation-diffraction pressures are to be transferred to a structural beam model.

Correspondence must be given for all basic panels.

PARAMETERS: elno selno seltyp index ssno

GROUP ssno1 ssno2 ssinc

External element number of 2D Morison, 3D Morison or pressure area element in the Morison model to which panels are linked.

Sub-element number of present element in the Morison model. The sub-element selno may be 0 when the element elno is a 2D Morison beam generated by a preprocessor or when the element is a 3D Morison or pressure area element.

Superelement number of the superelement in the panel model to which the current panels ssno1 ssno2 ... belong.

Superelement occurrence of seltyp

External element number of a panel to be linked to the present element and sub-element in the Morison model.

A group of panels to be linked to the present element and sub-element in the Morison model.

First panel number in the group

Last panel number in the group

Panel numbering step

**Note: Only elements that are below the mean free surface can be included in the panel number list.**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-5**

**DEFINE ELEMENT**

...

ELEMENT

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ANCHOR-ELEMENT

DRY-ELEMENT

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

END

...

...

elno node1 node2

GROUP elno1 elno2 elinc

END n1el1 n2el1 noinc

**PURPOSE:**

The command defines additional Morison elements.

**Note: Additional 2D Morison elements and dry elements should not be used when load transfer is specified.**

**PARAMETERS:**

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ANCHOR-ELEMENT

DRY-ELEMENT

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT elno node1

Define 2D Morison elements

Define 3D Morison elements

Define anchor elements

Define dry Morison elements

Define point masses

Define pressure area elements

Define TLP mooring elements for a tether system

Element number of a single element

Node number at one end of the element — fairlead of anchor elements

**Wadam**

5-6 node2

GROUP elno1 elno2 elinc n1el1 n2el1 noinc

**SESAM**

**Program version 8.1**

**22-JAN-2010**

Node number at the other end of the element, windlass of mooring elements. Not to be specified for 3D Morison, Point mass,

TLP mooring and Pressure area elements.

A group of elements

First element number in the group

Last element number in the group

Step in the element numbering

Node number at one end of the first element in the group

Node number at the other end of the first element in the group

Incremental step for node selection. The next element (elno1 + elinc) will have its nodes defined by (n1el1 + noinc) and (n2el1

+ noinc)

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-7**

**DEFINE ENVIRONMENT**

... ENVIRONMENT

CURRENT

X-AXIS

WAVE-DIRECTION

FREQUENCY-HEADING-PAIRS

LINEARISING-WAVE-HEIGHT

...

...

SURFACE-MODEL

WATER-DEPTH

...

WAVE-AMPLITUDE depth amp

END

...

refno locz vel dir

END

WAVE-DIRECTION dir

END

WAVE-FREQUENCY

WAVE-LENGTH

...

length

FINITE

INFINITE

WAVE-LENGTH-DEPENDENT

WAVE-PERIOD

END

WAVE-SPECTRUM ...

WAVE-SPREADING-FUNC USER-DEFINED

END weights

**PURPOSE:**

The command defines environmental data.

**PARAMETERS:**

CURRENT

X-AXIS

WAVE-DIRECTION refno locz

A current profile used in Morison’s equation is specified. The current velocities used are calculated by linear interpolation in the table given by this command.

The current direction will be given relative to the x-axis.

The current direction will be given relative to the wave direction.

Reference number of the vertical position in the current profile.

Up to 30 values may be specified.

Vertical position in the input coordinate system

**Wadam**

**5-8**

**SESAM**

**Program version 8.1**

22-JAN-2010 vel dir

FREQUENCY-HEADING-PAIRS

LINEARISING-WAVE-HEIGHT

SURFACE-MODEL

WATER-DEPTH depth

WAVE-AMPLITUDE amp

WAVE-DIRECTION dir

WAVE-LENGTH

WAVE-FREQUENCY

WAVE-PERIOD length

FINITE

INFINITE

WAVE-LENGTH-DEPENDENT

Absolute value of current velocity at given vertical position

Direction of current at given vertical position given in degrees

Frequency heading pairs used in the computation of sum and difference forces will be defined.

Specification of wave linearisation curves

Surface model will be defined.

Specification of water depth

Water depth

Specification of wave amplitude used in the time domain output format

Wave amplitude value

Specification of wave heading

Wave heading in degrees. The angle between the positive xaxis of the global coordinate system and the direction of wave propagation.

Specification of wave lengths

Specification of wave frequencies

Specification of wave periods

Wave length, period or frequency

Finite water depth is used for calculation of Green’s functions.

This option is recommended.

**Note: FINITE / INFINITE must be given for all wave lengths/frequencies/periods but the option specified for the first one will be used for all.**

Infinite water depth approximation used for calculation of

Green’s functions

**Note: If INFINITE is specified a large value (at least larger than the longest wave length) must be given for the WATER-DEPTH.**

This option is no longer supported and will be substituted by

FINITE if used.

**SESAM**

**Program version 8.1**

WAVE-SPECTRUM

WAVE-SPREADING

USER-DEFINED weights

**22-JAN-2010**

**Wadam**

**5-9**

Specification of wave spectrum for each heading (wave direction)

Specification of wave spreading

User definition is currently the only option for specifying wave spreading.

Weights given one-by-one for all wave directions. The weights must add up to 1. If at least one value is 1.0 then long crested sea is assumed for all wave directions.

**Note: Roll damping iteration requires long crested sea so in this case at least on weight must be given as 1.0.**

**Wadam**

**5-10**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE ENVIRONMENT FREQUENCY-HEADING-PAIRS**

...

FREQUENCY-HEADING-PAIRS ...

...

SUM-FREQUENCIES

DIFFERENCE-FREQUENCIES

END

...

ALL-COMBINATIONS

SELECTED-COMBINATIONS ...

**PURPOSE:**

The command defines pairs of frequencies and headings for the computation of second-order sum and difference frequency forces.

**PARAMETERS:**

SUM-FREQUENCIES

DIFFERENCE-FREQUENCIES

ALL-COMBINATIONS

SELECTED-COMBINATIONS

Defining sum frequency combinations.

Defining difference frequency combinations.

All the combinations of frequencies and headings specified with the ENVIRONMENT WAVE-DIRECTION and WAVE-

LENGTH commands will be used to define pairs of frequencies and headings for sum and difference frequency forces.

This option does not work.

**NOTES:**

If statistical postprocessing by Postresp is to be performed then both SUM-FREQUENCIES and DIFFER-

ENCE-FREQUENCIES must be specified. Furthermore, the wave components specified (at least two) in

DEFINE ENVIRONMENT must be equally spaced with respect to frequencies.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-11**

**DEFINE ENVIRONMENT LINEARISING-WAVE-HEIGHT**

...

LINEARISING-WAVE-HEIGHT nlin ...

For each wave direction give:

...

tlin-1 hlin-1 tlin-2 hlin-2 ...

tlin-nlin hlin-nlin

**PURPOSE:**

This command must be used if the regular wave linearisation method is to be used. The linearising wave periods and heights describe the curve in the T-H-space to be used for the drag force linearisation. The periods used in the motion analysis will be used to interpolate on this curve. The curves are given individually for the wave directions.

For computing maximum motion response hlin will correspond to the maximum wave height according to maximum steepness or Hmax-Tmax-contour curves. tlin and hlin must be given in pairs. For the next wave direction enter a new sequence of tlin and hlin data. The same number of pairs (nlin) are used for all wave directions.

PARAMETERS: nlin tlin-1 tlin-2 ... tlin-nlin hlin-1 hlin-2 ... hlin-nlin

Number of points on the T-H-curves for all wave directions.

Maximum = 20.

tlin is the linearising wave period hlin is the linearising wave height

**Wadam**

**5-12**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE ENVIRONMENT SURFACE-MODEL**

...

SURFACE-MODEL

SIF prefix

WAMIT filename topsel radius ntcl

**PURPOSE:**

The command defines the surface model for the second order sum- and difference frequency computation.

The free surface model shall have the same symmetry properties as the panel model.

**PARAMETERS:**

SIF prefix topsel radius ntcl

WAMIT filename

The surface model is found on an Input Interface File.

File prefix or directory where the file(s) are stored.

Top superelement number of the surface model.

Dimensional radius of the partition circle given in the same units as the model length unit.

The total number of segments (panels) on the partition circle.

**Note: The radius and ntcl parameters are dummy in the case of Wave Drift Damping.**

The surface model is represented on the WAMIT free surface format described below.

The name of the WAMIT free surface file (without the mandatory extension .FDF)

**NOTES:**

The WAMIT free surface format is defined as follows: header

PARTR

NPF NTCL

NAL DELR NCIRE NGSP

VERX(1,1) VERX(2,1) VERX(3,1) VERX(4,1)

VERY(1,1) VERY(2,1) VERY(3,1) VERY(4,1)

:

VERX(1,NPF) VERX(2,NPF) VERX(3,NPF) VERX(4,NPF)

VERY(1,NPF) VERY(2,NPF) VERY(3,NPF) VERY(4,NPF)

PARTR is the dimensional radius R of the partition circle measured in the same units as the characteristic length. The partition circle must enclose the body. It should be determined according to the decaying rate of local waves. An appropriate approximation is R ~ O(h) (h is water depth) for shallow water and R ~ O( λ)

( λ=longest wavelength involved) for deep water (h>>λ). The actual constants of proportionality R/λ may have to be substantially larger than one to achieve accuracy in deep water.

• NPF is the total number of panels on the free surface.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

• NTCL is the total number of segments (panels) on the partition circle.

• NAL is the number of annuli in intermediate region (may be 0)

• DELR is the radial increment for each annulus

• NCIRE is the number of nodes in the azimuthal integration in each annulus is 2

NCIRE+1

• NGSP is the number of nodes in radial integration on each annulus

• VERX(K,I), K=1,4 is the dimensional x coordinate of the K-th vertex of the I-th panel

• VERY(K,I), K=1,4 is the dimensional y coordinate of the K-th vertex of the I-th panel

**Wadam**

**5-13**

**Wadam**

**5-14**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE ENVIRONMENT WAVE-SPECTRUM**

...

WAVE-SPECTRUM

JONSWAP hs tz-or-tp gam siga sigb

PIERSON-MOSKOWITZ hs tz

TORSETHAUGEN hs tp

**PURPOSE:**

The command specifies the wave spectra to be used for the wave directions. The wave directions must already have been defined (DEFINE ENVIRONMENT WAVE-DIRECTION). The spectra are given for the directions one-by-one.

**PARAMETERS:**

JONSWAP

PIERSON-MOSKOWITZ

TORSETHAUGEN hs tz-or-tp gam siga sigb tp

Use wave spectrum of type JONSWAP

Use wave spectrum of type Pierson-Moskowitz

Use wave spectrum of type Torsethaugen

Significant wave height

Relevant for JONSWAP spectrum only: tz-or-tp > 0: Zero up-crossing wave period (tz = tz-or-tp) tz-or-tp < 0: Peak spectral wave period (tp = |tz-or-tp|)

Peak enhancement factor for JONSWAP

Left width parameter for JONSWAP

Right width parameter for JONSWAP

Peak spectral period for Torsethaugen

**NOTES:**

Either long- or short-crested waves may be used for roll motion. When short-crested wave are used only one main wave direction can be run.

In a subsequent Postresp run the same wave spectra and spreadings must be used to obtain consistent results.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL**

...

GENERAL

ANALYSIS-MODELS

CONSTANTS

EXECUTION-DIRECTIVES

GLOBAL-MATRICES

MULTI-BODY

OFFBODY-POINTS

PANEL-PRESSURE

ROLL-DAMPING-MODEL

SECTIONAL-LOADS

TANK-PRESSURE

TEXT

END

...

**PURPOSE:**

The command defines general parameters such as execution directives for Wadam.

**Wadam**

**5-15**

**Wadam**

**5-16**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL ANALYSIS-MODELS**

...

ANALYSIS-MODELS

DISTRIBUTED-MASS

MASS-MODEL

GLOBAL-MASS-MATRIX

MORISON-MODEL

SINK-SOURCE-MODEL

STRUCTURAL-MODEL

END

GENERATE topsel

USER-SPECIFIED ...

topsel topsel topsel

...

xg yg zg xrad yrad zrad xyrad xzrad yzrad tmass

**PURPOSE:**

The command defines the various analysis models.

**PARAMETERS:**

MASS-MODEL

MORISON-MODEL

SINK-SOURCE-MODEL

STRUCTURAL-MODEL topsel

DISTRIBUTED-MASS

GLOBAL-MASS-MATRIX

GENERATE

USER-SPECIFIED xg yg zg

To specify the mass input information.

To specify the Morison model to be used.

To specify the panel model to be used.

To specify the structural model to be used.

Top superelement number

A distributed mass formulation will be used. The mass distribution is defined by the Morison model.

A global mass formulation will be used.

The global mass matrix will be generated by Wadam from the mass model.

The global mass matrix will be specified directly by the user.

The x-coordinate of the centre of gravity in the input coordinate system.

The y-coordinate of the centre of gravity in the input coordinate system.

The z-coordinate of the centre of gravity in the input coordinate system.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

5-17 xrad yrad zrad xyrad xzrad yzrad tmass

Radius of gyration (square root of the moment of inertia divided by total mass) about an axis parallel with the input x-axis and through the motion reference point.

Radius of gyration about an axis parallel with the input y-axis and through the motion reference point.

Radius of gyration about an axis parallel with the input z-axis and through the motion reference point.

The negative of the specific product of inertia (The negative of the product of inertia divided by total mass) about axis parallel with the input x- and y-axis and through the motion reference point.

Negative specific product of inertia about axis parallel with the input x- and z-axis and through the motion reference point.

Negative specific product of inertia about axis parallel with the input y- and z-axis and through the motion reference point.

Total mass of the body.

**NOTES:**

See also DEFINE GENERAL GLOBAL-MATRIX for definition of user specified global mass matrices.

**Wadam**

**5-18**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL CONSTANTS**

...

CONSTANTS cleng rho grav amp zloc vol1 ar1 vcb1

**PURPOSE:**

The command defines general constants used in the analysis.

PARAMETERS: cleng rho grav amp zloc vol1 ar1 vcb1

Characteristic length for the hydrodynamic model

Density of sea water (in SI-units: 1025 kg/m3).

Constant of gravity (in SI-units: 9.81 m/s2).

Linearising velocity for the viscous drag. This should be a representative relative velocity between the structure and the fluid.

The z-coordinate of the origin of the input coordinate system. zloc is negative if the origin of the input coordinate system is below still water level.

Not used. A dummy value must be given.

Not used. A dummy value must be given.

Not used. A dummy value must be given.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES**

...

EXECUTION-DIRECTIVES

ANALYSIS-TYPE

DETERMINISTIC-MORISON

DRAG-LINEARISATION

DRIFT-FORCES

FIXED-FLOATING

HORISONTAL-DRIFT

MORISON-EQUATION

OUTPUT-FORMAT

POTENTIAL-THEORY

PRINT-SWITCH

RESULT-FILES

SAVE-RESTART

SECOND-ORDER-RESULTS

TOLERANCES

WAVE-DRIFT-DAMPING

END

**PURPOSE:**

The command defines control parameters for execution of Wadam.

...

**Wadam**

**5-19**

**Wadam**

**5-20**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES ANALYSIS-TYPE**

...

ANALYSIS-TYPE

DATACHECK

GLOBAL-RESPONSE

STRUCTURAL-LOADS

**PURPOSE:**

The command defines the calculation type.

**PARAMETERS:**

DATACHECK

GLOBAL-RESPONSE

STRUCTURAL-LOADS

Only data check and hydrostatic calculation will be performed.

Global response calculation will be performed.

Global response and detailed load calculation will be performed.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-21**

**DEFINE GENERAL EXECUTION-DIRECTIVES DETERMINISTIC-MORISON**

...

DETERMINISTIC-MORISON ...

...

DIFFRACTED-WAVE

INCIDENT-WAVE

...

NONLINEAR-DRAG

LINEAR-DRAG

STILL-WATER-LEVEL

FINITE-WAVE-ELEVATION

**PURPOSE:**

The command defines parameters for use in deterministic Morison calculation. This option is available with the time domain output format.

**PARAMETERS:**

DIFFRACTED-WAVE

INCIDENT-WAVE

LINEAR-DRAG

NONLINEAR-DRAG

STILL-WATER-LEVEL

FINITE-WAVE-ELEVATION

Velocity and acceleration due to the diffracted wave are used in

Morison’s equation. Radiation-diffraction theory must be used for parts of the structure.

Velocity and acceleration due to the incident wave are used in

Morison’s equation.

Linearised drag formulation is used in Morison’s equation with the linearised velocity given and amp defined by the DEFINE

GENERAL CONSTANTS command.

Non-linear drag formulation is used in Morison’s equation.

Loads will be calculated up to still water level.

Loads will be calculated up to finite wave elevation.

**Wadam**

**5-22**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES DRAG-LINEARISATION**

...

DRAG-LINEARISATION durhr-trac rotc maxit

**PURPOSE:**

This command is used for two different purposes:

Case 1: Drag linearisation.

This can be stochastic linearisation if combined with the commands DEFINE ENVIRONMENT WAVE-

SPECTRUM and DEFINE ENVIRONMENT WAVE-SPREADING-FUNCTION or regular wave linearisation if combined with the command DEFINE ENVIRONMENT LINEARISING-WAVE-HEIGHT.

Case 2: Roll damping.

When used together with the command DEFINE GENERAL ROLL-DAMPING-MODEL the command is used to specify that the roll angle iteration is to be performed. The maximum roll angle estimates (thmd values on DEFINE GENERAL ROLL-DAMPING-MODEL MAXIMUM-ROLL-ANGLE) are then used as start values in the iteration process.

If this command is not specified it is assumed that the input thmd-values are used as estimates according to the traditional method, hence no iteration will be performed.

PARAMETERS: durhr-trac rotc maxit

When drag linearisation is applied to the roll damping model this parameter is the duration of the sea state in hours (typically 3). It used to calculate the maximum roll angle from the standard deviation as the most probable largest value assuming a Rayleigh distribution.

When drag linearisation is applied to the Morison model this parameter is the convergence criterion for the translational modes.

Convergence criterion for the roll mode in case of roll damping model and for all angular modes in case of Morison model. It is given in percentage of the consecutive error. Default

= 0.1 %.

Maximum number of iterations in the drag linearisation. Default = 10, maximum allowed =

19.

**NOTES:**

Since there is only room for one command of this type iterative drag-linearisation and roll damping cannot be used in the same Wadam run.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-23**

**DEFINE GENERAL EXECUTION-DIRECTIVES DRIFT-FORCES**

...

DRIFT-FORCES

YES

NO

**PURPOSE:**

The command defines whether second order mean drift forces in six degrees of freedom shall be calculated or not. These forces are computed by pressure integration, hence this method may be used to compute the drift forces on each body in a multi-body analysis.

**PARAMETERS:**

YES

NO

Second order mean drift forces will be calculated.

Second order mean drift forces will not be calculated.

**NOTE:**

Computation of drift forces by pressure integration requires a much finer discretisation to converge than the computation of drift forces by far field integration (HORISONTAL-DRIFT). Also the CPU-cost for a given discretisation increases by a factor of 2 when this option is included.

**Wadam**

**5-24**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES FIXED-FLOATING**

...

FIXED-FLOATING

FIXED

FLOATING

XZ-PLANE

YZ-PLANE

YZ-XZ-PLANE

NONE

XZ-PLANE

YZ-PLANE

YZ-XZ-PLANE

NONE

...

YES

NO

**PURPOSE:**

The command specifies the structure to be fixed or floating as well as symmetry plane(s).

**PARAMETERS:**

FIXED

FLOATING

XZ-PLANE

YZ-PLANE

YZ-XZ-PLANE

NONE

Fixed structure, only exciting and drift forces may be calculated.

Floating structure, added mass and damping is calculated and the equation of motion is solved. Answer YES or NO to whether natural periods (eigenvalues) for rigid body degrees of freedom shall be computed or not.

The panel model has the xz-plane as its symmetry plane.

The panel model has the yz-plane as its symmetry plane.

The panel model has both the yz-plane and xz-plane as symmetry planes.

The panel model has no planes of symmetry.

**NOTE:**

No panel may have more than two nodes in the free surface or at the sea bed. In addition no panel must have more than one node in a plane of symmetry.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-25**

**DEFINE GENERAL EXECUTION-DIRECTIVES HORISONTAL-DRIFT**

...

HORISONTAL-DRIFT

YES

NO

**PURPOSE:**

The command defines whether second order mean horizontal drift forces shall be calculated or not. This computation give the surge and sway force and yaw moment. The forces are computed by far field integration, hence in a multi-body case this will only give the total drift force on all bodies. If drift forces on individual bodies in a multi-body problem is wanted the similar command DRIFT-FORCES must be given.

**PARAMETERS:**

YES

NO

Second order mean horizontal drift forces will be calculated.

Second order mean horizontal drift forces will not be calculated.

**Wadam**

**5-26 22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES MORISON-EQUATION**

...

MORISON-EQUATION ...

**PURPOSE:**

This command is currently not in use.

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-27**

**DEFINE GENERAL EXECUTION-DIRECTIVES OUTPUT-FORMAT**

...

OUTPUT-FORMAT

FREQUENCY-DOMAIN phase

TIME-DOMAIN

GROUP phf phl inc phf phl inc

**PURPOSE:**

The command defines the domain in which the results from Wadam shall be given. This concerns both results on the print file and loads on the Loads Interface File.

**PARAMETERS:**

FREQUENCY-DOMAIN

TIME-DOMAIN phase

GROUP

All results will be presented as complex values.

All results will be presented as real values for a set of phase angles. When the TIME-DOMAIN format is specified wave amplitudes must be specified by the DEFINE ENVIRONMENT

WAVE-AMPLITUDE command.

Phase angle(s) for which the results are given. Up to 8 phase angles may be specified. The specified phase angles will be used for all wave directions.

Phase angles given as a group. Using this option Wadam may handle up to 14 phase angles in the same run.

First phase angle in the group.

Last phase angle in the group.

Increment between the phase angles.

**Wadam**

**5-28**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES POTENTIAL-THEORY**

...

POTENTIAL-THEORY

EQUATION-SOLUTION

IRREGULAR-FREQUENCY

LOGARITHM-SINGULARITY

NUMERICAL-INTEG-TYPE

PANEL-DIMENSION

DIRECT

ITERATION

NO-REMOVAL

REMOVE alpha

NUMERICAL

ANALYTICAL

ONE-NODE-GAUSSIAN

FOUR-NODE-GAUSSIAN

AREA

MAXIMUM-DIAGONAL

END

**PURPOSE:**

The command defines execution directives for solving the radiation-diffraction problem in Wadam.

**PARAMETERS:**

EQUATION-SOLUTION

DIRECT

ITERATION

IRREGULAR-FREQUENCY

NO-REMOVAL

REMOVE alpha

LOGARITHM-SINGULARITY

NUMERICAL

ANALYTICAL

NUMERICAL-INTEG-TYPE

Specify in which way the equation system shall be solved.

Equation system solved by direct method. This is the recommended option when number of panels is less than 2000.

Equation system solved by iteration (default).

Specify whether irregular frequencies shall be removed or not.

Do not remove irregular frequencies (default).

Remove irregular frequencies.

Not used. A dummy value must be given.

Specify numerical or analytical integration of the logarithmic singularities of the Green’s function.

Gauss quadrature is used (numerical integration) (default).

The logarithmic singularities are integrated analytically.

Specify type of numerical integration of Green’s function and its derivatives.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-29**

ONE-NODE-GAUSSIAN

FOUR-NODE-GAUSSIAN

PANEL-DIMENSION

AREA

MAXIMUM-DIAGONAL

Single-node Gauss quadrature is used (default).

Four-node Gauss quadrature is used.

Specify the panel dimension to which the distance between the panel centroids are compared in determining those pairs of panels where the above analytical integration is required.

Square root of the panel areas are used (default).

The maximum diagonal of the panels are used.

**NOTES:**

The direct solver is switched to a block-iterative solver if the number of panels is larger than the maximum allowed in-core matrix size. This parameter is found as the fourth number on the WWAMOPT card in the

Wadam*.FEM file (last card on the file before IEND). The default value is 2000. If you have more than

2000 panels and a computer with sufficient memory consider increasing this number to some number larger than the number of panels. The direct solver is quite competitive even for much more than 2000 panels. The block-iterative solver is always slower than the fully iterative solver, but it is more robust.

The option IRREGULAR-FREQUENCY REMOVE will increase the number of panels since additional panels on the ‘interior free surface’ is automatically added.

The AREA/MAXIMUM-DIAGONAL options are only relevant in combination with the ANALYTICAL option. If the panels are very elongated we recommend to use ANALYTICAL + MAXIMUM-DAIGONAL.

This is always a more robust option, but gives a moderate increase in CPU-time.

**Wadam**

**5-30**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES PRINT-SWITCH**

...

PRINT-SWITCH

DUMP-OF-LOAD-DISTRIBUTION

DUMP-OF-LOAD-TRANSFER

DUMP-OF-MODEL-DATA

MAXIMUM-PRINT

NO-EXTRA-PRINT

NORMAL-PRINT

**PURPOSE:**

The command sets Wadam print switches. Note that a print switch other than NO-EXTRA-PRINT and

NORMAL-PRINT may result in large output print files.

**Note: The print switches are referred to as print level numbers in the table of contents of the Wadam print file (Wadam#.LIS).**

**PARAMETERS:**

DUMP-OF-LOAD-DISTRIBUTION

DUMP-OF-LOAD-TRANSFER

DUMP-OF-MODEL-DATA

MAXIMUM-PRINT

NO-EXTRA-PRINT

NORMAL-PRINT

Detailed load distribution in addition to dump of model data

(level 3). In addition more load sums and details of the mass distribution is printed.

Detailed loading on all elements in the Morison model in addition to the dump of load transfer (level 4)

Detailed model data in addition to normal print (level 2)

Maximum print value (level 5). This gives an extensive amount of maintenance print relevant only for debugging purposes.

Minimum amount of print (level 0). This is the default. Almost only results from the data check are printed.

Normal amount of print (level 1). This is the most commonly used level. This option includes print of hydrodynamic coefficients, rigid body motion and sectional loads.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-31**

**DEFINE GENERAL EXECUTION-DIRECTIVES RESULT-FILES**

...

RESULT-FILES ...

GLOBAL-RESPONSE

NONE

SIF-FORMATTED

SIN-NORSAM

SIU-UNFORMATTED

...

LOAD-TRANSFER-OPT

FILE-FORMAT

GRAVITY-LOAD

HYDRO-DYNAMIC-LOAD

HYDRO-STATIC-LOAD

INERTIA-LOAD

INERTIA-RELIEF

FORMATTED

UNFORMATTED lcn

NO-GRAVITY-LOAD lcn

NO-DYNAMIC-LOAD lcn

NO-STATIC-LOAD lcn

NO-ACCELERATIONS

ON

OFF

NO-SYMMETRY

ONE-PLANE-SYM LOAD-SYMMERY

STRUCTURAL-LOADS

OFFSET-IN-LOAD-CASE-N

TANK-PRESSURE

WAVE-STRETCHING

END

BEAM-STRUCTURAL-MOD anc

COMPOSITE-STRUCTURAL stalo

SHELL-STRUCTURAL-MOD stalo

TWO-PLANE-SYM lcn

AUTOMATIC

ON

OFF

ON

OFF

END

XZ-PLANE

YZ-PLANE ...

ANTI

BOTH

SYMM add stalo

**Wadam**

**5-32**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**PURPOSE:**

The command specifies which analysis results files to generate and their contents.

**PARAMETERS:**

GLOBAL-RESPONSE

NONE

SIF-FORMATTED

SIN-NORSAM

SIU-UNFORMATTED

LOAD-TRANSFER-OPTION

FILE-FORMAT

FORMATTED

UNFORMATTED

GRAVITY-LOAD lcn

NO-GRAVITY-LOAD

HYDRO-DYNAMIC-LOAD

NO-DYNAMIC-LOAD

HYDRO-STATIC-LOAD

NO-STATIC-LOAD

INERTIA-LOAD

Generation of a Hydrodynamic Results Interface File.

No Hydrodynamic Results Interface File will be generated.

The global responses will be written to a sequential formatted

Hydrodynamic Results Interface File named Gn.SIF.

The global responses will be written to a direct access Hydrodynamic Results Interface File named Gn.SIN.

The global responses will be written to a sequential unformatted Hydrodynamic Results Interface File named Gn.SIU.

To specify load cases, load case options and format of the

Loads Interface Files. Except for FILE-FORMAT this option can only be used for shell models.

Specify format of the Loads Interface File.

The generated Loads Interface Files will be formatted.

The generated Loads Interface Files will be unformatted.

Set load case number for the gravity load. It is not recommended to use this option.

Global load case number to start off each load type. If zero,

Wadam will set load cases numbers according to the type of analysis which have been specified.

The static load written to the Loads Interface File will not include gravity.

Set start load case number for the hydrodynamic loads. It is not recommended to use this option.

No hydrodynamic loads will be written to the Loads Interface

File.

Set load case number for the hydrostatic load. It is not recommended to use this option.

No hydrostatic load will be written to the Loads Interface File.

Set start load case number for the inertia loads. It is not recommended to use this option.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-33**

NO-ACCELERATIONS

INERTIA-RELIEF

LOAD-SYMMETRY

NO-SYMMETRY

ONE-PLANE-SYM

XZ-PLANE

YZ-PLANE

ANTI

BOTH

SYMM

TWO-PLANE-SYM

OFFSET-IN-LOAD-CASE-NUMBERS

AUTOMATIC

TANK-PRESSURE

WAVE-STRETCHING

STRUCTURAL-LOAD

BEAM-STRUCTURAL-MODEL anc add

No inertia loads will be written to the Loads Interface File.

Switch inertia relief ON or OFF

Specify type of symmetry.

No symmetric or antisymmetric loads will be calculated.

Symmetric and/or antisymmetric loads about the XZ- or YZ-

PLANE

XZ-plane symmetry will be generated.

YZ-plane symmetry will be generated.

Antisymmetric loads will be generated.

Both symmetric and antisymmetric loads will be generated.

Symmetric loads will be generated.

Symmetric and/or antisymmetric load about both the XZ- and the YZ-plane will be generated.

Lowest load case number used by Wadam when generating loads for the Loads Interface Files

The load case numbers used by Wadam will start with the highest load case number found on each Input Interface File for each superelement type of the structural model plus one. This option cannot be used in connection with fatigue calculations

(the S-file will then not be created).

Switch ON or OFF calculation of tank pressure when transferring pressures to the Loads Interface Files.

Switch ON or OFF calculation of wave pressures to finite water surface by stretching when transferring pressures to the Loads

Interface Files. This option is valid only for time domain.

To specify generation of Loads Interface Files.

Loads Interface Files (Ln.FEM) will be generated with loads on a beam structural model.

Answer YES or NO to whether the static and dynamic mooring forces shall be included in the loads written to the Loads Interface File (default).

Answer YES or NO to writing added mass (from wet beams and 3D Morison elements only) as separate inertia forces (for structural dynamics) on the Loads Interface Files. Answer NO involves that added mass is only included in added mass force.

**Wadam**

**5-34**

**SESAM**

**Program version 8.1**

22-JAN-2010 stalo Answer YES or NO to writing both static and dynamic loads on the Loads Interface Files. Answer NO involves that only dynamic loads are written.

COMPOSITE-STRUCTURAL-MODEL Loads Interface Files (Ln.FEM) will be generated with loads on a combined beam and shell/solid structural model. In this case the shell/solid model is specified as the structural model. The beam model is assumed identical to the Morison model.

SHELL-STRUCTURAL-MODEL Loads Interface Files (Ln.FEM) will be generated with loads on a shell/solid structural model.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-35**

**DEFINE GENERAL EXECUTION-DIRECTIVES SAVE-RESTART**

...

SAVE-RESTART

AUTO-SAVE-RESTART

NO-SAVE-RESTART

RESTORE-POTENTIAL-SOLUTION

SAVE-POTENTIAL-SOLUTION

**PURPOSE:**

The command specifies use of save and restart facilities in Wadam.

**PARAMETERS:**

AUTO-SAVE-RESTART

NO-SAVE-RESTART

RESTORE-POTENTIAL-SOLUTION

SAVE-POTENTIAL-SOLUTION

Wadam will automatically restart and append new calculated data to an existing save-file, otherwise Wadam will create a new save-file.

No saving, no restart, this is the default option.

Restore the radiation-diffraction solution for the panel model.

Save the radiation-diffraction solution for the panel model.

**Wadam**

**5-36**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES SECOND-ORDER-RESULTS**

...

EXECUTION-DIRECTIVES SECOND-ORDER-RESULTS ...

...

MODES

QUADRATIC-SECOND-ORDER-FORCES

FORCE-BY-INDIRECT-METHOD

FORCE-BY-DIRECT-METHOD

PRESSURE-ON-BODY

PRESSURE-IN-FLUID

WAVE-ELEVATION

NO-COMPUTATION

END dof1 dof2 dof3 dof4 dof5 dof6

...

ON

OFF

**PURPOSE:**

The command defines the second-order calculation types for the sum and/or difference frequencies defined on the DEFINE ENVIRONMENT FREQUENCY-HEADING-PAIRS command.

**PARAMETERS:**

MODES dof1 dof2 dof3 dof4 dof5 dof6

QUADRATIC-SECOND-ORDER-FORCES

FORCE-BY-DIRECT-METHOD

FORCE-BY-INDIRECT-METHOD

PRESSURE-ON-BODY

PRESSURE-IN-FLUID

WAVE-ELEVATION

Specify which degrees of freedom shall be computed.

ON/OFF for each of the six degrees of freedom.

Compute (ON) the quadratic second order forces.

Compute (ON) second-order forces by direct method.

Compute (ON) second-order forces by indirect method.

**Note: Always use FORCE-BY-INDIRECT-**

**METHOD ON when second-order results are wanted.**

Compute (ON) second-order pressure on the body.

Compute (ON) second-order pressure in the fluid domain (output only in Wamit format).

Compute (ON) second-order wave elevation (output only in Wamit format).

**SESAM**

**Program version 8.1**

NO-COMPUTATION

**22-JAN-2010**

**Wadam**

**5-37**

Restriction: The program will currently compute all MODES irrespective of the specifications in this command.

**Wadam**

**5-38**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL EXECUTION-DIRECTIVES TOLERANCES**

...

TOLERANCES

COMPUTED-TOLERANCES tolw1 tolcg

CRITICAL-WAVE-LENGTH wave

END distol angtol

**PURPOSE:**

The command sets user defined tolerances for the analysis. distol and angtol are tolerances on geometrical matching between elements of the shell/solid structural model and panels of the panel model. If exceeded by the 25 closest panels no pressure load is transferred to the structural element in question.

**PARAMETERS:**

COMPUTED-TOLERANCES tolwl tolcg distol angtol

CRITICAL-WAVE-LENGTH wave

Computed tolerances is used by Wadam in different internal checks to verify the consistency of the input model and various parameters.

Tolerance on the computed z-coordinate of the water line as a percentage of the characteristic length. If this tolerance is exceeded the program stops.

Tolerance on the horizontal distances between the centre of gravity and the centre of buoyancy (measured along the coordinate axes x and y) as a percentage of the characteristic length.

If this tolerance is exceeded the program stops.

Marginal difference between the area of the panel and the area of the triangles defined by the vertices of the panel model and the geometric centre of the structural element surface (in percent of the panel area).

Maximum angle between the normal vectors of the panel model and the structural element surface given in degrees.

This option does not function as initially planned (and as indicated by the option name). The given wave length must be larger than all given wave lengths.

Wave length larger than all given wave lengths.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-39**

**DEFINE GENERAL EXECUTION-DIRECTIVES WAVE-DRIFT-DAMPING**

...

WAVE-DRIFT-DAMPING

YES

NO

**PURPOSE:**

The command defines whether the 3x3 Wave Drift damping matrix (for the modes surge, sway and yaw) shall be calculated or not.

**PARAMETERS:**

YES

NO

Wave Drift damping matrix will be calculated.

Wave Drift damping matrix will not be calculated (Default).

**NOTES:**

Wave Drift damping, like Drift forces, require a finer mesh for convergence than other global results.

Computation of Wave Drift damping requires a free surface model.

**Wadam**

**5-40**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL GLOBAL-MATRICES**

...

GLOBAL-MATRICES

CRITICAL-DAMPING-MATRIX

DAMPING-MATRIX

MASS-MATRIX wavlen

INDEPENDENT ibody delem frac

END elem damp

END jbody elem damp

END elem mass

END

RESTORING-MATRIX

END elem

END rest

USE-OF-INPUT-MAT

DAMPING-MATRIX

ADD

OVERWRITE

END

END

**PURPOSE:**

The command defines additional global matrices to be used in Wadam. The matrices will be added to matrices calculated by Wadam, with a possible exception for the damping matrix where the user specifies whether it is to be added to or replace the matrix computed by Wadam. If for instance mooring forces are given through anchor elements and the user specifies a restoring matrix both will contribute to the total restoring forces. The matrix is by default a zero matrix. The user must only specify those matrix elements which are different from zero. There is no assumption of symmetry, so all non-zero elements must be specified on both side of the diagonal. The global matrices will not contribute to distributed loads and sectional loads.

Additional or alternative global damping matrix based on the critical damping of the system in question may be generated or the user may alternatively specify it directly. User specified damping matrices will be added to the critical damping matrix.

Note that the specification of global-mass matrices is available for a multiple body system. If a single system shall be analysed this command may still be used. However giving body identification number equal to

1. Only the body mass matrices are available in a multi body system. Hence no mechanical coupling matrices between the bodies can be specified.

For body 2, 3 aso. in a multi-body system the MASS-MATRIX command is the only available way to specify the mass data.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-41**

tions the Body Coordinate system is identical to the Global system.

**PARAMETERS:**

CRITICAL-DAMPING-MATRIX delem frac

DAMPING-MATRIX

MASS-MATRIX

RESTORING-MATRIX

INDEPENDENT wavlen elem damp rest ibody jbody mass

USE-OF-INPUT-MAT

ADD

OVERWRITE

Information related to generation of damping matrices based on critical damping will be given.

Diagonal element for which the fraction of critical damping will be specified = 11,...,66 (only the diagonal entries may be given).

Fraction of critical damping of the degree of freedom in question. Default values are zero.

A damping matrix, frequency (wave length) dependent or not will be given.

One mass matrix for each body may be specified.

A restoring matrix will be given.

A frequency independent matrix is specified.

Wave length/period/frequency for which a frequency dependent matrix will be specified. The wave length/period/frequency must be specified by the DEFINE ENVIRONMENT command beforehand.

Selected element in the 6x6 matrix. This element number must be given as 11, 12, 13, ... 16, 21, ... 66.

Actual damping value for given element.

Actual restoring value for given element.

Body identification of body number i.

Body identification of body number j.

Actual mass for body no. i and body no. j for given element.

The use of input global matrices will be specified. By default the input matrices including any generated critical damping matrices will be added to the corresponding matrices calculated by Wadam.

The input matrices in question will be added to the corresponding matrices calculated by Wadam.

The input matrices in question will overwrite the corresponding matrices calculated by Wadam.

**Wadam**

**5-42**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**NOTES:**

This command may create imbalance in the loads for a load transfer analysis. This may also lead to inaccurate or erroneous sectional loads due to lack of detailed information.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-43**

**DEFINE GENERAL MULTI-BODY**

...

MULTI-BODY

MODELS

STRUCTURE-IDENTIFICATION

END

...

**PURPOSE:**

The command defines multiple body parameters. If any of this data is specified some of the single body related data specified elsewhere will be neglected by Wadam.

These are:

• Sink-source (or panel) model specified using DEFINE GENERAL ANALYSIS-MODELS

• Symmetry plan definition using DEFINE GENERAL EXECUTION-DIRECTIVES

• Characteristic length using DEFINE GENERAL CONSTANT

• Calculation of sectional loads by using DEFINE GENERAL SECTIONAL-LOADS

**Wadam**

**5-44**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL MULTI-BODY MODELS**

...

MODELS body PANEL-MODEL direc topsel xm ym zm delta

XZ-PLANE

YZ-PLANE

YZ-XZ-PLANE

NONE

END

**PURPOSE:**

The command is used for two purposes:

• Definition of the analysis model for each body by their prefix and superelement number.

Presently only the panel models may have multiple body specification. The other analysis models shall be specified using the DEFINE GENERAL ANALYSIS-MODELS command and the DEFINE GENERAL

GLOBAL-MATRICES MASS-MATRIX command.

• Reading of panel model from Wamit gdf-files. (Multi-body panel models cannot presently be interpreted from the gdf format.)

Note that the definition of symmetry plane and zm will override equivalent information specified with other Prewad commands. Furthermore, the WADAMn.FEM file created by Prewad must be manually edited by altering the third parameter (the fourth field counting the record name field) of the HYDMODID record from 1. to 11.

PARAMETERS: body

PANEL-MODEL direc topsel xm ym

Body identification number. Note that the body numbers must be consecutively ordered.

In case of reading gdf-files this parameter must be 1.

Panel model used in the hydrodynamic analysis.

File prefix, or directory where the file(s) are stored.

In case of reading gdf-file this is the file name of the Wamit gdf-file without the

.gdf extension.

Top superelement number.

In case of reading gdf-file this parameter is not used.

X-coordinate of the origin of the input coordinate system given in the body coordinate system.

Y-coordinate of the origin of the input coordinate system given in the body coordinate system.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

5-45 zm delta

XZ-PLANE

YZ-PLANE

YZ-XZ-PLANE

NONE

Z-coordinate of the origin of the input coordinate system given in the body coordinate system.

Angle between the input x-axis and the body x-axis in degrees. The angle is given from the input x-axis to the body x-axis. Positive direction is counter-clockwise.

The panel model has the xz-plane as its symmetry plane.

The panel model has the yz-plane as its symmetry plane.

The panel model has both the yz-plane and xz-plane as symmetry planes.

The panel model has no planes of symmetry.

**Wadam**

**5-46**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL MULTI-BODY STRUCTURE-IDENTIFICATION**

...

STRUCTURE-IDENTIFICATION ...

...

body cleng xb yb zb delta ORIGIN-OF-BODY

END

**PURPOSE:**

The command defines the structure dependent data for each body. These data are common for all different models representing the structure.

PARAMETERS: body cleng xb yb zb delta

ORIGIN-OF-BODY

Body identification number. Note that the body numbers must be consecutively ordered.

Characteristic length of the body. Usually the largest horizontal distance between

2 points on the average immersed surface.

X-coordinate of the origin of the body coordinate system given in the global coordinate system.

Y-coordinate of the origin of the body coordinate system given in the global coordinate system.

Z-coordinate of the origin of the body coordinate system given in the global coordinate system.

Angle between the body x-axis and the global x-axis in degrees. The angle is given from the body x-axis to the global x-axis. Positive direction is counter-clockwise.

The origin of the body coordinate system will be used as the results reference point.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-47**

**DEFINE GENERAL OFFBODY-POINTS**

...

OFFBODY-POINTS xcoor ycoor zcoor

END

SURFACE-MODEL prefix topsel

**PURPOSE:**

The command defines points in the fluid where wave kinematics shall be calculated. All points must be given because no symmetry is taken into account.

PARAMETERS: xcoor ycoor zcoor

SURFACE-MODEL prefix topsel

The x-coordinate with respect to the global coordinate system of the point in the fluid.

The y-coordinate with respect to the global coordinate system of the point in the fluid.

The z-coordinate with respect to the global coordinate system of the point in the fluid.

The off-body points are given as nodes as part of a 4 node shell element model on an Input Interface File.

File prefix or directory where the file is stored

The superelement number (which must be a single first level superelement)

**NOTES:**

The SURFACE-MODEL option must be used for animation of free surface elevation in Xtract. The SUR-

FACE-MODEL option must not be used for Postresp.

The CHANGE command corresponding to this DEFINE command deviates in that there is an additional parameter refno:

CHANGE GENERAL OFFBODY-POINTS refno xcoor ycoor zcoor refno is the reference number of the offbody point to change (1, 2, 3, ...).

**Wadam**

**5-48**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL PANEL-PRESSURE**

ALL-ELEMENTS

INTERVAL

...

PANEL-PRESSURE selno index

ELEMENT-NUMBER iel-first iel-last step iel

END

END

**PURPOSE:**

The command transfers computed pressures to the Hydrodynamic Results Interface File (G-file). (These pressures can then be read as transfer functions and presented by Postresp.)

In Postresp the panel pressures are identified by the Wadam internal panel index and a reflection index.

The correspondence between the element data and the panel indices is printed on the Wadam print file if the print switch is set to DUMP-OF-MODEL-DATA or higher.

PARAMETERS: selno index

ALL-ELEMENTS

INTERVAL

Superelement number within the sink-source model

Superelement index of the given superelement

Pressures for all elements of the superelement will be written to the Hydrodynamic

Results Interface File (G-file).

Pressures for all elements in a specified interval will be written to the Hydrodynamic Results Interface File (G-file).

First element in interval

Last element in interval iel-first iel-last step Increment in element number

ELEMENT-NUMBER Pressures for a listed sequence of elements will be written to the Hydrodynamic

Results Interface File (G-file).

iel List of element numbers closed by END

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-49**

**DEFINE GENERAL ROLL-DAMPING-MODEL**

...

ROLL-DAMPING-MODEL ...

...

BILGE-KEEL

GZ-CURVE

MAXIMUM-ROLL-ANGLE xfr

NONE hang

END thmd

END bilgl gz

STRIP-MODEL

WATER-PARAMETERS

END nos xoff

LAMINAR

TURBULENT bilgb xbow visc y

FP-TO-AP

AP-TO-FP z phi bst bilgr sect

**PURPOSE:**

The command defines a roll damping model based on ordinary strip theory.

**Note: The roll damping model can only be applied when xz-symmetry is used.**

**Note: The y, z and phi parameters are repeated for each strip that is fully or partly intersected by the bilge keel.**

**PARAMETERS:**

BILGE-KEEL

NONE xfr bilgl bilgb y

Defining parameters for a bilge keel. The strip model must be defined first. See note above on repetition of the y, z and phi parameters.

No bilge keel model specified.

X-coordinate of the front part of the bilge keel.

Length of bilge keel along the ship.

Beam (width) of bilge keel.

**Note: Be careful with very small bilge keels, cf. Section **

Distance from centre line to bilge keel hull intersection point.

nos xoff xbow

FP-TO-AP

AP-TO-FP bst

**Wadam**

5-50 z phi

GZ-CURVE hang gz

MAXIMUM-ROLL-ANGLE thmd

STRIP-MODEL

**SESAM**

**Program version 8.1**

**22-JAN-2010**

Distance from mean water line to bilge keel hull intersection point.

Bilge keel angle in degrees. I.e. angle between the line from the origin to the bilge keel hull intersection point and a line through the web of the bilge keel (the sign is of no consequence as only the cosine of the angle is used).

GZ-curve data as input.

Heel angle in degrees.

Restoring moment arm in roll (GZ).

**Note: Maximum number of points on GZ-curve is 50.**

Estimated maximum roll angle for each wave direction. The number of angles and their sequence correspond to the wave directions previously defined. This option is mandatory for the roll damping model.

Estimated maximum roll angle in degrees. It will be used to calculate a linearised viscous and eddy-making damping and will therefore significantly affect the transfer functions at wavelengths close to resonance. The angle cannot be set to zero but it may be set to a very low value (0.001) in which case all viscous effects are neglected. The chosen value of the angle may strongly affect the calculation results if roll resonance occurs at wavelengths at which appreciable wave energy is present.

Defining parameters for the strip model. Note that this must be specified before defining a bilge keel model. The strips should always be given from bow to stern meaning that for the FP-TO-

AP option the strips are given in the order of increasing x-value while they are given in the order of decreasing x-value for AP-

TO-FP option.

Number of strips used in the roll damping calculations. Maximum is 25.

X-coordinate of fore perpendicular (FP) in global coordinate system (dummy)

X-coordinate of the midpoint of the first strip

X-axis positive from fore perpendicular (FP) to aft perpendicular (AP) (default)

X-axis positive from aft perpendicular (AP) to fore perpendicular (FP)

Length of each strip. This is repeated nos times.

**SESAM**

**Program version 8.1**

bilgr sect

WATER-PARAMETERS

LAMINAR-FLOW

TURBULENT-FLOW

**22-JAN-2010**

**Wadam**

**5-51**

Radius of a bilge at strip. This is repeated nos times.

Parameter for eddy-making roll damping calculations. It is determined by the sectional area coefficient BOG/BS where BOG is the distance from the bottom of the strip to a line through centre of gravity of the ship and parallel with the x-axis in the global coordinate system and BS is the beam of the strip at the water-plane. (This is repeated nos times.) sect can take the following:

BOW-SECTION: Apply the roll damping model for bow sections.

MID-SECTION: Apply the roll damping model for mid-sections.

STERN-SECTION: Apply the roll damping model for stern sections.

OTHER-TYPE: To be used for all section types not defined by the parameters for bow, midship and stern (there will be no roll damping from this section).

NOT-SPECIFIED: The program will determine the section type for this strip. If the section is in the forward ¼ of the ship and BOG/BS > 1.2 the section is set as a BOW-SECTION. If the section is in the back ¼ of the ship and BS/BOG > 1.0 the section is set as a STERN-SECTION. If the section is in the middle half of the length and the sectional area coefficient is larger than 0.95 the section is set as a MID-SECTION. In other cases no roll damping will be computed for the section.

**Note: It may well be relevant to use the MID-SECTION model for sections in the first and last quarter of the length. In such cases the sections must be explicitly defined as MID-SECTIONs. For barge type vessels this type should be used for all sections.**

**Note: BOG is the distance from the bottom of the strip to a line through the centre of gravity of the ship and parallel with the x-axis.**

**Note: BS is the beam of the strip at the water-plane.**

Water dependent parameters like viscosity and flow information.

Laminar flow around the hull (used when comparing calculation results and model tests performed with laminar flow around the ship hull).

Turbulent flow around the hull (recommended).

**Wadam**

**5-52**

**SESAM**

**Program version 8.1**

22-JAN-2010 visc Kinematic viscosity of water

**NOTES:**

The warning “Panels are not connected” in the Wadam print file means that the strips will not contribute to the roll damping.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-53**

**DEFINE GENERAL SECTIONAL-LOADS**

... SECTIONAL-LOADS secno

XY-PLANE

YZ-PLANE

XZ-PLANE

POSITIVE-SIDE

...

NEGATIVE-SIDE ax ay az

END

**PURPOSE:**

The command defines sectional planes where sectional loads will be calculated.

PARAMETERS: secno

XY-PLANE

YZ-PLANE

XZ-PLANE

POSITIVE-SIDE

NEGATIVE-SIDE ax ay az

Section identification number.

The section is parallel with the xy-plane of the input coordinate system.

The section is parallel with the yz-plane of the input coordinate system.

The section is parallel with the xz-plane of the input coordinate system.

Sectional loads are calculated on the positive side of the sectional plane.

Sectional loads are calculated on the negative side of the sectional plane.

The x-coordinate with respect to the input coordinate system of a point in the sectional plane. This point defines the position of the sectional plane and of the axis used for the calculation of the sectional moments. The moment axis are parallel with the input axis.

The y-coordinate of the point.

The z-coordinate of the point.

**Wadam**

**5-54**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE GENERAL TANK-PRESSURE**

...

TANK-PRESSURE

ALL tank_i

END rho_all rho_i

**PURPOSE:**

The command defines density of the fluid in the tanks.

**PARAMETERS:**

ALL rho_all tank_i rho_i

The density is the same in all tanks.

The density of the fluid in all the tanks.

Tank number. This is the same number as the load case number used in the definition of the Hydro - Element uniform/HYDRO-PRESSURE load cases.

The density of the fluid in tank number tank_i.

**NOTES:**

To perform the actual load transfer of pressure in tanks the command

### ...RESULT-FILE LOAD-TRANSFER TANK-PRESSURE ON

must be given

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-55**

**DEFINE GENERAL TEXT**

...

TEXT text

END

**PURPOSE:**

The command defines identification text strings for the analysis.

PARAMETERS: text Text given by the user to describe the analysis. Maximum 3 lines can be given. Enclose each text line in apostrophes (' ') when spaces are used.

**Wadam**

**5-56**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE HYDRODYNAMIC-PROPERTY**

...

HYDRODYNAMIC-PROPERTY

CONNECT

SECTION

END

...

**PURPOSE:**

The command defines sectional dependent hydrodynamic data of the Morison model and connects specified section numbers to Morison elements defined in Prewad. The definition of the hydrodynamic properties will also select 2 node beam elements given on the Input Interface File containing the Morison model as 2D

Morison elements. All other 2 node beam elements will become Dry Morison elements.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-57**

**DEFINE HYDRODYNAMIC-PROPERTY CONNECT**

...

CONNECT ref elno

GROUP e1 e2 einc

END

GROUP ref1

END ref2 rinc er einc

**PURPOSE:**

The command connects additional Morison elements (defined in Prewad) with hydrodynamic properties.

PARAMETERS: e2 einc ref1 ref2 ref elno

GROUP e1 rinc er

Reference number of section to be connected.

Element number of a single element.

A group of elements and sections to be connected.

First element number in the group.

Last element number in the group.

Step in the Element numbering.

First reference number in the group.

Last reference number in the group.

Step in the reference numbering.

First element in a group of elements to be coupled to a group of sections.

**Wadam**

**5-58**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION**

...

SECTION ref

END

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ANCHOR-ELEMENT

DRY-ELEMENT

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

...

**PURPOSE:**

The command defines hydrodynamic properties for different element types.

Hydrodynamic properties are connected to sections. Each section is given a reference number.

PARAMETERS: ref Reference number of section. The reference number of sections to be connected to additional elements defined in Prewad must be different from any cross-section reference numbers defined on the Input Interface File containing the Morison model.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-59**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 2D-MORISON-ELEMENT**

...

2D-MORISON-ELEMENT stot dia

RETAINED

...

dm

RETAINED cksi czeta aksi azeta

**PURPOSE:**

The command defines hydrodynamic properties for 2D Morison elements. Two-node beam elements on the

Input Interface File with cross section reference number equal to the hydrodynamic property section reference number ref are defined as 2D Morison elements. All other 2 node beam elements are defined as Dry

Morison elements with RETAINED mass pr. unit length.

All the sub-elements of a 2D Morison element will initially receive the same hydro properties.

To define a section containing sub-elements of varying length and/or properties the user must enter the

CHANGE command after specifying the hydrodynamic properties.

PARAMETERS: dm cksi czeta aksi azeta stot Total number of sub-elements.

RETAINED The equivalent diameter or the distributed mass defined on the Input Interface File will be used. Retained equivalent diameter may only be used for section type PIPE.

dia Equivalent diameter.

Distributed mass of element. Give mass per unit length.

Drag coefficient along the ξ-axis.

Drag coefficient along the ζ-axis.

Added mass coefficient along the ξ-axis.

Added mass coefficient along the ζ-axis.

**NOTES:**

The CHANGE command corresponding to this DEFINE command deviates in that there are two additional parameters, selno and sl:

CHANGE HYDRODYNAMIC-PROPERTY SECTION ref 2D-MORISON-ELEMENT stot selno sl ...

selno and sl are the sub-element number and sub-element length, correspondingly.

**Wadam**

**5-60**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 3D-MORISON-ELEMENT**

...

3D-MORISON-ELEMENT

BOTH

HYDRODYNAMIC

HYDROSTATIC

...

...

dia dm cksi czeta ceta aksi azeta aeta x2 y2 z2

**PURPOSE:**

The command defines hydrodynamic properties for 3D Morison elements.

PARAMETERS: ceta aksi azeta aeta x2

HYDROSTATIC

HYDRODYNAMIC

BOTH dia dm cksi czeta y2 z2

Only buoyancy force will be calculated.

Only wave exciting forces (inertia and drag) will be calculated.

Both wave exciting forces and buoyancy force will be calculated.

Equivalent diameter.

Mass of element.

Drag coefficient along the ξ-axis.

Drag coefficient along the ζ-axis.

Drag coefficient along the η-axis.

Added mass coefficient along the ξ-axis.

Added mass coefficient along the ζ-axis.

Added mass coefficient along the η-axis.

The x-coordinate of a guiding point for the local coordinate system. (Give zero if the element coordinate system is parallel with the global coordinate system. See

The y-coordinate of the guiding point.

The z-coordinate of the guiding pint.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-61**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref ANCHOR-ELEMENT**

...

ANCHOR-ELEMENT angin angx force skh skv

**PURPOSE:**

The command defines hydrodynamic properties for mooring (anchor) elements. See Figure 2.15.

PARAMETERS: angin angx force skh skv

Angle in degrees between the mooring line and the water surface at fairlead.

Angle in degrees between projection of mooring line onto the horizontal plane and the global x-axis.

Static mooring line force (pre-tension) (unit: force).

Spring constant for horizontal displacement of the structure (unit: force per length).

Spring constant for vertical displacement of the structure (unit: force per length).

**Wadam**

**5-62**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref DRY-ELEMENT**

...

DRY-ELEMENT stot dm

**PURPOSE:**

The command defines hydrodynamic properties for additional dry Morison elements.

Each section is given a reference number. Properties assigned to a given section may contain several subelements of equal length.

To define a section containing sub-elements of different lengths the user must enter the CHANGE command after specifying the hydrodynamic properties.

PARAMETERS: stot dm

Total number of sub-elements.

Distributed mass of element specified in mass per unit length.

**NOTES:**

The CHANGE command corresponding to this DEFINE command deviates in that there are two additional parameters, selno and sl:

CHANGE HYDRODYNAMIC-PROPERTY SECTION ref DRY-ELEMENT stot selno sl dm selno and sl are the sub-element number and sub-element length, correspondingly.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-63**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref POINT-MASS**

...

POINT-MASS dm

**PURPOSE:**

The command defines hydrodynamic properties for point mass elements. This will be additional to nodal masses on the Input Interface File.

PARAMETERS: dm Mass of element

**Wadam**

**5-64**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref PRESSURE-AREA-ELEMENT**

...

PRESSURE-AREA-ELEMENT

ALWAYS

WAVE-LENGTH-DEPENDENT dia x2 y2 z2

**PURPOSE:**

The command defines hydrodynamic properties for pressure area elements.

**PARAMETERS:**

ALWAYS

WAVE-LENGTH-DEPENDENT dia x2 y2 z2

Pressure area element always used.

Pressure area element is not used for dynamic loading when the wave length is less than or equal to the critical wave length.

Equivalent diameter.

The x-coordinate of the guiding point for the direction of the pressure force on the pressure area element in the input coordinate system.

The y-coordinate of the guiding point.

The z-coordinate of the guiding point.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**DEFINE HYDRODYNAMIC-PROPERTY SECTION ref TLP-MOORING-ELEMENT**

...

TLP-MOORING-ELEMENT len pre stiff xoff yoff

**PURPOSE:**

The command defines hydrodynamic properties for TLP mooring elements. See Figure 2.16.

PARAMETERS: len pre stiff xoff yoff

Length of the tethers.

Pre-tension in the tethers (unit: force).

Elastic stiffness of the tethers per length of the tether (unit: force per length).

Offset of the platform in x-direction in the input coordinate system.

Offset of the platform in y-direction in the input coordinate system.

**5-65**

**Wadam**

**5-66**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**DELETE**

DELETE

CORRESPONDANCE

ELEMENT

ENVIRONMENT

GENERAL

HYDRODYNAMIC-PROPERTY

END

...

**PURPOSE:**

The command deletes previously given input.

For explanation of the parameters of this command see the corresponding alternatives in the DEFINE command.

**SESAM**

**Program version 8.1**

**EXIT**

EXIT

**PURPOSE:**

The command causes exit from Prewad.

**22-JAN-2010**

**Wadam**

**5-67**

**Wadam**

**5-68**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**HELP**

HELP

SUPPORT

GENERAL-SYNTAX

SPECIAL-KEYS

STATUS-LIST

**PURPOSE:**

The command provides information on subjects.

**PARAMETERS:**

SUPPORT

GENERAL-SYNTAX Information on how to enter commands and text is provided. The information is printed in the print window (line-mode window on Unix).

SPECIAL-KEYS Information on some special keys is provided. The information is printed in the print window (line-mode window on Unix).

STATUS-LIST

The telephone and telefax numbers and the Internet address for requesting support is printed together with detailed information on the program version used. This information is of interest in connection with support requests. The information is printed in the print window (line-mode window on Unix).

If the program is used in line-mode (Unix only) the Status List is printed on the screen.

If the program is used in graphic input mode the Status program is started.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-69**

**PRINT**

ALL

CORRESPONDANCE

DATASET

ELEMENT

ENVIRONMENT

GENERAL

HYDRODYNAMIC-PROPERTY

OVERVIEW

END

...

...

**PURPOSE:**

The command prints selected information on the screen or to a file. The options are the same as for the

DEFINE command except for the three additional options ALL, DATASET and OVERVIEW that give status of the interactive run.

**PARAMETERS:**

ALL

DATASET

This gives a print of all the data existing on the Prewad data base.

This gives a list of available datasets on the Prewad data base and which one of these that is current.

OVERVIEW This gives a table containing a global overview of the different data available in the Prewad data base and a summary of the data defined.

**Wadam**

**5-70**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**PRINT CORRESPONDANCE**

...

CORRESPONDANCE elno

ALL

OVERVIEW

END

**PURPOSE:**

The command prints specified correspondence between elements in the Morison model and panels in the panel model.

PARAMETERS: elno External element number of 2D Morison, 3D Morison or pressure area element in the Morison model to which panels are linked.

ALL All specified correspondence will be printed.

OVERVIEW A summary of the specified correspondence will be printed.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-71**

**PRINT ELEMENT**

...

ELEMENT

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ALL

ANCHOR-ELEMENT

DRY-ELEMENT

OVERVIEW

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

END

**PURPOSE:**

The command prints additional Morison elements.

**PARAMETERS:**

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ALL

ANCHOR-ELEMENT

DRY-ELEMENT

OVERVIEW

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

Print 2D Morison elements.

Print 3D Morison elements.

All additional defined elements will be printed.

Print mooring elements.

Print dry Morison elements.

A summary of the additional defined elements will be printed.

Print point mass elements.

Print pressure area elements.

Print TLP mooring elements.

**Wadam**

**5-72**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**PRINT ENVIRONMENT**

...

ENVIRONMENT

ALL

CURRENT

FREQUENCY-HEADING-PAIRS

OVERVIEW

SURFACE-MODEL

WAVE-AMPLITUDE

WATER-DEPTH

WAVE-DIRECTION

WAVE-LENGTH

END

**PURPOSE:**

The command prints environmental data.

**PARAMETERS:**

ALL

CURRENT

FREQUENCY-HEADING-PAIRS

OVERVIEW

SURFACE-MODEL

WAVE-AMPLITUDE

WATER-DEPTH

WAVE-DIRECTION

WAVE-LENGTH

All specified environmental data will be printed.

The current profile will be printed.

Frequency heading pairs used in the computation of sum and difference forces will be printed

A summary of the environmental data will be printed.

Surface model defined will be printed.

All specified wave amplitudes will be printed.

Specified water depth will be printed.

All specified wave headings will be printed.

All specified wave lengths will be printed. If wave period or wave frequency is used as input this option will be WAVE-PE-

RIOD or WAVE-FREQUENCY respectively.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-73**

**PRINT GENERAL**

...

GENERAL

ALL

ANALYSIS-MODELS

CONSTANTS

EXECUTION-DIRECTIVES

GLOBAL-MATRICES

MULTI-BODY

CRITICAL-DAMPING

DAMPING-MATRIX

MASS-MATRIX

RESTORING-MATRIX

END

MODELS ibody PANEL-MODEL

END ibody

STRUCTURE-IDENTIFICATION

END

END

OFFBODY-POINTS

OVERVIEW

ROLL-DAMPING-MODEL

SECTIONAL-LOADS

TANK-PRESSURE

TEXT

END

**PURPOSE:**

The command prints user specified general parameters or matrices.

**PARAMETERS:**

ALL

ANALYSIS-MODELS

CONSTANTS

EXECUTION-DIRECTIVES

All specified general parameters will be printed.

All analysis models specified will be printed.

All constants specified will be printed.

All execution directives specified will be printed.

**Wadam**

**5-74**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

GLOBAL-MATRICES

CRITICAL-DAMPING

DAMPING-MATRIX

MASS-MATRIX

RESTORING-MATRIX

MULTI-BODY

MODELS ibody

PANEL-MODEL

STRUCTURE-IDENTIFICATION

OFFBODY-POINTS

OVERVIEW

ROLL-DAMPING-MODEL

SECTIONAL-LOADS

TANK-PRESSURE

TEXT

Specified global matrices will be printed.

The critical damping matrices will be printed.

All specified damping matrices will be printed.

All specified mass matrices will be printed.

The restoring matrix will be printed.

Data connected to multiple bodies will be printed.

Print specific analysis model connected to body.

Body identification of body number i.

Analysis model is a panel model.

Print structure dependent data for given body.

All off-body points will be printed.

A summary of the general parameters will be printed.

All data connected to a roll damping model based on strip theory will be printed.

All specified sections will be printed.

All specified tanks with given fluid density will be printed.

All text strings specified will be printed.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-75**

**PRINT HYDRODYNAMIC-PROPERTY**

...

HYDRODYNAMIC

ALL

CONNECT

OVERVIEW

SECTION

END ref

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ANCHOR-ELEMENT

DRY-ELEMENT

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

**PURPOSE:**

The command prints sectional dependent hydrodynamic data or connection between section numbers and

Morison elements.

**PARAMETERS:**

ALL

CONNECT

2D-MORISON-ELEMENT

3D-MORISON-ELEMENT

ANCHOR-ELEMENT

DRY-ELEMENT

POINT-MASS

PRESSURE-AREA-ELEMENT

TLP-MOORING-ELEMENT

OVERVIEW

All specified sectional hydrodynamic properties will be printed.

Connection between section reference numbers and elements will be printed.

Print all connected 2D Morison elements.

Print all connected 3D Morison elements.

Print all connected anchor elements.

Print all connected dry Morison elements.

Print all connected point mass elements.

Print all connected pressure area elements.

Print all connected TLP mooring elements.

A summary of the sectional hydrodynamic properties will be printed.

**Wadam**

**5-76**

SECTION ref

**22-JAN-2010**

Section properties will be printed.

Reference number of section.

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-77**

**READ**

READ prefix number

**PURPOSE:**

The command reads an old Wadam analysis control data file and sets the specified dataset number as current. The file name must be prefixWADAMdataset-number.FEM where dataset-number is an integer. If the dataset number already exists in the Prewad database then the Wadam analysis control data file must be renamed (use another dataset-number). Alternatively, exit Prewad and re-enter creating a new database.

PARAMETERS: prefix number

File name prefix.

Dataset number of the Wadam analysis control data file.

**Wadam**

**5-78**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**SET**

SET

COMMAND-INPUT-FILE com-name

DATASET number

MODEL-FILE

PRINT prefix

DESTINATION

FILE

FORMAT

PAGESIZE mod-name

NEW

OLD

FILE

SCREEN

LINEPRINTER

NAME

E

F

G

FILE

SCREEN print-name lines

END

END

**PURPOSE:**

The command sets different parameters for print, batch execution and changing of command file, database or dataset.

**PARAMETERS:**

COMMAND-INPUT-FILE com-name

DATASET number

MODEL-FILE

Open a command input file containing Prewad commands. The

# command is used to read a specified number of commands.

Name on the command input file. It must be different from the command log and database files of Prewad.

Switch to another dataset. The dataset number forms a part of the analysis control data file name.

New dataset number.

Close the current Prewad database (model) file and open another without exiting and re-entering the program. Identify the alternative database file by giving prefix and file name without extension (mod-name). Use NEW for a currently non-existing file (a new one will be opened) and OLD for a currently existing file.

**SESAM**

**Program version 8.1**

DESTINATION

FILE

FORMAT

PAGESIZE

**22-JAN-2010**

**Wadam**

**5-79**

The destination of the print may either be the SCREEN or a

FILE. Use SET PRINT FILE NAME to give the name of the print file.

Set the NAME of the print file (print-name). Do not include the extension. The full name of the print file will be printname.LIS.

Alternatively direct the print to an on-line printer (LINE-

PRINTER).

Set the format of numbers in the print. The letter refer to FOR-

TRAN E, F and G formats. F is the default format.

Set the page size of the print to FILE or SCREEN in terms of number of lines.

**Wadam**

**5-80**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**WRITE**

WRITE prefix number

**PURPOSE:**

The command writes a new Wadam analysis control data file with a user defined dataset number. This integer number need not be the same as the current dataset number. The file will be named prefixWADAMdataset-number.FEM where dataset-number is the dataset number (an integer).

**Note: Subject to proper setting when starting Prewad from Manager the Wadam analysis control data is automatically written.**

PARAMETERS: prefix number

File name prefix.

Dataset number of the Wadam analysis control data file.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**5-81**

**#**

# ncomnd

ALL

**PURPOSE:**

The command reads commands from the command input file. The command input file is opened by the command SET COMMAND-INPUT-FILE. The command input file can either be a log file from a previous run or a file prepared by a text editor.

The program will execute commands until either an end-of-file is detected, a ‘^Z’ is read from the file or the specified number of commands have been read.

Exit from this command is carried out by typing either ‘..’ or ‘$’.

PARAMETERS: ncomnd

ALL

Number of commands to be read from command input file. When the same command is repeated in the command input file the command lines will count as one command only.

Prewad will read and execute all commands available on the command input file.

**Wadam**

**5-82 22-JAN-2010**

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**A-1**

**APPENDIX A TUTORIAL EXAMPLES**

table of contents common for all Wadam print files is given for reference purposes.

**A 1 Motion Response of a Floating Box**

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Example 3.1.1 - A Floating Box 90m x 90m at draft of 40m

% Motions response analysis only

%

% Output from - T1.FEM - will be used in Wadam

% as the panel (sink-source) model

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Generate surfaces to form a 'box' 45 x 45 x 40 m, i.e. 1/4 of structure

%

GENERATE SURFACE A 1 2 1 5 1 2 1 5 1 2 1 4

CARTESIAN

0 0 0

45 0 0 END 0 45 0 END 0 0 40 END

%

% Remove unwanted sides of 'box' on x-z and y-z planes and the 'top'

%

DELETE GEOMETRY ( AS111 AT111 AU112 )

END

%

% Set the element type to be 4 node shell to represent each panel of

% the hydrodynamic model

%

SET ELEMENT-TYPE SURFACE ALL-SURFACES-INCLUDED SHELL-4NODES END

**Wadam**

**A-2**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

END

%

% Mesh all surfaces

%

MESH ALL

%

% Set the inside surface of the panel elements to be inside the box

%

SET INSIDE A* POINT AP112

END

END

%

% Define a loadcase 1 to be hydrodynamic pressure applied

% to the OUTSIDE surface of all elements, i.e. the

% wetted surface of the 1/4 floating box.

%

PROPERTY LOAD 1 HYDRO-PRESSURE ALL-SURFACES-INCLUDED OUTSIDE

OUTSIDE-SURFACE

END

END

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% E N D O F P R E F E M I N P U T

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**A-3**

**A 2 Motion Response of a Floating box Tethered to the Sea Bottom**

This section presents the following:

• Preframe input for creating a Morison model (also represented in the structural model) consisting of four nodes only

• input for creating a quarter of the structural model

• Presel input for assembling the structural model

**A 2.1 Preframe Input for the Morison Model (Tethers)**

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% MORISON MODEL FOR TETHERS

% SUPERELEMENT No. 2

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

NODE 1 45.0 45.0 .0

2 45.0 -45.0 .0

3 -45.0 -45.0 .0

4 -45.0 45.0 .0

..

%

BOUNDARY SUPER SUPER SUPER SUPER SUPER SUPER GLOBAL ALL

%

PROPERTY MATERIAL 1 SPRING-TO-GROUND STIFFNESS 6 1.E06 .0 .0 .0 .0 .0

1.E06 .0 .0 .0 .0 1.E06 .0 .0 .0 1.E06 .0 .0 1.E06 .0 1.E06

..

%

ELEMENT SPRING-TO-GROUND-(GSPR)

1 1 GLOBAL 1

2 2 GLOBAL 1

3 3 GLOBAL 1

4 4 GLOBAL 1

END

END

**A 2.2 Input for the Structural Model**

% EXAMPLE 3.1.2 - A FLOATING BOX 90M X 90M AT DRAFT OF 40M

% BOX TETHERED TO SEA-BED AT 4-CORNERS OF BOX

% MOTIONS RESPONSE ANALYSIS AND TRANSFER OF LOADS

% TO SHELL STRUCTURAL MODEL OF COMPLETE BOX

%

**Wadam**

**A-4**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

% STRUCTURAL MODEL FOR 1/4 OF BOX (WITH TOP)

% SUPERELEMENT NO. 3

%

% GENERATE SURFACES TO FORM A QUARTER OF THE 'BOX' 45 X 45 X 60 METRES

%

GENERATE SURFACE A 1 2 1 5 1 2 1 5 1 2 1 6

CARTESIAN

0 0 0

45 0 0 END 0 45 0 END 0 0 60 END

%

% REMOVE UNWANTED SIDES OF 'BOX' ON X-Z AND Y-Z PLANES

%

DELETE GEOMETRY ( AS111 AT111 )

END

%

% SET THE ELEMENT TYPE TO BE 4-NODE SHELL TO REPRESENT EACH PANEL OF

% THE HYDRODYNAMIC MODEL

%

SET ELEMENT-TYPE SURFACE ALL-SURFACES-INCLUDED SHELL-4NODES END

END

%

% MESH ALL SUFACES

%

MESH ALL

%

% SET THE INSIDE SURFACE OF THE PANEL ELEMENTS TO BE INSIDE THE BOX

% USING A POINT 'A' AT CENTRE OF BOX

%

DEFINE POINT A 0 0 30 END END

SET INSIDE A* POINT A

END

END

%

% DEFINE YOUNGS MODULUS = 2.1 X 10**11 N/M**2

% POISSONS RATIO = 0.3

% DENSITY OF STEEL = 7850. KG/M**3

% THICKNESS OF ALL SURFACES AS 0.1 M

%

PROPERTY MATERIAL ELAST ELASTIC .21E+12 .3 7850.0 .0 .0

END

THICKNESS ALL-SURFACES-INCLUDED 1.

END

END

CONNECT MATERIAL ELAST ALL-SURFACES-INCLUDED END

%

% DEFINE 'DUMMY' LOADCASE NO. 1 TO TELL WADAM THAT ALL SURFACES

% ARE TO BE LOADED WITH HYDRODYNAMIC PRESSURE (WHERE RELEVANT

% I.E. BELOW STILL WATER LINE)

%

PROPERTY LOAD 1 HYDRO-PRESSURE ALL-SURFACES-INCLUDED OUTSIDE

OUTSIDE-SURFACE

END

**SESAM**

**Program version 8.1**

**22-JAN-2010**

END

%

% DEFINE SUPERNODES ON PLANES OF SYMMETRY AND AT CORNER WHERE

% TETHER IS TO BE CONNECTED

%

PROPERTY BOUNDARY-CONDITION ( AI11& AJ11& AK121 AK211 )

SUPERNODE SUPERNODE SUPERNODE SUPERNODE SUPERNODE SUPERNODE

GLOBAL

AP221

SUPERNODE SUPERNODE SUPERNODE SUPERNODE SUPERNODE SUPERNODE

GLOBAL

END

END

**A 2.3 Presel Input for Assembling the Structural Model**

% ASSEMBLY OF MODEL OF TETHERED BOX

% Superelement NO. 21

%

READ

2

3

END

ASSEMBLY NEW 21

INCLUDE 3 NOPRINT-CHECK-INCLUDE

PERFORM-INCLUDE

3 ROTATE GLOBAL-AXIS Z-AXIS 90.0

NOPRINT-CHECK-INCLUDE

PERFORM-INCLUDE

3 ROTATE GLOBAL-AXIS Z-AXIS 180.0

NOPRINT-CHECK-INCLUDE

PERFORM-INCLUDE

3 ROTATE GLOBAL-AXIS Z-AXIS -90.0

NOPRINT-CHECK-INCLUDE

PERFORM-INCLUDE

2 NOPRINT-CHECK-INCLUDE

PERFORM-INCLUDE

END

**Wadam**

**A-5**

**Wadam**

**A-6**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**A 3 The Wadam Print File List of Contents**

The Wadam print file begins with a list of contents. This list of contents shows which data will be printed depending on the chosen print switch (see DEFINE GENERAL EXECUTION-DIRECTIVES PRINT-

SWITCH). The list of contents which is common for all analyses is presented below for reference purposes.

CONTENTS OF THE WADAM LISTING:

------------------------------

PRINTED RESULTS FOR THE VARIOUS PRINT ALTERNATIVES: ....... 0 1 2 3 4 5

1. CONTENTS AND LIMITATIONS

1.1 CONTENTS OF THE WADAM LISTING............................ X X X X X X

1.2 LIMITATIONS IN THIS VERSION OF WADAM..................... X X X X X X

2. DATA AND MODEL GENERATION

INPUT CARD DECK (IF BATCH CARD INPUT).................... X X X X X X

2.1 ANALYSIS CONTROL DATA INCLUDING

- EXECUTION DIRECTIVES................................... X X X X X X

- MODEL INFORMATION...................................... X X X X X X

- TOLERANCES AND CRITICAL WAVE LENGTH.................... X X X X X X

- CONSISTENCY OF ANALYSIS CONTROL DATA................... X X X X X X

2.2 DATA SPECIFYING THE MORISON MODEL INCLUDING.............. X X X X X X

- INPUT INTERFACE FILES.................................. X X X X X X

- DUMP OF INTERFACE FILES................................ X

- DUMP OF ELEMENT TRANSFORMATION MATRICES................ X X

2.3 DATA SPECIFYING THE PANEL MODEL INCLUDING................ X X X X X X

- INPUT INTERFACE FILES.................................. X X X X X X

- DUMP OF INTERFACE FILES................................ X

2.4 DATA SPECIFYING THE MASS INPUT INFORMATION INCLUDING..... X X X X X X

- INPUT INTERFACE FILES.................................. X X X X X X

- DUMP OF INTERFACE FILES................................ X

- DUMP OF MASS DATA...................................... X X X

2.5 DATA SPECIFYING THE RESTORING INPUT INFORMATION INCLUDING X X X X X X

- RESTORING DATA FOR EACH INDIVIDUAL INPUT MODEL......... X X X

2.6 CHECK OF DATA ON SAVE FILE............................... X X X X X X

2.7 SUMMARY OF MODEL PROPERTIES.............................. X X X X X X

2.8 ENVIRONMENTAL DATA....................................... X X X X X X

2.9 MORISON ELEMENT DATA..................................... X X X X X

2.10 MORISON NODE DATA........................................ X X X X X

2.11 PANEL DATA FOR BASIC PART................................ X X X X X

2.12 PANELS AND MORISON ELEMENTS CORRESPONDANCE DATA.......... X X X X X

2.13 DEFINITION OF SECTIONS FOR SECTIONAL LOADS .............. X X X X X X

2.14 DATACHECK SUMMARY........................................ X X X X X X

3. EXECUTION MESSAGES, SAVE/RESTART, VISCOUS FORCES

3.1 COMMENTS ON THE CALCULATION PERFORMANCE.................. X X X X X X

3.2 GENERATION OF SAVE FILE.................................. X X X X X X

3.3 DRAG FORCE LINEARISATION BY ITERATION.................... X X X X X X

3.4 VISCOUS ROLL DAMPING MODEL............................... X X X X X X

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**A-7**

4. PRESENTATION OF RESULTS

4.1 EXPLANATION OF THE RESULTS............................... X X X X X

4.2 STATIC RESULTS........................................... X X X X X

4.3 GLOBAL HYDRODYNAMIC RESULTS INCLUDING

- FREQUENCY INDEPENDENT MATRICES......................... X X X X X

- FREQUENCY DEPENDENT MATRICES........................... X X X X X

- EIGEN SOLUTIONS........................................ X X X X X

- RESULTS FROM INDIVIDUAL THEORIES....................... X X X X

- TOTAL EXCITING FORCES.................................. X X X X X

- MOTIONS................................................ X X X X X

- DRIFT FORCES........................................... X X X X X

- SUM OF DISTRIBUTED LOADS............................... X X X X X

4.4 LOAD DISTRIBUTION ON THE MORISON MODEL................... X X X X

4.5 PRESSURE DISTRIBUTION ON THE PANEL MODEL................. X X X X

4.6 OFFBODY CALCULATIONS INCLUDING

- FLUID PRESSURE AT SPECIFIED POINTS..................... X X X X X X

- FLUID VELOCITIES AT SPECIFIED POINTS................... X X X X X X

4.7 SECTIONAL LOADS ON THE PANEL MODEL....................... X X X X

4.8 SECTIONAL LOADS ON THE MORISON MODEL..................... X X X X

4.8b SECTIONAL LOADS ON THE COMPOSITE MODEL................... X X X X

4.9 GLOBAL SECOND-ORDER FORCES............................... X X X X X X

4.10 SECOND-ORDER PANEL PRESSURE DISTRIBUTION................. X X X X X X

5. TRANSFER OF RESULTS FOR FURTHER ANALYSIS AND PRESENTATION

5.1 GENERATION OF LOADS INTERFACE FILES INCLUDING

- INPUT INTERFACE FILES.................................. X X X X X X

- SUBELEMENT LOADS TRANSFERRED TO LOADS INTERFACE FILES.. X X X

- LOADCASE OVERVIEW...................................... X X X X X X

- MATCHING INFORMATION FOR LOADS TO A SHELL/SOLID MODEL.. X X X X

- SUM OF LOADS WRITTEN TO THE LOADS INTERFACE FILE....... X X X X X X

- SUM OF CALCULATED LOADS ON THE PANEL MODEL............. X X X X X X

5.2 GENERATION OF GLOBAL RESPONSE INTERFACE FILE............. X X X X X X

5.3 GENERATION OF GLOBAL RESPONSE FILE (NV1473).............. X X X X X X

SUMMARY OF TIMING INFORMATION............................ X X X X X X

SUMMARY OF FILE USAGE.................................... X X X X X X

**Wadam**

**A-8 22-JAN-2010**

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**REFERENCES-1**

**REFERENCES**

1 Newman, J.N.

"Marine Hydrodynamics"

The MIT Press, 1977

2 WAMIT Users Manual, Version 5.3S

Department of Ocean Engineering, Massachusetts Institute of Technology

3 C.-H. Lee, J.N. Newman, M.-H. Kim & D.K.P Yue:

"The computation of second-order wave loads"

Published in the OMAE ’91 conference proceedings, Stavanger, Norway 1991

4 The Implementation of Second-order Force Computation in Wadam,

DNV Sesam Report No.: 93-7081, Rev. 0, Oct. 1993

5 M. H. Patel and E.J. Lynch:

"Coupled dynamics of tension buoyant platforms and mooring tethers"

Eng. Struct., Vol.5, October 1983

6 N. Tanaka:

"A Study on the Bilge Keel, Part 4. On the Eddy-Making Resistance to the Rolling of a Ship Hull"

Japan Soc. of Naval Arch., Vol. 109, 1960

7 H. Kato:

"Effect of Bilge Keels on the Rolling of Ships"

Memories of the defence Academy, Japan, Vol. IV, No. 3, pp. 369-384, 1966

8 Sarpkaya, T. and Isaacson M:

"Mechanics of Wave Forces on Offshore Structures"

Van Nostrand Reinhold Company, New York, 1981

9 Finne, S., Grue j. and Nestegård, A.:

"Prediction of the complete second-order Wave Drift Damping force for offshore structures"

Proceedings, ISOPE 2000, Seattle.

**Wadam**

**REFERENCES-2 22-JAN-2010**

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**B-1**

**APPENDIX B THEORY**

**B 1 Hydrostatic Forces**

**B 1.1**

**Hydrostatic Coefficients**

*Wadam calculates the non-zero coefficients C ij*

in the hydrostatic restoring matrix as follows:

*C*

33

= ρ*gS*

*C*

43

= ρ*gS*

2

*= C*

34

*C*

53

= – ρ*gS*

1

*= C*

35

*C*

44

=

22

*+ V w z*

*B*

*C*

54

= – ρ*gS*

12

*= C*

45

–

*G*

*C*

46

*= – ρ gV w x*

*B*

*+ mgx*

*G*

*C*

55

=

11

*+ V w z b*

*C*

56

*= – ρ gV w y*

*B*

*+ mgy*

*G*

*G*

Here:

*( x*

*B y*

*B z*

*B*

) is the centre of buoyancy

*( x*

*G*

*, y*

*G*

*, z*

*G*

) is the centre of gravity

ρ is the density of the fluid

**Wadam**

**B-2**

**SESAM**

**Program version 8.1**

*22-JAN-2010 g*

*V w*

*S*

S i is the acceleration of gravity is the volume of the wetted part of the body

S ij is the water plane area

= ∫

*S*

0 x i d S i = 1 2 …

= ∫

*S*

0 x i x j d S = 1 2 …

*S*

*0*

refers to the body in a static condition.

**B 2 Morison Element Formulations**

**B 2.1**

**The Anchor Element Formulation**

*The mooring stiffness matrices K m*

*K m*

for each anchor element in a Morison model are described below. The

* matrices are accumulated into the global restoring matrix for the rigid body equation of motion. Since the K m*

matrices are established directly in the motion reference coordinate system, no transformations are needed in the accumulation process.

**SESAM**

**Program version 8.1**

**22-JAN-2010**

*The non-zero terms in the matrix K m*

* are defined as follows: k*

11

= S h cos

2

*α x k*

21

*= S h cos α x sin α x k*

22

= S h sin

*2 α x k*

33

*= S v k*

41

*= k*

*31 21 z k*

51

*= k*

*11 k*

61

*= k*

21

*31 x*

*11 y k*

42

*= k*

32

–

*22 z k*

52

*= k*

21

–

*32 x k*

62

*= k*

*22 21 y k*

43

*= k*

33

–

*32 z k*

53

*= k*

31

–

*33 x where k*

63

*= k*

*32 k*

44

*= k*

*43 k*

54

*= k*

*14 k*

64

*= k*

*24 k*

55

*= k*

*51 k*

65

*= k*

*52 k*

66

*= k*

62

*31 y*

*42 z + P z*

*43 x – P x y*

*41 y – P x z*

*53 x + P x*

*+ z z*

43 y – P y z ,

*61 y + P y*

*+ x x y y*

,

*, k*

45

*= k*

*14 k*

46

*= k*

24

*43 x – P y z*

*41 y – P z x k*

56

*= k*

*52 43 y – P z y*

**Wadam**

**B-3**

**Wadam**

**B-4**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

*S h*

*S v*

*α x*

(*x*,* y*, *z*) is the horizontal spring constant is the vertical spring constant

are the coordinates of the fairlead relative to the motion reference point

*P x*

P y is the x-component of the pre-tension is the y-component of the pre-tension

P z is the z-component of the pre-tension

*The matrix is symmetric ( k ij*

* = k ji*

) except for the terms *k*

54

, *k*

64

and *k*

65

.

*Having solved the equation of motion x g vector f g*

represents the global motion of the rigid body system. The force

* for each fairlead node, described in the result reference coordinate system, is then computed as f g*

*= – K m x g*

(B.1)

B.1

**Figure B.1 Anchor element definitions**

**B 2.2**

**The TLP Mooring Element Formulation**

*The mooring stiffness matrices K m*

* for each TLP element in a Morison model are accumulated into the global restoring matrix for the rigid body equation of motion. The K m*

matrices are established directly in the

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

B-5 motion reference coordinate system and hence no transformations are needed in the accumulation process.

*The non-zero terms in the matrix K m*

* are defined as follows: k*

11

= λcos 2

+ ---sin

*2 α k*

21

=

⎛

⎝

*L*

⎠

*⎞ cos α cos β = k*

*12 k*

22

= λcos 2

+ ---sin

*2 β k*

31

=

⎛

⎝

*L*

⎠

*⎞ cos α cos γ = k*

*13 k*

32

=

⎛

⎝

*L*

⎠

*⎞ cos β cos γ = k*

*23 k*

33

*= λcos 2 2 γ k*

41

*= k*

*31 y*

2

*– k*

*21 z*

2

*= k*

*14 k*

51

*= k*

*11 z*

2

*– k*

*31 x*

2

*= k*

15

**Wadam**

*B-6 22-JAN-2010 k*

61

*= k*

*21 x*

2

*– k*

*11 y*

2

*= k*

*16 k*

42

*= k*

*32 y*

2

*– k*

*22 z*

2

*= k*

*24 k*

52

*= k*

*21 z*

2

*– k*

*32 x*

2

*= k*

*25 k*

62

*= k*

*22 x*

2

*– k*

*21 y*

2

*= k*

*26 k*

43

*= k*

*33 y*

2

*– k*

*32 z*

2

*= k*

*34 k*

53

*= k*

*31 z*

2

*– k*

*33 x*

2

*= k*

*35 k*

63

*= k*

*32 x*

2

*– k*

*31 y*

2

*= k*

*36 k*

44

*= k*

*33 y*

2

2

– 2*k*

*32 y*

*2 z*

2

*+ k*

*22 z*

2

*2 k*

54

*= k*

*31 y*

*2 z*

2

*– k*

*21 z*

2

2

*– k*

*33 y*

*2 x*

2

*+ k*

*32 x*

*2 z*

2

*– T x y k*

45

*= k*

*31 y*

*2 z*

2

*– k*

*21 z*

2

2

*– k*

*33 y*

*2 x*

2

*+ k*

*32 x*

*2 z*

2

*– T y x k*

64

*= k*

*32 x*

*2 y*

2

*– k*

*31 y*

2

2

*– k*

*22 x*

*2 z*

2

*+ k*

*21 y*

*2 z*

2

*– T x z k*

46

*= k*

*32 x*

*2 y*

2

*– k*

*31 y*

2

2

*– k*

*22 x*

*2 z*

2

*+ k*

*21 y*

*2 z*

2

*– T z x k*

55

*= k*

*11 z*

2

2

– 2*k*

*31 x*

*2 z*

2

*+ k*

*33 x*

2

2

*+ T x*

*+ z z k*

65

*= – k*

*11 y*

*2 z*

2

*+ k*

*21 x*

*2 z*

2

*+ k*

*13 x*

*2 y*

2

*– k*

*23 x*

2

2

*– T y z k*

56

*= – k*

*11 y*

*2 z*

2

*+ k*

*21 x*

*2 z*

2

*+ k*

*13 x*

*2 y*

2

*– k*

*23 x*

2

2

*– T z y where k*

66

*= k*

*11 y*

2

2

– 2*k*

*21 x*

*2 y*

2

*+ k*

*22 x*

2

2

*+ T y*

*+ x x*

**SESAM**

**Program version 8.1**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

**B-7**

λ

T is elastic stiffness (force per length) is the constant pre-tension

L is the specified tether length at a given offset position

*T x*

*T y*

T z is the x-component of the pre-tension is the y-component of the pre-tension is the z-component of the pre-tension

*The matrix is symmetric ( k ij*

* = k ji*

) except for the terms *k*

54

, *k*

64

and *k*

65

.

The direction cosines: cos α, cosβ and cosγ are defined as follows: cos α =

2

–

*L x*

1 cos β =

2

–

*L y*

1 cos γ =

2

–

*L z*

1

*The separate K m*

matrices for each TLP node are described with respect to the (*x*

1

, *y*

1

coordinates at the TLP node and the sea-bed, see Figure B.2.

, *z*

1

) and (*x*

2

, *y*

2

, *z*

2

)

B.2

**Figure B.2 TLP element coordinates**

*Having solved the equation of motion, x g vector f g*

represents the global motion of the rigid body system. The force

* for each TLP node, described in the result reference coordinate system, is then computed as f g*

*= – K m x g*

(B.2)

**Wadam**

**B-8**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**B 3 Calculation Methods**

**B 3.1**

**Linearisation of Roll Restoring**

The linear roll restoring moment is based on the initial metacentric height (GM) calculated from the model geometry and specified mass properties and is only valid at small heeling angles. From hydrostatics calculations the GZ-curve is normally known also for large heeling angles. This information may be utilised in

Wadam by specifying the appropriate GZ-curve as input to Prewad. The restoring roll moment at an angle

η

4

= φ may be written as

*M r*

φ = ( ) where *V* is the submerged volume of the hull and *GZ* φ ing the ship through an angle η

4

from 0 to φ may be written as:

*W r*

= ∫

φ

0

*M r*

= ∫

φ

0

*= ρ gVA r*

*φ where A r*

is the area under the righting arm curve as shown in Figure B.3.

B.3

(φ)

**Figure B.3 Linearised Roll Restoring Moment from the GZ-curve**

At small angles the restoring work may be expanded in a Taylor series giving

*W ri*

=

1

2

*ρ gVGZ i*

*φ = ρ gVA ri*

**SESAM**

**Program version 8.1**

**22-JAN-2010**

**Wadam**

*B-9 where GZ i*

, the initial moment arm, is related to *GM*

*T*

, the initial transverse metacentric height, as follows:

*GZ i*

*= GM*

*T*

⋅ ηˆ

4

At large angles the linearised roll restoring coefficient is defined as:

*C*

44

= ⋅

*T where the factor f is defined as the ratio between the area A r*

* under the GZ-curve from 0 to φ and the area A ri below a straight line from 0 to φ with slope equal to GZ i*

⁄ ηˆ

4

*= GM*

*T*

*: f = r*

*W ri*

*= r*

*A ri*

*= r*

*GZ i*

ηˆ

4

*= r*

*GM*

*T*

ηˆ

2

4

**B 3.2**

**Calculation of Line Loads**

The line load on a beam finite element is represented as a sequence of constant line load segments. Each segment will automatically correspond to a sub-element of a 2D Morison element.

The load evaluated at the centre of gravity of each Morison sub-element is represented as constant load intensities with x, y and z force components acting over the line segments. This is so both for hydrostatic and hydrodynamic loads. The line loads produced by Wadam do not include any eccentricities which may

ments.

B.4

**Figure B.4 Line loads in Wadam**

**B 3.3**

**The Mapping of Loads from Panel Models to Finite Element Models**

The hydrodynamic pressure distribution on a panel model is described as a piece wise constant pressure variation. Each panel is represented with a constant pressure value which is calculated at its centroid. The mapping of loads from panels to finite elements is based on a minimal distance criteria between the centroids of panels and structural finite elements. That is, each wetted side of a finite element will receive the constant pressure of the closest panel while satisfying user specified distance and out-of-plane criteria.

**Wadam**

**B-10**

**SESAM**

**Program version 8.1**

**22-JAN-2010**

The mapping algorithm may be described as: For each element assign normal pressure from the closest

panel (centroid to centroid) provided that Equation (B.3) and Equation (B.3) are satisfied.

points C p

and C fe

represent the panel and finite element centroids respectively. The shaded rectangular elements represent finite elements receiving pressure loads.

B.5

**Figure B.5 The mapping of loads from panels to finite elements**

The functionality of the user specified tolerance parameters DISTOL and ANGTOL, which controls the mapping between panels and finite elements may be described as follows.

The panel with its centroid closest to the finite element centroid is a candidate as the source for pressure transfer to a finite element if the formula

Σ

*A panel*

(B.3) is satisfied. Here *A*

Σ

is the sum of the four shaded triangles S i

, i=1,2,3,4, shown in Figure B.6 (a) and *A*

*panel*

teria

(B.4) is accepted.

φ is defined by Figure B.6 (b). Both φ and ANGTOL are given in degrees.

**SESAM**

**Program version 8.1**

B.6

**22-JAN-2010**

**Wadam**

**B-11**

**Figure B.6 The DISTOL and ANGTOL functionality**

Wadam reports information from the actual mapping on the form (NDIST, NANG, NOPP) where NDIST

φ is replaced by

φ + 180. NOPP is indicating that normal vectors of the panel and finite element are pointing in the opposite direction.

The number of finite elements in the structural model with no matching panel is reported by Wadam.

**B 3.4**

**Calculation of Tank Pressures**

The loads are calculated by applying a hydrostatic pressure distribution in the accelerated reference frame fixed with respect to the tank. The pressure load is divided in a constant and an oscillating part and represented by separate load cases. The pressure gradient is given by

∇*p* = ( )

(B.5) where **g** is the acceleration due to gravity, **a** is the complex acceleration of the mid-point of the tank and ρ is the mass density of water. The gravity vector described in a coordinate system oscillating with the body, has a constant and an oscillating part. Accordingly, the pressure gradient described in the body-fixed coordinate system has a constant part, ρ**g**, and an oscillating or fluctuating part:

*∇ p f*

*= f*

*– a ) (B.6) where g f*

is the fluctuating part of gravity.

The mid-point is taken as the centroid of the extreme coordinates of the tank. For a cubic tank the extreme coordinates are the corners of the tank. If the tank is spherical, the extreme coordinates will be the corners in a cube circumscribing the sphere. In both these cases the centroid of the corner points will coincide with the centroid of the tank, but generally, for arbitrary geometrical shapes, it is an approximation.

The oscillating contribution to the total pressure is represented as a complex load case. The zero-level for the pressure is the extreme-point of the tank where the real part of the total pressure has its minimum value.

This is actually approximately correct only for the phase equal to zero and can be a quite crude approxima-

**Wadam**

**B-12**

**SESAM**

**Program version 8.1**

22-JAN-2010 tion for other phases. If the pressure loads are applied for other phases, the user should therefore find the minimum pressure value and subtract this from all the pressure loads on the tank for the given phase. That way a correct reference level (zero-level) for the pressure will be obtained.

The pressure loads should preserve load balance. The total force from the fluid on the tank is given by

F =

∫ p **n ***S*

*S d*

(B.7) where **n** is the unit normal vector pointing out of the tank and *S* is the surface inside the tank. By Gauss theorem we then have

F =

∫

*V*

(B.8) where *V* is the space inside the tank filled with fluid. Substituting for ∇*p* this gives

*F = m f*

*( ) (B.9) m f*

is the mass of the fluid in the tank. Similarly, the total moment **M** on the tank can be seen to be given by

*M = x f*

**× F**

*(B.10) where x f*

is the position of the centroid of the tank. This shows that the force and moment from the fluid is balanced by the gravity force on the fluid and the inertia force and moments of the fluid. This is independent of the reference level of the pressure. Provided an exact load integration and an exact centroid calculation, the load balance will then be exact if the mass of the fluid is placed in the centroid of the tank in the mass model.

**B 3.5**

**Global drag-coefficient for roll**

The quadratic roll-damping coefficient may be found in model-tests for given ship-hull types, independent of sea-state .

For the actual sea-state in which the ship is to be analysed, stochastic linearization of the quadratic damping may be performed. The quadratic drag in the roll-motion gives a contribution to the moment about the x-axis on the form:

*F*

44

*= – B*

2

44

η·

4

η·

4 (B.11) where *B*

( )

44

)

4

.is the velocity in roll. Substituting *B*

2

44 linearized damping-coefficient *B*

( )

44

)

, the error random process due to linearization is:

η·

4

* with a e t = B*

44

η

4 44

η·

4

The requirement that the expectation-value of the squared error has a minimum is

(B.12)

**SESAM**

**Program version 8.1**

*B*

1

44

=

2

44

E ( η·

4

*E*

2 2

4

3

)

**22-JAN-2010**

**Wadam**

**B-13**

(B.13)

Obviously:

E η·

2

4

= σ

η

·

4

4

is normally distributed, the half-normal distribution for η·

4

gives

E ( η·

4

3

) = ------σ

3

η

·

4

(B.14)

(B.15) where σ

η

·

4

4

. Substituting the two expectation values above in the formula for *B*

1

44

gives the well-known relation for stochastic linearization of a quadratic drag-term:

*B*

44

=

*B*

( )

44

σ

2

η

·

4

8

σ

3

η

·

4 = ------σ

η

·

4

*B*

44

(B.16)

The equation of motion η

1

, …η

6

, with the stochastically linearized roll-drag included, may be written:

*M ij*

*η· j*

*+ b ij*

*η· j*

*+ B*

1

44

*δ ij*

*η· j*

*+ c ij*

*η j*

*= X i*

(B.17)

*Here, M ij*

* is the sum of the body-mass matrix and added mass matrix. b ij*

* is the potential damping and c ij*

* is the restoring. X i*

* is the excitation-force. An initial estimate of η j*

for all wave-frequancies is made, giving a corresponding estimate of the standard-deviation and thereby *B*

( )

44

)

*. Then an iteration process is run on η j*

until a reasonable agreement between the estimate of σ

η

·

4

from the previous and next calculation of motion is obtained. The motion will then be correct in the least square sense.

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### Key Features

- Hydrostatic loads calculation
- Global response analysis
- Detailed loads calculation
- Morison’s equation support
- Potential theory support
- Load transfer to FE model
- Time domain results
- Second order analysis
- Multi-body modelling
- Save/restart system

### Related manuals

### Frequently Answers and Questions

###### What is Wadam?

###### What analysis capabilities does Wadam offer?

###### What calculation methods does Wadam use?

###### What are the limitations of Wadam?

###### How can I get support for Wadam?

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#### Table of contents

- 11 1.1 Wadam — Wave Analysis by Diffraction and Morison Theory
- 12 1.2 Wadam in the SESAM System
- 13 Figure 1.1 SESAM overview
- 14 1.3 How to read this Manual
- 14 1.4 Terminology and Notation
- 15 1.5 Status List
- 15 1.6 Wadam Extensions
- 17 2.1 Definition of Model Types in Wadam
- 17 Figure 2.1 Overview of model types in Wadam
- 18 Figure 2.2 Hydro model combinations
- 18 Table 2.1 Overview of SESAM element types interpreted in the various Wadam models
- 19 2.1.1 The Coordinate Systems
- 20 Figure 2.3 2D representation of a TLP hull with input coordinate system below the swl, ZLOC=-h
- 21 Figure 2.4 2D representation of a semi-submersible with centre of gravity along the global z-axis, ZLOC=-h
- 21 2.1.2 The Panel Model
- 21 Figure 2.5 Symmetry plane definitions
- 22 Figure 2.6 Panel adjustments at the still water level
- 23 Figure 2.7 The basic part of a TLP panel model
- 23 2.1.3 The Morison Model
- 24 Figure 2.8 2 node beam element model of a semi-submersible platform
- 25 Figure 2.9 Morison model representation of a semi-submersible platform with 2D Morison elements and pressure area elements
- 26 Figure 2.10 Equivalent diameters for non-circular cross sections
- 27 Figure 2.11 The sub-element division of 2D Morison elements
- 28 Figure 2.12 Local coordinate system of 2D and 3D Morison elements
- 29 Figure 2.13 The pressure area element definition
- 29 Figure 2.14 Application areas for the pressure area element
- 31 Figure 2.15 Mooring element definitions
- 32 Figure 2.16 The TLP mooring element
- 32 2.1.4 The Dual Model
- 32 Figure 2.17 A dual model with both a panel model and a Morison model representing a structure
- 33 Figure 2.18 The correspondence between panels and a 2D Morison element
- 34 Figure 2.19 Dual model with a two-plane symmetric panel model
- 34 2.1.5 The Composite Model
- 35 Figure 2.20 Example of a composite model with a panel model and a non-overlapping Morison model
- 35 2.1.6 Single Super element Composite model
- 35 2.1.7 Multi-Body Modelling
- 36 Figure 2.21 The hierarchical coordinate system definition
- 36 2.1.8 Mass Modelling
- 37 2.1.9 Structural Modelling
- 39 Figure 2.22 Idealised view of hydro pressures on structural element sides
- 39 2.1.10 Free Surface Modelling
- 39 Figure 2.23 Free surface mesh
- 40 2.1.11 Load Case Numbering and Load Case Combinations
- 41 Example 2.1 Load case numbering for a single superelement model
- 41 Table 2.2 Load case numbering for a single superelement structural models
- 42 Example 2.2 Load case numbering for a model assembled in a superelement hierarchy
- 42 Figure 2.24 Two-level superelement hierarchy with occurrence 1 and 2 of superelement 10 included in superelement 100
- 42 Table 2.3 Load case numbering for a model assembled in a superelement hierarchy
- 43 2.2 Global Response Analysis
- 43 2.2.1 General
- 43 2.2.2 Computation of Wave Loads
- 44 2.2.3 The Global Response Results
- 44 2.3 The Calculation of Detailed Loads on a Structural Model
- 44 2.3.1 General
- 45 2.3.2 The Structural Load Types
- 45 2.3.3 Deterministic Loads
- 45 2.3.4 Detailed Loads Transfer to a Model with Shell or Solid Elements
- 46 2.3.5 Detailed Loads Transfer to a Model with Beam Elements
- 46 2.4 Environmental Description
- 46 2.4.1 Surface Waves
- 47 Figure 2.25 Surface wave definitions
- 48 2.4.2 Current Profiles
- 48 Figure 2.26 Current profile definition
- 49 2.4.3 Water Depth
- 49 2.5 Results Types Reported from Wadam
- 49 2.5.1 Units
- 50 2.5.2 Result Reference Point
- 50 2.5.3 Dimensioning of Results
- 50 Table 2.4 Dimensionalising factors for matrices
- 51 Table 2.5 Dimensionalising factors for results
- 51 2.5.4 Transfer Functions and Phase Definitions
- 52 Figure 2.27 Definition of phase between the response and the incident wave
- 52 2.5.5 Hydrostatic Restoring Results
- 53 2.5.6 Global Mass Matrix
- 54 2.5.7 Added Mass Matrix
- 54 2.5.8 Damping Matrix
- 54 2.5.9 Exciting Forces and Moments
- 55 2.5.10 Rigid Body Motion
- 55 2.5.11 Second Order Mean Drift Forces
- 55 2.5.12 Second Order Sum and Difference Frequency Results
- 55 2.5.13 Fluid Kinematics
- 56 2.5.14 Wave Drift Damping
- 56 2.5.15 Distributed Hydrostatic Loads
- 57 2.5.16 Distributed Hydrodynamic Loads
- 58 2.5.17 Load Sum Reports
- 59 2.5.18 Sectional Loads
- 59 Figure 2.28 Sectional loads at a plane through x=0
- 60 2.5.19 Roll Damping Coefficients
- 61 2.5.20 Global drag-coefficient for roll-damping
- 62 2.6 Calculation Methods
- 62 2.6.1 Calculation of Wave Loads from Potential Theory
- 63 2.6.2 Calculation of Wave Loads from Second Order Potential Theory
- 63 2.6.3 Removal of Irregular Frequencies
- 63 2.6.4 Morison’s Equation
- 65 2.6.5 The Equation of Motion
- 66 2.6.6 Calculation of Tank Pressures
- 66 2.6.7 Pressure Loads up to Free Surface
- 67 Figure 2.29 Constant extrapolation of panel pressures to the free surface
- 67 2.6.8 Reduced pressure up to the free surface
- 68 2.7 The Save-Restart System
- 70 3.1 Simple Examples
- 70 3.1.1 Motion Response of Floating Box
- 70 Figure 3.1 Prefem plot of the panel model representing a quarter of the box. Notice the arrows showing the direction of the HYDRO-PRESSURE load.
- 71 Figure 3.2 HydroD wizard for the floating box example.
- 71 Figure 3.3 Display of HYDRO-PRESSURE load in HydroD.
- 72 Figure 3.4 Starting Prewad and Wadam from SESAM Manager.
- 74 3.1.2 Motion Response of Floating Box Tethered to the Sea-Bed
- 75 Figure 3.5 Structural model assembly of simple box model tethered to the sea-bed
- 78 Figure 3.6 HydroD wizard for the tethered box example (left) and the TLP example in Section 3.2 (right).
- 78 3.2 Engineering Application Examples
- 80 3.2.1 TLP Global Response Analysis
- 81 Figure 3.7 TLP geometry
- 81 Figure 3.8 Basic part of the TLP panel model from two view points
- 83 Figure 3.9 Morison model
- 84 3.2.2 TLP Load Transfer to a Shell Structural Model
- 85 Figure 3.10 The sub-sea part of the structural shell model
- 86 Figure 3.11 The geometry assembly for the structural shell model
- 88 3.2.3 TLP Load Transfer to Beam Element Model
- 90 Figure 3.12 (a) Extra superelement for connection of Morison model to the rest of the structural model and (b) Example of use of the extra superelement
- 90 Figure 3.13 Geometry assembly for the TLP structural model
- 92 3.2.4 Global Response of a Semi-Submersible using Dual Model
- 93 Figure 3.14 Geometry of the semi-submersible
- 94 Figure 3.15 Quarter of a double symmetric panel model for the semi-submersible
- 95 Figure 3.16 Beam elements of the Morison model
- 96 3.2.5 Global Response for a Ship
- 97 Figure 3.17 Total panel model of the ship including reflected part
- 98 Figure 3.18 Mass model for the ship
- 101 4.1 Program Environment
- 101 Figure 4.1 HydroD (or Prewad) -Wadam communication
- 102 Figure 4.2 The HydroD GUI and the command for executing Wadam.
- 103 4.1.1 Starting Prewad from Manager
- 103 4.1.2 Reading a Command Input File into Prewad and Running Wadam
- 104 Figure 4.3 Manager and the Hydro Modelling window with Command input file specification
- 104 4.1.3 The Input Files
- 105 4.1.4 Output Files
- 105 4.1.5 The Save-Restart File
- 106 4.2 Program Requirements
- 106 4.3 Program Limitations
- 106 4.4 Warnings and Error Messages
- 110 CHANGE
- 111 DEFINE
- 112 DEFINE CORRESPONDANCE
- 113 DEFINE ELEMENT
- 115 DEFINE ENVIRONMENT
- 118 DEFINE ENVIRONMENT FREQUENCY-HEADING-PAIRS
- 119 DEFINE ENVIRONMENT LINEARISING-WAVE-HEIGHT
- 120 DEFINE ENVIRONMENT SURFACE-MODEL
- 122 DEFINE ENVIRONMENT WAVE-SPECTRUM
- 123 DEFINE GENERAL
- 124 DEFINE GENERAL ANALYSIS-MODELS
- 126 DEFINE GENERAL CONSTANTS
- 127 DEFINE GENERAL EXECUTION-DIRECTIVES
- 128 DEFINE GENERAL EXECUTION-DIRECTIVES ANALYSIS-TYPE
- 129 DEFINE GENERAL EXECUTION-DIRECTIVES DETERMINISTIC-MORISON
- 130 DEFINE GENERAL EXECUTION-DIRECTIVES DRAG-LINEARISATION
- 131 DEFINE GENERAL EXECUTION-DIRECTIVES DRIFT-FORCES
- 132 DEFINE GENERAL EXECUTION-DIRECTIVES FIXED-FLOATING
- 133 DEFINE GENERAL EXECUTION-DIRECTIVES HORISONTAL-DRIFT
- 134 DEFINE GENERAL EXECUTION-DIRECTIVES MORISON-EQUATION
- 135 DEFINE GENERAL EXECUTION-DIRECTIVES OUTPUT-FORMAT
- 136 DEFINE GENERAL EXECUTION-DIRECTIVES POTENTIAL-THEORY
- 138 DEFINE GENERAL EXECUTION-DIRECTIVES PRINT-SWITCH
- 139 DEFINE GENERAL EXECUTION-DIRECTIVES RESULT-FILES
- 143 DEFINE GENERAL EXECUTION-DIRECTIVES SAVE-RESTART
- 144 DEFINE GENERAL EXECUTION-DIRECTIVES SECOND-ORDER-RESULTS
- 146 DEFINE GENERAL EXECUTION-DIRECTIVES TOLERANCES
- 147 DEFINE GENERAL EXECUTION-DIRECTIVES WAVE-DRIFT-DAMPING
- 148 DEFINE GENERAL GLOBAL-MATRICES
- 151 DEFINE GENERAL MULTI-BODY
- 152 DEFINE GENERAL MULTI-BODY MODELS
- 154 DEFINE GENERAL MULTI-BODY STRUCTURE-IDENTIFICATION
- 155 DEFINE GENERAL OFFBODY-POINTS
- 156 DEFINE GENERAL PANEL-PRESSURE
- 157 DEFINE GENERAL ROLL-DAMPING-MODEL
- 161 DEFINE GENERAL SECTIONAL-LOADS
- 162 DEFINE GENERAL TANK-PRESSURE
- 163 DEFINE GENERAL TEXT
- 164 DEFINE HYDRODYNAMIC-PROPERTY
- 165 DEFINE HYDRODYNAMIC-PROPERTY CONNECT
- 166 DEFINE HYDRODYNAMIC-PROPERTY SECTION
- 167 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 2D-MORISON-ELEMENT
- 168 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref 3D-MORISON-ELEMENT
- 169 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref ANCHOR-ELEMENT
- 170 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref DRY-ELEMENT
- 171 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref POINT-MASS
- 172 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref PRESSURE-AREA-ELEMENT
- 173 DEFINE HYDRODYNAMIC-PROPERTY SECTION ref TLP-MOORING-ELEMENT
- 174 DELETE
- 175 EXIT
- 176 HELP
- 177 PRINT
- 178 PRINT CORRESPONDANCE
- 179 PRINT ELEMENT
- 180 PRINT ENVIRONMENT
- 181 PRINT GENERAL
- 183 PRINT HYDRODYNAMIC-PROPERTY
- 185 READ
- 186 SET
- 188 WRITE
- 189 #
- 191 A 1 Motion Response of a Floating Box
- 193 A 2 Motion Response of a Floating box Tethered to the Sea Bottom
- 193 A 2.1 Preframe Input for the Morison Model (Tethers)
- 193 A 2.2 Input for the Structural Model
- 195 A 2.3 Presel Input for Assembling the Structural Model
- 196 A 3 The Wadam Print File List of Contents
- 201 B 1 Hydrostatic Forces
- 201 B 1.1 Hydrostatic Coefficients
- 202 B 2 Morison Element Formulations
- 202 B 2.1 The Anchor Element Formulation
- 204 Figure B.1 Anchor element definitions
- 204 B 2.2 The TLP Mooring Element Formulation
- 207 Figure B.2 TLP element coordinates
- 208 B 3 Calculation Methods
- 208 B 3.1 Linearisation of Roll Restoring
- 208 Figure B.3 Linearised Roll Restoring Moment from the GZ-curve
- 209 B 3.2 Calculation of Line Loads
- 209 Figure B.4 Line loads in Wadam
- 209 B 3.3 The Mapping of Loads from Panel Models to Finite Element Models
- 210 Figure B.5 The mapping of loads from panels to finite elements
- 211 Figure B.6 The DISTOL and ANGTOL functionality
- 211 B 3.4 Calculation of Tank Pressures
- 212 B 3.5 Global drag-coefficient for roll