结构拓扑优化的一些基本概念和研究方法1)

doi:10.6052/1000-0879-18-054

Abstract

Abstract:

Some fundamental concepts and problems in the research field of the structural topology optimization are introduced briefly. The essential characteristics of the truss-like and its discretization are analyzed. The classical analytical solutions as the benchmarks are listed in the references. The optimization strategies and the characteristics of various numerical methods for the structural topology optimization are reviewed. The numerical instabilities, such as the mesh-dependencies, the singular optima, the checkerboards and the local constraints, commonly in the structural topology optimization, are explained. The fundamental principles of the optimality criteria, the sequential programming and the heuristic methods are discussed.

Key words:

structural optimization|topology optimization|mathematical programming

CLC Number:

O342

ZHOU Kemin. SOME FUNDAMENTAL CONCEPTS AND RESEARCH METHOD OF STRUCTURAL TOPOLOGY OPTIMIZATION[J].Mechanics in Engineering, 2018, 40(3): 245-252.

References

1 Rozvany GIN, Lewinski T.Topology Optimization in Structural and Continuum Mechanics. Vienna: Springer, 2014
2 Sigmund O, Maute K.Topology optimization approaches a comparative review. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031-1055
3 Guo X, Cheng GD.Recent development in structural design and optimization. Acta Mechanic Sinica, 2010, 26: 807-823
4 Michell AGM.The limits of economy of material in frame-structure. Philosophical Magazine, 1904, 8: 589-597
5 Hemp WS. Optimum Structure.Oxford: Clarendon Press, 1973
6 Rozvany GIN.Generalized Michell structures—exact least-weight truss layouts for combined stress and displacement constraints: part I-general theory for plane trusses. Structural and Multidisciplinary Optimization, 1995, 9(3): 178-188
7 Rozvany GIN.Generalized Michell structures—exact least-weight truss layouts for combined stress and displacement constraints: part II—analytical solutions within a two-bar topology. Structural and Multidisciplinary Optimization, 1995, 9(3): 214-219
8 Rozvany GIN.Exact analytical solutions for some popular benchmark problems in topology optimization. Structural and Multidisciplinary Optimization, 1998, 15(1): 42-48
9 Lewinski T, Rozvany GIN.Exact analytical solutions for some popular benchmark problems in topology optimization II: three-sided polygonal supports. Structural and Multidisciplinary Optimization, 2007, 33(4-5): 337-349
10 Lewinski T, Rozvany GIN.Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains. Structural and Multidisciplinary Optimization, 2008, 35(2): 165-174
11 Lewinski T, Rozvany GIN.Analytical benchmarks for topological optimization IV: square-shaped line support. Structural and Multidisciplinary Optimization, 2008, 36(2): 143-158
12 Sokol T, Lewinski T.Optimal design of a class of symmetric plane frameworks of least weight. Structural and Multidisciplinary Optimization, 2011, 44(5): 729-734
13 Sokol T, Rozvany GIN.New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports. Structural and Multidisciplinary Optimization, 2012, 46(4): 477-486
14 Espi MV.New analytical benchmarks for topology optimization and their implications. Structural and Multidisciplinary Optimization, 2013, 47(1): 149-150
15 Rozvany GIN.Optimal load transmission by flexure. Computer Methods in Applied Mechanics and Engineering, 1972, 1(3): 253-263
16 Rozvany GIN.Grillages of maximum strength and maximum stiffness. International Journal of Mechanical Sciences, 1972, 14(10): 651-666
17 Lowe PG, Melchers RE.On the theory of optimal constant thickness, fibre-reinforced plates I. International Journal of Mechanical Sciences, 1972, 14(5): 311-324
18 Lowe PG, Melchers RE.On the theory of optimal constant thickness, fibre-reinforced plates II. International Journal of Mechanical Sciences, 1973, 15(2): 157-170
19 Lowe PG, Melchers RE.On the theory of optimal constant thickness, fibre-reinforced plates III. International Journal of Mechanical Sciences, 1973, 15(9): 711-726
20 Prager W, Rozvany GIN.Optimal layout of grillages. Journal of Structural Mechanics, 1977, 5(1): 1-18
21 Rozvany GIN, Prager W.A new class of structural optimization problem: optimal archgrids. Computer Methods in Applied Mechanics and Engineering, 1979, 19(1): 127-150
22 Ansola R, Canales J, Tárrago JA, et al.An integrated approach for shape and topology optimization of shell structures. Computers & Structures, 2002, 80(5): 449-458
23 Zhou K, Li J.The exact weight of discretized Michell trusses for a central point load. Structural and Multidisciplinary Optimization, 2004, 28(1): 69-72
24 Xie YM, Steven GP.A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885-896
25 Xie YM, Steven GP. Evolutionary Structural Optimization. London: Springer, 1997
26 Zhu JH, Zhang WH, Qiu KP.Bi-directional evolutionary topology optimization using element replaceable method. Computational Mechanics, 2007, 40(1): 97-109
27 Bendsoe MP, Kikuchi N.Generating optimal topologies in optimal design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224
28 Allaire G.Shape Optimization by the Homogenization Method. New York: Springer, 2001
29 Bendsoe MP.Optimal shape design as a material distribution problem. Structural and Multidisciplinary Optimization, 1989, 1(4): 193-202
30 Sigmund O.A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 2001, 21(2): 120-127
31 Sui YK, Yang DQ.A new method for structural topological optimization based on the concept of independent continuous variables and smooth model. Acta Mechanica Sinica, 1998, 14(2): 179-185
32 隋允康,杨德庆,王备. 多工况应力和位移约束下连续体结构拓扑优化. 力学学报, 2000,32(2): 171-179
33 Sethian JA, Wiegmann A.Structural boundary design via level set and immersed interface methods. Journal of Computational Physics, 2000, 163(2): 489-528
34 Wang MY, Wang X, Guo DM.A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2): 227-246
35 Eschenauer HA, Kobelev HA, Schumacher A.Bubble method for topology and shape optimization of structures. Structural and Multidisciplinary Optimization, 1994, 8(1): 42-51
36 Guo X, Zhang WS, Zhong WL.Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. Journal of Applied Mechanics, 2014, 81(8): 081009
37 Zhang WS, Yang WY, Zhou JH, et al.Structural topology optimization through explicit boundary evolution. Journal of Applied Mechanics, 2016, 84(1): 1011011
38 Bendsoe MP, Guades JM, Haber R, et al.An analytical model to predict optimal material properties in the context of optimal structural design. Journal of Applied Mechanics, 1994, 61(4): 930-937
39 Guedes JM, Taylor JE.On the prediction of material properties and topology for optimal continuum structures. Structural and Multidisciplinary Optimization, 1997, 14(3): 193-199
40 Taylor JE.An energy model for optimal design of linear continuum structures. Structural and Multidisciplinary Optimization, 1998, 16(2-3): 116-127
41 Bendsoe MP, Diaz AR, Lipton R, et al.Optimal design of material properties and material distribution for multiple loading conditions. International Journal for Numerical Methods in Engineering, 1995, 38(7): 1149-1170
42 Hornlein HREM, Kocvara M, Werner R.Material optimization: bridging the gap between conceptual and preliminary design. Aerospace Science and Technology, 2001, 5(8): 541-554
43 Bendsoe MP, Sigmund O.Material interpolations in topology optimization. Archive of Applied Mechanics, 1999, 69(9-10): 635-654
44 周克民, 胡云昌. 利用有限元构造Michell桁架的一种方法. 力学学报, 2002, 34(6): 935-940
45 周克民, 李俊峰. 有限元方法形成三维Michell桁架. 应用数学和力学, 2005, 26(3): 349-355
46 Zhou K, Li X.Topology optimization for minimum compliance under multiple loads based on continuous distribution of members. Structural and Multidisciplinary Optimization, 2008, 37(1): 49-56
47 Cheng GD, Jiang Z.Study on topology optimization with stress constraints. Engineering Optimization, 1992, 20(2): 129-148
48 Cheng GD.ε-relaxed approach in structural topology optimization. Structural and Multidisciplinary Optimization, 1997, 13(4): 258-266
49 Guo X, Cheng GD.A new approach for the solution of singular optimum in structural topology optimization. Acta Mechanica Sinica, 1997, 13(2): 171-178
50 Guo X, Cheng G, Yamazaki K.A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints. Structural and Multidisciplinary Optimization, 2001, 22(5): 364-373
51 Duysinx P, Bendsøe M.Topology optimization of continuum structures with local stress constraints. International Journal for Numerical Method in Engineering, 1998, 43(2): 1453-1478
52 Yang RJ, Chen CJ.Stress-based topology optimization. Structural and Multidisciplinary Optimization, 1996, 12(2): 98-105
53 Cheng KT, Olhoff N.An investigation concerning optimal design of solid elastic plates. International Journal of Solids & Structure, 1981, 17(3): 305-323
54 Diaz AR, Signmud O.Checkerboard patterns in layout optimization. Structural and Multidisciplinary Optimization, 1995, 10(1): 40-45
55 Sigmund O, Petersson J.Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural and Multidisciplinary Optimization, 1998, 16(1): 68-75
56 Beyer HG, Sendhoff B.Robust optimization—a comprehensive survey. Computer Methods in Applied Mechanics & Engineering, 2007, 196(33): 3190-3218
57 Valdebenito MA, Schueller GI.A survey on approaches for reliability-based optimization. Structural and Multidisciplinary Optimization, 2010, 42(5): 645-663
58 Kang Z, Bai S.On robust design optimization of truss structures with bounded uncertainties. Structural and Multidisciplinary Optimization, 2013, 47(5): 699-714
59 Zhou K, Zhou Y.Analytical solutions for two-bar structures under loads along uncertain direction. Structural and Multidisciplinary Optimization, 2016, 53(6): 1179-1183
60 闫军,程耿东, 刘岭. 基于均匀材料微结构模型的热弹性结构与材料并发优化. 计算力学学报, 2009, 26(1): 1-7
61 Liu L, Yan J, Cheng GD.Optimum structure with homogeneous optimum truss-like material. Computer & Structures, 2008, 86: 1417-1425
62 Barthelemy JFM, Haftka RT.Approximation concepts for optimum structural design—a review. Structural and Multidisciplinary Optimization, 1993, 5(3): 129-144
63 Fleury C.First and second order convex approximation strategies in structural optimization. Structural and Multidisciplinary Optimization, 1989, 1(1): 3-10
64 Zhang WH, Fleury C.A modification of convex approximation methods for structural optimization. Computers & Structures, 1997, 64(l-4): 89-95
65 Svanberg K.The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Method in Engineering, 1987, 24: 359-373
66 Bruyneel M, Duysinx P, Fleury C.A family of MMA approximations for structural optimization. Structural and Multidisciplinary Optimization, 2002, 24(4): 263-276
67 Arora JS, Haug E.Methods of design sensitivity analysis in structural optimization. AIAA Journal, 1979, 17(9): 970-974
68 Holland JH.Adaptation in Natural and Artificial System. Ann Arbor: University of Michigan Press, 1975
69 许素强,夏人伟. 桁架结构拓扑优化与遗传算法. 计算结构力学及其应用, 1994, 11(4): 436-445
70 Hajela P, Lee E.Genetic algorithms in truss topological optimization. International Journal of Solids and Structures, 1995, 32(22): 3341-3357
71 Rajan SD.Sizing, shape, and topology design optimization of trusses using genetic algorithm. Journal of Structural Engineering, 1995, 121(10): 1480-1487
72 Shim PY, Manoochehei S.Generating optimal configurations in structural design using simulated annealing. International Journal for Numerical Methods in Engineering, 1997, 40(6): 1053-1069

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SOME FUNDAMENTAL CONCEPTS AND RESEARCH METHOD OF STRUCTURAL TOPOLOGY OPTIMIZATION

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