Demonstration of a Robust Method for Section and Thickness

Demonstration of a Robust Method for Section and Thickness
Demonstration of a Robust Method for Section and Thickness
Optimization of Automotive Body Structures Using Optistruct
Vishal K Sinha
Sampath K Vanimisetti
Biswajit Tripathy
Student Intern
Vehicle Optimization CAE
GM Technical Center India
UGF, Innovator, ITPL
Bengaluru 560066 INDIA
[email protected]
Senior Technical Lead
Vehicle Optimization CAE
GM Technical Center India
UGF, Innovator, ITPL
Bengaluru 560066 INDIA
[email protected]
Sr. Technical Lead and Manager
Vehicle Optimization CAE
GM Technical Center India
UGF, Innovator, ITPL
Bengaluru 560066 INDIA
[email protected]
Abbreviations: BIW – body-in-white, CAE – computer-aided engineering, MFD – method of
feasible direction, SQP – sequential quadratic programming, GSO – global search option, GRSM –
global response surface method, GA – genetic algorithm.
Keywords: Optimization, Shape, Gage, Global Search, Robust Methods
Abstract
Refinement of the body-in-white (BIW) design to satisfy performance requirements, maximize passenger space, while minimizing the
overall mass, is a key design objective for many automotive OEMs. Part thicknesses and section shapes (e.g., rocker, B-pillar) are the
key design variables that are often subjected to various manufacturing and packaging constraints. Sizing and shape optimization
techniques, available in Altair’s OptiStruct®, have been applied routinely to regions of BIW, albeit independently. The design optimization
problem is increasingly becoming complex as a large number of thickness and section shape variables, that span the complete BIW,
have to be considered. There is a strong need for an efficient optimization method to facilitate the body design process. In this paper, we
explore this need using problem formulations, algorithmic settings and global search techniques available in OptiStruct®. A representative
model of the BIW is used to demonstrate combined thickness and section shape optimization to meet global torsion, bending and local
stiffness targets. The results are also compared to those obtained using global optimization techniques available in HyperStudy®. It was
found that the Sequential Quadratic Programming (SQP) algorithm was able to reach the lowest (global) minima with a superior rate of
convergence as compared to other methods available in Optistruct®, as well as HyperStudy®. Recommendations for performing thickness
and section optimization using Optistruct® are also discussed.
Introduction
The increasing emphasis on passenger vehicle fuel economy and future regulatory requirements are forcing
automotive OEMs to use newer technology in the vehicle [1]. One of the most critical aspects is lightweighting
of the vehicle. The overall savings in the vehicle are significant as each of the subsystem mass is reduced
due to the mass decompounding effect [2]. The body-in-white (BIW) structure is one of the significant
contributors to the mass decompounding effect. To design a cost-effective lightweight BIW structure,
especially for high-volume product lines, automotive OEMs are optimizing existing designs that are based on
conventional materials such as steel, rather than using lightweight materials such as aluminum. The body
design parameters such as part thickness and section dimensions/shapes are modified in order to meet the
performance targets. In addition, there are constraints on the design parameters due to manufacturing and
packaging consideration. For example, the designers modify the thickness and section dimension of rocker,
A-pillar, hinge-pillar and the B-pillar regions to improve torsional and bending stiffness of the BIW structure,
while not sacrificing the entry and egress space available to the passenger. The design process becomes
extremely complex when a large number of thickness and section shape variables, that span the complete
BIW, are considered simultaneously in order to satisfy performance targets, maximize passenger space, while
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minimizing the overall mass. Such a design task is too enormous for the designers to complete solely using
experience and rules-of-thumb. The emphasis on lightweighting, increasing number of design variables and
shortening of product cycles in the automotive industry necessitates the need for efficient design practices.
Cross-Bow
Roof-Bows
Roof-Rail
Header
A-Pillar
B-Pillar
IP Beam
1600 mm
Under-body
Rail
Front-Rail
Dash
Vertical Bar
Bottom
Cross-bar
2800 mm
1700 mm
Rocker
Cross-Bar #3
Cross-Bar #2
Cross-Bar #1
Hinge-Pillar
Figure 1: A representative model of an automotive Body-in-White
A typical BIW comprises of many sections, each influencing various performance parameters. In this study, a
representative vehicle BIW is used to investigate efficient design techniques. The BIW is shown in Figure 1,
illustrating the key components that are typically designed by the body engineers. Some of the key
performance metrics that are evaluated for the BIW, are shown in Figure 2.
SPC Constraint
For Bending & Local
Stiffness Loadcases
Loads for Torsional
Stiffness (KT)
SPC Constraint For
Bending, Torsion and Local
Stiffness Loadcases
Loads for Local
Stiffness at Bar 1 & 3
(KX, KY, KZ)
Loads for Bending
Stiffness (KB)
Figure 2: Illustration of stiffness loadcases used for performance assessment of BIW
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In Figure 2, KT is the torsional stiffness, KB is bending stiffness and KX/KY/KZ are the local stiffness in global
direction evaluated at cross-bar 1 and 3. The stiffness performance for the BIW is evaluated using the
following equations.
;
,
∈
, ,
(1)
(2)
In equation (1),
is 10 kN whereas, and
are 1 kN loads applied on the bending, torsion and local (bar
1 and 3) stiffness measurement locations as shown in Figure 2.
and
are the respective load point
deflections. In equation (2),
is the torsion couple and Θ is the twist angle computed using (
/ .
and
are the load point deflections where the torsion couple is applied as shown in Figure 2. The
Here,
baseline performance of the representative model described above is listed in Table I.
TABLE I
BASELINE MODEL PERFORMANCE DATA
Mass (kg)
Bending stiffness, KB (kN/mm)
Torsional stiffness, KT (kN-m/rad)
Local stiffness at Bar 1, [KX1,KY1,KZ1]
Local stiffness at Bar 3, [KX3,KY3,KZ3]
153.2
8.46
419.5
[8.41,8.61,6.52]
[8.41,9.18,7.07]
During the design process, thickness and section shape parameters are optimized to achieve desired
performance. Sizing and shape optimization techniques, available in many commercial structural design
optimization software, have been applied routinely to regions of BIW considering thickness and shape
independently. In practice, the design engineer first varies the section sizes based on prior experience, and
then perform part thickness optimization to recover mass. As the number of design variables and performance
targets increase, engineers have to comprehend multiple design iterations to arrive at the optimal solution.
Ideally, for the design optimization process to be efficient, both thickness and section shape changes should
be considered together to achieve the best mass savings.
Although structural shape optimization techniques were available for long time [3-5], only recently have these
techniques been applied to automotive body structure optimization [6-12]. In particular, free-form shape
optimization [8,10,11] promises an efficient BIW design exploration technique. Recent advances in highperformance computing technology, CAE solvers and design optimization tools provides a platform for an
efficient design optimization process. Large scale shape optimization capabilities in Optistruct® [13], which
when combined with gage optimization capability, can ideally provide a single step optimization process. This
technique can also address practical packaging constraints encountered during the vehicle design process.
To this end, the influence of optimizer settings on robustness of optimization process and its ability to achieve
global mass optimum needs to be understood. In this study, various optimization settings for performing gage
and shape optimization in Optistruct® are investigated. The results are compared to those obtained from
parametric design optimization using global optimization techniques available in HyperStudy®, such as global
response surface methodology (GRSM) and genetic algorithm (GA). The advantages of the shape
optimization using Optistruct® are discussed.
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Identify Designable
Components and Sections
Create Gage and Section
Design Variable
Create Shape Morphing
Blocks and Perturbations
Define Optimization
• Variable bounds
• Formulation
• Solver Settings
Optimize
Post Process
Figure 3: Methodology to perform combined thickness and shape optimization.
Process Methodology
An overview of the methodology used in this study is shown in Figure 3. The property thickness for the
component is linked to a design variable, whereas the section shape change is also linked to a design variable.
The optimization problem is defined as minimize mass or maximize performance formulation, and the
appropriate method (MFD or SQP) is selected. The design variable bounds are defined using manufacturing
constraints for thickness and packaging bounds for section shape. The responses are mass and stiffness data
shown in Figure 2. For the representative BIW model show in Figure 3, the design variables listed in Table II
were used. In the table, columns 1-2 represent the thickness variables, whereas columns 3-10 represent
shape variables. A total of 111 design variables was used in the study – 15 thickness variables and 96 section
shape variables. The optimizer’s capability was studied using choice of two methods, MFD and SQP.
Furthermore, the global search option (GSO), which uses multiple start points, was also investigated.
TABLE II
DESIGN VARIABLES USED IN THIS STUDY [THICKNESS: DV# 1-15; SECTION SHAPE: DV# 16-111]
DV#
LABEL
DV#
LABEL
DV#
LABEL
DV#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
T_Rocker
T_HingePillar
T_BPillar
T_RoofRail
T_RoofBow1
T_RoofBow2
T_CrossBow
T_BtmCrsBar
T_UdrBdyRail
T_DashVertical
T_IPBeam
T_APillar
T_Header
T_FrontRail
T_AllOthers
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
S_Rocker_ZS_Rocker_YS_Rocker_Y+
S_Rocker_Z+
S_RoofBow1_Z+
S_RoofBow1_ZS_RoofBow1_X+
S_RoofBow1_XS_RoofBow2_Z+
S_RoofBow2_ZS_RoofBow2_X+
S_RoofBow2_XS_RoofBow3_Z+
S_RoofBow3_ZS_RoofBow3_X+
S_RoofBow3_XS_Header1_X+
S_Header1_XS_Header1_Z+
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
S_UdBdyRail_Z+
S_UdrBdyRail _ZS_UdrBdyRail _Y+
S_UdrBdyRail _Y S_CrossBar1_X+
S_CrossBar1_XS_CrossBar1_Z+
S_CrossBar1_ZS_CrossBar2_X+
S_CrossBar2_XS_CrossBar2_Z+
S_CrossBar2_ZS_CrossBar3_X+
S_CrossBar3_X S_CrossBar3_Z+
S_CrossBar3_ZS_APillar1_Y+
S_APillar1_YS_APillar1_X+
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
LABEL
S_BPillar_X+
S_BPillar_XS_BPillar_Y+
S_BPillar_YS_IPBeam1_X+
S_IPBeam1_XS_IPBeam1_Z+
S_IPBeam1_ZS_IPBeam2_X+
S_IPBeam2_XS_IPBeam2_Z+
S_IPBeam2_ZS_HngPillar1_X+
S_HngPillar1_XS_HngPillar1_Y+
S_HngPillar1_YS_HngPillar2_X+
S_HngPillar2_XS_HngPillar2_Y+
DV#
LABEL
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
S_DshVrtBar2_X+
S_DshVrtBar2_XS_DshVrtBar2_Y+
S_DshVrtBar2_YS_BtmCrsBar1_X+
S_BtmCrsBar1_XS_BtmCrsBar1_Z+
S_BtmCrsBar1_ZS_BtmCrsBar2_X+
S_BtmCrsBar2_XS_BtmCrsBar2_Z+
S_BtmCrsBar2_ZS_FrontRail1_Y+
S_FrontRail1_YS_FrontRail1_Z+
S_FrontRail1_ZS_FrontRail2_Y+
S_FrontRail2_YS_FrontRail2_Z+
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35
36
37
38
39
S_Header1_ZS_Header2_Z+
S_Header2_ZS_Header2_X+
S_Header2_X-
59
60
61
62
63
S_APillar1_XS_APillar2_X+
S_APillar2_XS_APillar2_Y+
S_APillar2_Y-
83
84
85
86
87
x 103
160
12
S_HngPillar2_YS_DshVrtBar1_X+
S_DshVrtBar1_XS_DshVrtBar1_Y+
S_DshVrtBar1_Y-
107
108
109
110
111
Baseline
SQP
MFD
S_FrontRail2_ZS_RoofRail_Z+
S_RoofRail_ZS_RoofRail_YS_RoofRail_Y+
150
10
140
-24.6
130
8
-28.2
-33.2
-33.2
120
6
110
4
2
KB
KT(x10) KX1
(a)
KY1
KZ1
KX3
KY3
KZ3
(b)
Figure 4: Comparison of optimizer method choices for (a) Min. Mass (b) Max. Performance formulations.
Results & Discussions
1.0
Thickness Change
Thickness Change
The results comparing the choice of optimizer method are shown in Figure 4 for two design formulation:
minimize mass for given set of performance targets or maximize performance for given mass budget. These
design formulations are relevant in the context of BIW design. For minimize mass formulation, the lower bound
constraint on performance was set to the baseline, whereas for maximize performance, the upper bound
constraint on mass was set to the baseline. It can be seen from the results that SQP outperforms MFD for
both the formulations. Furthermore, SQP and SQP+GSO reached the same optimum for minimize mass
formulation, despite the two starting from very distinct starting points. This indicates that the SQP method is
able to converge to the global optimum starting from the baseline design.
Min. Mass
0.5
0.0
-0.5
-1.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
MDF
SQP
MFD+GSO
1.0
Max. Perf.
0.5
0.0
-0.5
-1.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
SQP+GSO
MDF
(a)
SQP
MFD+GSO
SQP+GSO
(c)
Shape Change
10.0
Min. Mass
5.0
0.0
-5.0
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
100
103
106
109
-10.0
MDF
SQP
MFD+GSO
SQP+GSO
(b)
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Shape Change
10.0
Max. Perf.
5.0
0.0
-5.0
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
100
103
106
109
-10.0
MDF
SQP
MFD+GSO
SQP+GSO
(d)
Figure 5: Change in thickness and shape design variables from baseline for
minimize mass formulation (a,b) and maximize mass formulation (c,d).
Note: ‘0’ on ordinate is starting design, +ve value is growth and –ve is reduction. Abscissa labels are DV# from Table II.
To further investigate the reasons for difference in MDF, the design variable levels at the final iteration are
plotted in Figure 5. For the GSO, the starting point that results in the lowest mass or the highest performance
was selected. It can be clearly seen from Figure 5a and 5c that the thickness changes are more or less similar
for all methods and formulations. However, the shape changes are significantly different (see Figure 5b and
5d). In fact, MFD by itself was unable to incorporate shape changes in the design optimization process. When
GSO was used with MFD, a better participation from shape variables was observed. SQP by itself is able to
easily incorporate shape changes in the design optimization process. It is also interesting to observe from
Figure 5b that the SQP and SQP+GSO final iteration design variables (follow and compare solid green with
dotted dark-green lines) are almost identical. This observation along with the fact that the final mass for these
two method was same indicates the SQP, by itself, is able to reach the global optimum. This suggests that
SQP is a very efficient method for combined thickness and section shape optimization problems.
To further investigate this observation, the SQP method was compared with global optimization techniques
such GRSM and GA using parametric optimization capabilities in HyperStudy®. Only minimize mass
formulation was investigated. For GA, the optimization was performed on a Kriging response surface obtained
from a HyperKriging Fit study using 250 Latin HperCube design points. The algorithm settings, iterations to
convergence and the final design objective are presented in Table III. The evolution of the design objective
for the three methods are shown in Figure 6. It can be clearly seen from both Table III and Figure 6 that the
SQP method is able to converge to the lowest objective (120 kg) within significantly less number of iterations
(6 iterations) and shorter total solution time (45 minutes) than GRSM and GA methods. This observation has
significant implications for thickness and shape optimization as SQP can provide better results faster.
TABLE III
COMPARISON OF PARAMETERS AND RESULTS FOR GLOBAL OPTIMIZATION METHODS
Algorithm
Solver and
Optimization Settings
Iterations to
convergence
Solution
Time* (hrs)
DOPTPRM, OPTMETH SQP
5
0.75
DOPTPRM, SHAPEOPT 2
Total Iterations 100
No. of initial iterations 20
GRSM
41
7.5
Random Seed 1
Constraint Violation Tolerance 0.5%
Constraint threshold 1E-4
Population Size 385
Min and Max Iterations [25,100]
Constraint Violation Tolerance 0.5%
Discrete States 1024
GA
31
62
Mutation rate and elites% [0.01, 10%]
Random seed and contenders [1,2]
Hybrid Algorithm Hooke-Jeeves
* All analyses was carried out on a Windows 7 x64 Workstation with 8 cores at 2.4GHz and 48GB RAM.
SQP
Optimized
Mass (kgs)
120
135
127
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SQP
160.0
GRSM
GA
Mass (kgs)
134.77
140.0
120.0
126.7
120.0
100.0
0
10
20
30
Iteration #
40
50
Figure 6: Evolution of the design objective (mass) for SQP, GRSM and GA methods
Benefits Summary
The ability to perform BIW structure design in a single optimization step using a large number of thickness
and section shape variables, along with manufacturing and packaging constraints will significantly improve
the efficiency and throughput during the vehicle development process. Due to superior performance of SQP
method and shape optimization capability, Optistruct® presents a valuable tool to perform large-scale
thickness and section shape optimization in the context of BIW structure design. Many more complex shape
constraints that emanate from subsystem packaging or Human-Vehicle Interaction (HVI) considerations, can
be easily accommodated using this technique.
Future Plans
Further detailed investigation needs to be carried out to compare other Global Optimization algorithms with
the SQP method. Shape optimization capabilities in Optistruct® also allow for defining complex 3-D packaging
constraints. The performance of the SQP method for a large number of complex 3-D shape change constraints
needs to be investigated.
Conclusions
Design optimization of a representative automotive body structure to meet multiple performance constraints
was carried in Optistruct®. For combined thickness and section shape optimization, the Sequential Quadratic
Programming (SQP) method yielded superior results as it was able to incorporate more section shape
changes than the default Method of Feasible Direction (MFD). The SQP method also attained the best
objective function overall, i.e., lowest mass for mass minimization formulation and highest performance for
maximize performance formulation. The performance of SQP method was comparable to the result obtained
by the Global Search Option (GSO), indicating that it was able to achieve the global optimum. The SQP
method also achieved a lower minima in fewer iterations than global optimization techniques such as Global
Response Surface Methodology (GRSM) and Genetic Algorithms (GA) available in HyperStudy®. The SQP
method available in Optistruct® offers a superior and highly efficient technique suitable for performing largescale structural optimization of automotive body structure using thickness and complex 3-D section shape
changes subjected to manufacturing and packaging constraints.
ACKNOWLEDGEMENTS
The authors would like to thank Mr. Varun Agarwal from Vehicle Optimization Group, GM Technical Center
India; Mr. Rajan Chakravarty and Mr. Simon Xu from Vehicle Optimization Group, GM Technical Center
Warren (USA); Dr. Boris Kuenkler and Prof. Dr. Lothar Harzheim from GM Europe Adam Opel for their
valuable inputs.
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