Bidirectional evolutionary structural optimization (BESO) method has been successfully applied for a wide range of topology optimization problems. In this paper, the BESO method is further extended to the optimal design of an automotive tailor-welded blank (TWB) door with multiple thicknesses. Different from the traditional topology optimization for solid-void designs, topology optimization of the TWB door needs to identify the weld lines which joint sheets with different thicknesses. The finite element (FE) model of the automotive door assembly is established and verified by a series of stiffness experiments. Then, the proposed optimization procedure is applied to the optimization of the automotive TWB indoor panel for the optimal thickness layout and weld lines locations. Numerical results give guidelines for the lightweight design of TWB components to some extent.

References

References
1.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.10.1016/0045-7825(88)90086-2
2.
Rozvany
,
G. I. N.
,
Zhou
,
M.
, and
Birker
,
T.
,
1992
, “
Generalized Shape Optimization Without Homogenization
,”
Struct. Optim.
,
4
(
3–4
), pp.
250
252
.10.1007/BF01742754
3.
Rozvany
,
G. I. N.
,
Bendsøe
,
M. P.
, and
Kirsch
,
U.
,
1995
, “
Layout Optimization of Structures
,”
ASME Appl. Mech. Rev.
,
48
(
2
), p.
41
.10.1115/1.3005097
4.
Xie
,
Y. M.
, and
Steven
,
G. P.
,
1993
, “
A Simple Evolutionary Procedure for Structural Optimization
,”
Comput. Struct.
,
49
(
5
), pp.
885
896
.10.1016/0045-7949(93)90035-C
5.
Maute
,
K.
, and
Frangopol
,
D. M.
,
2003
, “
Reliability-Based Design of MEMS Mechanisms by Topology Optimization
,”
Comput. Struct.
,
81
(
8–11
), pp.
813
824
.10.1016/S0045-7949(03)00008-7
6.
Kang
,
Z.
, and
Tong
,
L.
,
2008
, “
Integrated Optimization of Material Layout and Control Voltage for Piezoelectric Laminated Plates
,”
J. Intell. Mater. Syst. Struct.
,
19
(
8
), pp.
889
904
.10.1177/1045389X07084527
7.
Paulino
,
G. H.
,
Silva
,
E. C. N.
, and
Le
,
C. H.
,
2009
, “
Optimal Design of Periodic Functionally Graded Composites With Prescribed Properties
,”
Struct. Multidiscip. Optim.
,
38
(
5
), pp.
469
489
.10.1007/s00158-008-0300-1
8.
Andreasen
,
C. S.
,
Gersborg
,
A. R.
, and
Sigmund
,
O.
,
2009
, “
Topology Optimization of Microfluidic Mixers
,”
Int. J. Numer. Methods Fluids
,
61
(
5
), pp.
498
513
.10.1002/fld.1964
9.
Diaz
,
A. R.
, and
Sigmund
,
O.
,
2010
, “
A Topology Optimization Method for Design of Negative Permeability Metamaterials
,”
Struct. Multidiscip. Optim.
,
41
(
2
), pp.
163
177
.10.1007/s00158-009-0416-y
10.
Xie
,
Y. M.
, and
Steven
,
G. P.
,
1997
,
Basic Evolutionary Structural Optimization
,
Springer-Verlag
,
Berlin, Germany
.
11.
Chu
,
D. N.
,
Xie
,
Y. M.
,
Hira
,
A.
, and
Steven
,
G. P.
,
1996
, “
Evolutionary Structural Optimization for Problems With Stiffness Constraints
,”
Finite Elem. Anal. Des.
,
21
(
4
), pp.
239
251
.10.1016/0168-874X(95)00043-S
12.
Xie
,
Y. M.
, and
Steven
,
G. P.
,
1996
, “
Evolutionary Structural Optimization for Dynamic Problems
,”
Comput. Struct.
,
58
(
6
), pp.
1067
1073
.10.1016/0045-7949(95)00235-9
13.
Jiao
,
H. Y.
,
Zhou
,
Q. C.
,
Li
,
W. J.
, and
Li
,
Y.
,
2012
, “
A New Algorithm for Evolutionary Structural Optimization in Mechanical Engineering
,”
Adv. Mech. Electron. Eng.
,
176
, pp.
303
309
.10.1007/978-3-642-31507-7
14.
Hu
,
X.
,
Cheng
,
H.
, and
Tao
,
Y.
,
2012
, “
Modified Rejection Ratio for Multiple Load Cases Evolutionary Structural Optimization
,”
Procedia Eng.
,
31
, pp.
627
633
.10.1016/j.proeng.2012.01.1077
15.
Huang
,
X.
, and
Xie
,
Y. M.
,
2010
,
Evolutionary Topology Optimization of Continuum Structures: Methods and Applications
,
John Wiley & Sons
,
Chichester, UK
.
16.
Huang
,
X.
,
Xie
,
Y. M.
, and
Burry
,
M. C.
,
2007
, “
Advantages of Bi-Directional Evolutionary Structural Optimization (BESO) Over Evolutionary Structural Optimization (ESO)
,”
Adv. Struct. Eng.
,
10
(
6
), pp.
727
737
.10.1260/136943307783571436
17.
Querin
,
O. M.
,
Young
,
V.
,
Steven
,
G. P.
, and
Xie
,
Y. M.
,
2000
, “
Computational Efficiency and Validation of Bi-Directional Evolutionary Structural Optimisation
,”
Comput. Methods Appl. Mech. Eng.
,
189
(
2
), pp.
559
573
.10.1016/S0045-7825(99)00309-6
18.
Yang
,
X. Y.
,
Xie
,
Y. M.
,
Steven
,
G. P.
, and
Querin
,
O. M.
,
1999
, “
Bidirectional Evolutionary Method for Stiffness Optimization
,”
AIAA J.
,
37
(
11
), pp.
1483
1488
.10.2514/2.626
19.
Huang
,
X.
, and
Xie
,
Y. M.
,
2007
, “
Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method
,”
Finite Elem. Anal. Des.
,
43
(
14
), pp.
1039
1049
.10.1016/j.finel.2007.06.006
20.
Huang
,
X.
,
Zuo
,
Z. H.
, and
Xie
,
Y. M.
,
2010
, “
Evolutionary Topology Optimization of Vibrating Continuum Structures for Natural Frequencies
,”
Comput. Struct.
,
88
(
5–6
), pp.
357
364
.10.1016/j.compstruc.2009.11.011
21.
Huang
,
X.
,
Xie
,
Y. M.
, and
Lu
,
G.
,
2007
, “
Topology Optimization of Energy Absorption Structures
,”
Int. J. Crashworthiness
,
12
(
6
), pp.
663
675
.10.1080/13588260701497862
22.
Huang
,
X.
, and
Xie
,
Y. M.
,
2009
, “
Bi-Directional Evolutionary Topology Optimization of Continuum Structures With One or Multiple Materials
,”
Comput. Mech.
,
43
(
3
), pp.
393
401
.10.1007/s00466-008-0312-0
23.
Michell
,
A. G. M.
,
1904
, “
LVIII. The Limits of Economy of Material in Frame-structures
,”
Phil. Mag.
,
8
(
47
), pp.
589
597
.10.1080/14786440409463229
24.
Bulman
,
S.
,
Sienz
,
J.
, and
Hinton
,
E.
,
2001
, “
Comparisons Between Algorithms The London, Edinburgh, and Dublin Philosophical Mag for Structural Topology Optimization Using a Aeries of Benchmark Studies
,”
Comput. Struct.
,
79
(
12
), pp.
1203
1218
.10.1016/S0045-7949(01)00012-8
25.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
1999
, “
Material Interpolation Schemes in Topology Optimization
,”
Arch. Appl. Mech.
,
69
(
9–10
), pp.
635
654
.10.1007/s004190050248
26.
Huang
,
X.
, and
Xie
,
Y. M.
,
2010
, “
A Further Review of ESO Type Methods for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
41
(
5
), pp.
671
683
.10.1007/s00158-010-0487-9
27.
Young
,
V.
,
Querin
,
O. M.
,
Steven
,
G. P.
, and
Xie
,
Y. M.
,
1999
, “
3D and Multiple Load Case Bi-Directional Evolutionary Structural Optimization (BESO)
,”
Struct. Multidiscip. Optim.
,
18
(
2–3
), pp.
183
192
.10.1007/BF01195993
28.
Young
,
V.
,
Querin
,
O. M.
,
Steven
,
G. P.
, and
Xie
,
Y. M.
,
1998
, “
3D Bi-directional Evolutionary Structural Optimisation (BESO)
,” Proceedings of the Australasian Conference on Structural Optimization, Sydney, Australia, pp.
275
282
.
29.
Cai
,
K.
,
Gao
,
Z.
, and
Shi
,
J.
,
2012
, “
Compliance Optimization of a Continuum With Bimodulus Material Under Multiple Load Cases
,”
Comput. Aided Des.
,
45
(
2
), pp.
195
203
.10.1016/j.cad.2012.07.009
30.
Pan
,
F.
,
Zhu
,
P.
, and
Zhang
,
Y.
,
2010
, “
Metamodel-Based Lightweight Design of B-pillar With TWB Structure Via Support Vector Regression
,”
Comput. Struct.
,
88
(
1–2
), pp.
36
44
.10.1016/j.compstruc.2009.07.008
31.
Song
,
S. I.
, and
Park
,
G. J.
,
2006
, “
Multidisciplinary Optimization of an Automotive Door With a Tailored Blank
,”
Proc. Inst. Mech. Eng., Part D.
,
220
(
2
), pp.
151
163
.10.1243/095440706X72772
32.
Chan
,
S. M.
,
Chan
,
L. C.
, and
Lee
,
T. C.
,
2003
, “
Tailor-Welded Blanks of Different Thickness Ratios Effects on Forming Limit Diagrams
,”
J. Mater. Process. Technol.
,
132
(
1–3
), pp.
95
101
.10.1016/S0924-0136(02)00407-7
33.
Kusuda
,
H.
,
Takasago
,
T.
, and
Natsumi
,
F.
,
1997
, “
Formability of Tailored Blanks
,”
J. Mater. Process. Technol.
,
71
(
1
), pp.
134
140
.10.1016/S0924-0136(97)00159-3
34.
Shin
,
J. K.
,
Lee
,
K. H.
,
Song
,
S. I.
, and
Park
,
G. J.
,
2002
, “
Automotive Door Design With the ULSAB Concept Using Structural Optimization
,”
Struct. Multidiscip. Optim.
,
23
(
4
), pp.
320
327
.10.1007/s00158-002-0189-z
35.
Lee
,
K. H.
,
Shin
,
J. K.
,
Song
,
S. I.
,
Yoo
,
Y. M.
, and
Park
,
G. J.
,
2003
, “
Automotive Door Design Using Structural Optimization and Design of Experiments
,”
Proc. Inst. Mech. Eng., Part D.
,
217
(
10
), pp.
855
865
.10.1243/095440703769683261
36.
Zienkiewicz
,
O. C.
,
1971
,
The Finite Element in Engineering Sciences
,
McGraw-Hill Co.
,
London, UK
.
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