Abstract

Topology optimization has been intensively studied and extensively applied in engineering design. However, the optimized results often take the form of a solid frame structure; hence, it is difficult to apply the topological results in the design of a thin-walled frame structure. Therefore, this paper proposes a novel bridging method to transform the topological results into a lightweight thin-walled frame structure while satisfying the stiffness and manufacturing requirements. First, the optimized topological results are obtained using the classical topology optimization method, which is smoothed to reduce structural complexity. Then, the initial thin-walled frame structure is created by referring to the smoothed topological results, in which the thin-walled cross section is designed according to the mechanical properties and manufacturing requirements. Furthermore, the size and shape of the thin-walled frame structure is optimized to minimize mass with the stiffness and manufacturing constraints. Finally, numerical examples demonstrate that the proposed method can reasonably design an optimized thin-walled frame structure from the topological results.

References

References
1.
Rozvany
,
G. I. N.
,
2001
, “
Aims, Scope, Methods, History and Unified Terminology of Computer-Aided Topology Optimization in Structural Mechanics
,”
Struct. Multidiscipl. Optim.
,
21
(
2
), pp.
90
108
. 10.1007/s001580050174
2.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization: Theory, Method, and Applications
,
Springer-Verlag
,
Berlin
.
3.
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
4.
Bendsøe
,
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
. 10.1007/BF01650949
5.
Zuo
,
W.
, and
Saitou
,
K.
,
2017
, “
Multi-material Topology Optimization Using Ordered SIMP Interpolation
,”
Struct. Multidiscipl. Optim.
,
55
(
2
), pp.
477
491
. 10.1007/s00158-016-1513-3
6.
Zhou
,
M.
, and
Rozvany
,
G.
,
1991
, “
The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
89
(
1–3
), pp.
309
336
. 10.1016/0045-7825(91)90046-9
7.
Wang
,
M. Y.
,
Wang
,
X.
, and
Guo
,
D.
,
2003
, “
A Level Set Method for Structural Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
1
), pp.
227
246
. 10.1016/S0045-7825(02)00559-5
8.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A. M.
,
2004
, “
Structural Optimization Using Sensitivity Analysis and a Level-Set Method
,”
J. Comput. Phys.
,
194
(
1
), pp.
363
393
. 10.1016/j.jcp.2003.09.032
9.
Wang
,
Y.
,
Wang
,
M. Y.
, and
Chen
,
F.
,
2016
, “
Structure-Material Integrated Design by Level Sets
,”
Struct. Multidiscipl. Optim.
,
54
(
5
), pp.
1145
1156
. 10.1007/s00158-016-1430-5
10.
Liu
,
J.
, and
Ma
,
Y.
,
2017
, “
Sustainable Design-Oriented Level Set Topology Optimization
,”
ASME J. Mech. Des.
,
139
(
1
), p.
011403
. 10.1115/1.4035052
11.
Xie
,
Y.
, 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
12.
Xie
,
Y.
, and
Steven
,
G. P.
,
1994
, “
Optimal Design of Multiple Load Case Structures Using an Evolutionary Procedure
,”
Eng. Computation
,
11
(
4
), pp.
295
302
. 10.1108/02644409410799290
13.
Steven
,
G.
,
Querin
,
O.
, and
Xie
,
M.
,
2000
, “
Evolutionary Structural Optimisation (ESO) for Combined Topology and Size Optimisation of Discrete Structures
,”
Comput. Methods Appl. Mech. Eng.
,
188
(
4
), pp.
743
754
. 10.1016/S0045-7825(99)00359-X
14.
Guo
,
X.
,
Zhang
,
W.
, and
Zhong
,
W.
,
2014
, “
Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework
,”
ASME J. Appl. Mech.
,
81
(
8
), p.
081009
. 10.1115/1.4027609
15.
Zhang
,
W.
,
Yuan
,
J.
,
Zhang
,
J.
, and
Guo
,
X.
,
2016
, “
A New Topology Optimization Approach Based on Moving Morphable Components (MMC) and the Ersatz Material Model
,”
Struct. Multidiscipl. Optim.
,
53
(
6
), pp.
1243
1260
. 10.1007/s00158-015-1372-3
16.
Zhang
,
W.
,
Liu
,
Y.
,
Du
,
Z.
,
Zhu
,
Y.
, and
Guo
,
X.
,
2018
, “
A Moving Morphable Component Based Topology Optimization Approach for Rib-Stiffened Structures Considering Buckling Constraints
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111404
. 10.1115/1.4041052
17.
Bai
,
J.
, and
Zuo
,
W.
,
2020
, “
Hollow Structural Design in Topology Optimization via Moving Morphable Component Method
,”
Struct. Multidiscipl. Optim.
,
61
(
1
), pp.
187
205
. 10.1007/s00158-019-02353-0
18.
Kalpakjian
,
S.
,
Schmid
,
S. R.
, and
Sekar
,
K. S. V.
,
2014
,
Manufacturing Engineering and Technology
,
Pearson
,
Singapore
.
19.
Andreassen
,
E.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2014
, “
Design of Manufacturable 3D Extremal Elastic Microstructure
,”
Mech. Mater.
,
69
(
1
), pp.
1
10
. 10.1016/j.mechmat.2013.09.018
20.
Zegard
,
T.
, and
Paulino
,
G. H.
,
2016
, “
Bridging Topology Optimization and Additive Manufacturing
,”
Struct. Multidiscipl. Optim.
,
53
(
1
), pp.
175
192
. 10.1007/s00158-015-1274-4
21.
Gaynor
,
A. T.
, and
Guest
,
J. K.
,
2016
, “
Topology Optimization Considering Overhang Constraints: Eliminating Sacrificial Support Material in Additive Manufacturing Through Design
,”
Struct. Multidiscipl. Optim.
,
54
(
5
), pp.
1157
1172
. 10.1007/s00158-016-1551-x
22.
Orme
,
M. E.
,
Gschweitl
,
M.
,
Ferrari
,
M.
,
Madera
,
I.
, and
Mouriaux
,
F.
,
2017
, “
Designing for Additive Manufacturing: Lightweighting Through Topology Optimization Enables Lunar Spacecraft
,”
ASME J. Mech. Des.
,
139
(
10
), p.
100905
. 10.1115/1.4037304
23.
Wang
,
Y.
,
Gao
,
J.
, and
Kang
,
Z.
,
2018
, “
Level Set-Based Topology Optimization With Overhang Constraint: Towards Support-Free Additive Manufacturing
,”
Comput. Methods Appl. Mech. Eng.
,
339
, pp.
591
614
. 10.1016/j.cma.2018.04.040
24.
Vatanabe
,
S. L.
,
Lippi
,
T. N.
,
Lima
,
C. R. d.
,
Paulino
,
G. H.
, and
Silva
,
E. C. N.
,
2016
, “
Topology Optimization With Manufacturing Constraints: A Unified Projection-Based Approach
,”
Adv. Eng. Softw.
,
100
, pp.
97
112
. 10.1016/j.advengsoft.2016.07.002
25.
Liu
,
J.
, and
To
,
A. C.
,
2020
, “
Computer-Aided Design-Based Topology Optimization System With Dynamic Feature Shape and Modeling History Evolution
,”
ASME J. Mech. Des.
,
142
(
7
), p.
071704
. 10.1115/1.4045301
26.
Ha
,
S.-H.
,
Lee
,
H. Y.
,
Hemker
,
K. J.
, and
Guest
,
J. K.
,
2019
, “
Topology Optimization of Three-Dimensional Woven Materials Using a Ground Structure Design Variable Representation
,”
ASME J. Mech. Des.
,
141
(
6
), p.
061403
. 10.1115/1.4042114
27.
Ulu
,
E.
,
Ulu
,
N. G.
,
Hsiao
,
W.
, and
Nelaturi
,
S.
,
2020
, “
Manufacturability Oriented Model Correction and Build Direction Optimization for Additive Manufacturing
,”
ASME J. Mech. Des.
,
142
(
6
), p.
062001
. 10.1115/1.4045107
28.
Ulu
,
E.
,
Huang
,
R.
,
Kara
,
L. B.
, and
Whitefoot
,
K. S.
,
2019
, “
Concurrent Structure and Process Optimization for Minimum Cost Metal Additive Manufacturing
,”
ASME J. Mech. Des.
,
141
(
6
), p.
061701
. 10.1115/1.4042112
29.
Zhou
,
M.
,
Fleury
,
R.
,
Shyy
,
Y. K.
,
Thomas
,
H.
, and
Brennan
,
J.
,
2002
, “
Progress in Topology Optimization with Manufacturing Constraints
,”
Proceedings of 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
Atlanta, GA
,
Sept. 4–6
.
30.
Ishii
,
K.
, and
Aomura
,
S.
,
2004
, “
Topology Optimization for the Extruded Three Dimensional Structure With Constant Cross Section
,”
JSME Int. J. Series A Solid Mech. Mate. Eng.
,
47
(
2
), pp.
198
206
. 10.1299/jsmea.47.198
31.
Gersborg
,
A. R.
, and
Andreasen
,
C. S.
,
2011
, “
An Explicit Parameterization for Casting Constraints in Gradient Driven Topology Optimization
,”
Struct. Multidiscipl. Optim.
,
44
(
6
), pp.
875
881
. 10.1007/s00158-011-0632-0
32.
Lu
,
J.
, and
Chen
,
Y.
,
2012
, “
Manufacturable Mechanical Part Design With Constrained Topology Optimization
,”
P I Mech. Eng. B-J. Eng.
,
226
(
10
), pp.
1727
1735
.
33.
Allaire
,
G.
,
Jouve
,
F.
, and
Michailidis
,
G.
,
2013
, “
Casting Constraints in Structural Optimization via a Level-set Method
,”
Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization
,
Orlando, FL
,
May 19–24
.
34.
Li
,
H.
,
Li
,
P.
,
Gao
,
L.
,
Zhang
,
L.
, and
Wu
,
T.
,
2015
, “
A Level Set Method for Topological Shape Optimization of 3D Structures With Extrusion Constraints
,”
Comput. Methods Appl. Mech. Eng.
,
283
, pp.
615
635
. 10.1016/j.cma.2014.10.006
35.
Guest
,
J. K.
,
Prevost
,
J. H.
, and
Belytschko
,
T.
,
2004
, “
Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions
,”
Int. J. Number Meth. Eng.
,
61
(
2
), pp.
238
254
. 10.1002/nme.1064
36.
Zhang
,
W.
,
Zhong
,
W.
, and
Guo
,
X.
,
2014
, “
An Explicit Length Scale Control Approach in SIMP-Based Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
282
, pp.
71
86
. 10.1016/j.cma.2014.08.027
37.
Zhou
,
M.
,
Lazarov
,
B.
,
Wang
,
F.
, and
Sigmund
,
O.
,
2015
, “
Minimum Length Scale in Topology Optimization by Geometric Constraints
,”
Comput. Methods Appl. Mech. Eng.
,
293
, pp.
266
282
. 10.1016/j.cma.2015.05.003
38.
Liu
,
J.
, and
Ma
,
Y.
,
2018
, “
A New Multi-material Level Set Topology Optimization Method With the Length Scale Control Capability
,”
Comput. Methods Appl. Mech. Eng.
,
329
, pp.
444
463
. 10.1016/j.cma.2017.10.011
39.
Luo
,
C.
, and
Guest
,
J. K.
,
2021
, “
Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites
,”
ASME J. Mech. Des.
,
143
(
2
), p.
021704
. 10.1115/detc2019-98386
40.
Carstensen
,
J. V.
, and
Guest
,
J. K.
,
2018
, “
Projection-Based Two-Phase Minimum and Maximum Length Scale Control in Topology Optimization
,”
Struct. Multidiscipl. Optim.
,
58
(
5
), pp.
1845
1860
. 10.1007/s00158-018-2066-4
41.
Baandrup
,
M.
,
Sigmund
,
O.
,
Polk
,
H.
, and
Aage
,
N.
,
2020
, “
Closing the Gap Towards Super-Long Suspension Bridges Using Computational Morphogenesis
,”
Nat. Commun.
,
11
(
1
), p.
2735
. 10.1038/s41467-020-16599-6
42.
Ma
,
Y.
,
Chen
,
R.
,
Bai
,
J.
, and
Zuo
,
W.
,
2020
, “
Shape Optimization of Thin-Walled Cross Section for Automobile Body Considering Stamping Cost, Manufacturability and Structural Stiffness
,”
Int. J. Automot. Technol.
,
21
(
2
), pp.
503
512
. 10.1007/s12239-020-0047-2
43.
Zuo
,
W.
, and
Bai
,
J.
,
2016
, “
Cross-sectional Shape Design and Optimization of Automotive Body With Stamping Constraints
,”
Int. J. Automot. Technol.
,
17
(
6
), pp.
1003
1011
. 10.1007/s12239-016-0098-6
44.
Zuo
,
W.
,
Li
,
W.
,
Xu
,
T.
,
Xuan
,
S.
, and
Na
,
J. X.
,
2012
, “
A Complete Development Process of Finite Element Software for Body-in-White Structure With Semi-rigid Beams in .NET Framework
,”
Adv. Eng. Softw
,
45
(
1
), pp.
261
271
. 10.1016/j.advengsoft.2011.10.005
45.
Balesdent
,
M.
,
Bérend
,
N.
,
Dépincé
,
P.
, and
Chriette
,
A.
,
2012
, “
A Survey of Multidisciplinary Design Optimization Methods in Launch Vehicle Design
,”
Struct. Multidiscipl. Optim.
,
45
(
5
), pp.
619
642
. 10.1007/s00158-011-0701-4
46.
Zuo
,
W.
,
2015
, “
Bi-level Optimization for the Cross-sectional Shape of a Thin-Walled Car Body Frame With Static Stiffness and Dynamic Frequency Stiffness Constraints
,”
P I Mech. Eng. D-J. Aut.
,
229
(
8
), pp.
1046
1059
. 10.1177/0954407014551585
47.
Zhou
,
L.
,
Li
,
M.
,
Meng
,
G.
, and
Zhao
,
H.
,
2018
, “
An Effective Cell-Based Smoothed Finite Element Model for the Transient Responses of Magneto-electro-elastic Structures
,”
J. Intel. Mat. Syst. Str.
,
29
(
14
), pp.
1
17
. 10.1177/1045389X18781258
48.
Gui
,
C.
,
Bai
,
J.
, and
Zuo
,
W.
,
2018
, “
Simplified Crashworthiness Method of Automotive Frame for Conceptual Design
,”
Thin. Wall Struct.
,
131
, pp.
324
335
. 10.1016/j.tws.2018.07.005
49.
Zhou
,
L.
,
Ren
,
S.
,
Liu
,
C.
, and
Ma
,
Z.
,
2019
, “
A Valid Inhomogeneous Cell-Based Smoothed Finite Element Model for the Transient Characteristics of Functionally Graded Magneto-electro-elastic Structures
,”
Compos. Struct.
,
208
, pp.
298
313
. 10.1016/j.compstruct.2018.09.074
50.
Kim
,
Y. Y.
, and
Kim
,
T. S.
,
2000
, “
Topology Optimization of Beam Cross Sections
,”
Int. J. Solids Struct.
,
37
(
3
), pp.
477
493
. 10.1016/S0020-7683(99)00015-3
51.
Jang
,
G. W.
,
Kim
,
M. J.
, and
Kim
,
Y. Y.
,
2012
, “
Analysis of Thin-Walled Straight Beams With Generally Shaped Closed Sections Using Numerically Determined Sectional Deformation Functions
,”
J. Struct. Eng.
,
138
(
12
), pp.
1427
1435
. 10.1061/(ASCE)ST.1943-541X.0000582
52.
Jang
,
G. W.
,
Choi
,
S. M.
, and
Kim
,
Y. Y.
,
2012
, “
Analysis of Three Thin-Walled Box Beams Connected at a Joint Under Out-of-Plane Bending Loads
,”
J. Eng. Mech.
,
139
(
10
), pp.
1350
1361
. 10.1061/(ASCE)EM.1943-7889.0000584
53.
Kim
,
D. M.
,
Kim
,
S. I.
,
Choi
,
S.
,
Jang
,
G. W.
, and
Kim
,
Y. Y.
,
2016
, “
Topology Optimization of Thin-Walled Box Beam Structures Based on the Higher-Order Beam Theory
,”
Int. J. Number Meth. Eng.
,
106
(
7
), pp.
576
590
. 10.1002/nme.5143
54.
Nguyen
,
N. L.
,
Jang
,
G. W.
,
Choi
,
S.
,
Kim
,
J.
, and
Kim
,
Y. Y.
,
2018
, “
Analysis of Thin-Walled Beam-Shell Structures for Concept Modeling Based on Higher-Order Beam Theory
,”
Comput. Struct.
,
195
, pp.
16
33
. 10.1016/j.compstruc.2017.09.009
55.
Bai
,
J.
,
Meng
,
G.
,
Wu
,
H.
, and
Zuo
,
W.
,
2019
, “
Bending Collapse of Dual Rectangle Thin-Walled Tubes for Conceptual Design
,”
Thin. Wall Struct.
,
135
, pp.
185
195
. 10.1016/j.tws.2018.11.014
56.
Bai
,
J.
,
Meng
,
G.
, and
Zuo
,
W.
,
2019
, “
Rollover Crashworthiness Analysis and Optimization of Bus Frame for Conceptual Design
,”
J. Mech. Sci. Technol.
,
33
(
7
), pp.
3363
3373
. 10.1007/s12206-019-0631-4
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