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.
Issue Section:
Design Automation
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/s0015800501742.
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)90086-24.
Bendsøe
, M. P.
, 1989
, “Optimal Shape Design as a Material Distribution Problem
,” Struct. Optim.
, 1
(4
), pp. 193
–202
. 10.1007/BF016509495.
Zuo
, W.
, and Saitou
, K.
, 2017
, “Multi-material Topology Optimization Using Ordered SIMP Interpolation
,” Struct. Multidiscipl. Optim.
, 55
(2
), pp. 477
–491
. 10.1007/s00158-016-1513-36.
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)90046-97.
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)00559-58.
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.2003.09.0329.
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/s00158-016-1430-510.
Liu
, J.
, and Ma
, Y.
, 2017
, “Sustainable Design-Oriented Level Set Topology Optimization
,” ASME J. Mech. Des.
, 139
(1
), p. 011403
. 10.1115/1.403505211.
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-C12.
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
. 10.1108/0264440941079929013.
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-X14.
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
. 10.1115/1.402760915.
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/s00158-015-1372-316.
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
. 10.1115/1.404105217.
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/s00158-019-02353-018.
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.2013.09.01820.
Zegard
, T.
, and Paulino
, G. H.
, 2016
, “Bridging Topology Optimization and Additive Manufacturing
,” Struct. Multidiscipl. Optim.
, 53
(1
), pp. 175
–192
. 10.1007/s00158-015-1274-421.
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-x22.
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
. 10.1115/1.403730423.
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.2018.04.04024.
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.2016.07.00225.
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
. 10.1115/1.404530126.
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
. 10.1115/1.404211427.
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
. 10.1115/1.404510728.
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
. 10.1115/1.404211229.
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.47.19831.
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/s00158-011-0632-032.
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.2014.10.00635.
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.106436.
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.2014.08.02737.
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.2015.05.00338.
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.2017.10.01139.
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/detc2019-9838640.
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/s00158-018-2066-441.
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/s41467-020-16599-642.
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/s12239-020-0047-243.
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/s12239-016-0098-644.
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.2011.10.00545.
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/s00158-011-0701-446.
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
. 10.1177/095440701455158547.
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
. 10.1177/1045389X1878125848.
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.2018.07.00549.
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.2018.09.07450.
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)00015-351.
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.000058252.
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.1943-7889.000058453.
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.514354.
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.2017.09.00955.
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.2018.11.01456.
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/s12206-019-0631-4Copyright © 2021 by ASME
You do not currently have access to this content.
