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Structural and Multidisciplinary Optimization

Erschienen in:

15.02.2021 | Educational Paper

An efficient 137-line MATLAB code for geometrically nonlinear topology optimization using bi-directional evolutionary structural optimization method

verfasst von: Yongsheng Han, Bin Xu, Yuanhao Liu

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 5/2021

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Abstract

Topology optimization, as a powerful conceptual design method, has been widely adopted in both academic research and industrial applications. To further promote the development of topology optimization, many computer programs have been published for educational purposes over the past decades. However, most of the computer programs are constructed based on a linear assumption. On the basis of bi-directional evolutionary structural optimization (BESO) method, the paper presents a MATLAB implementation of the geometrically nonlinear topology optimization code for compliance minimization of statically loaded structures. Excluding 19 lines which are used for explanation, only 118 lines are needed for the initialization of the design parameters, nonlinear finite element analysis, sensitivity calculation, sensitivity filtration, and topological design variables update. Different design problems can be solved by modifying several lines in the proposed program. The complete 137-line code is included as an Appendix and is intended for educational purposes only.

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Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in Matlab using 88 lines of code. Struct Multidiscip Optim 43(1):1–16. https://doi.org/10.1007/s00158-010-0594-7CrossRefMATH

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202. https://doi.org/10.1007/BF01650949CrossRef

Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224. https://doi.org/10.1016/0045-7825(88)90086-2MathSciNetCrossRefMATH

Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, BerlinMATH

Challis VJ (2010) A discrete level-set topology optimization code written in Matlab. Struct Multidiscip Optim 41(3):453–464. https://doi.org/10.1007/s00158-009-0430-0MathSciNetCrossRefMATH

Chen Q, Zhang X, Zhu B (2019) A 213-line topology optimization code for geometrically nonlinear structures. Struct Multidiscip Optim 59(5):1863–1879. https://doi.org/10.1007/s00158-018-2138-5MathSciNetCrossRef

Crisfield MA (1991) Non-linear finite element analysis of solids and structures. Wiley, New YorkMATH

Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38. https://doi.org/10.1007/s00158-013-0956-zMathSciNetCrossRef

Ferrari F, Sigmund O (2020) A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Struct Multidiscip Optim 62(4):2211–2228. https://doi.org/10.1007/s00158-020-02629-wMathSciNetCrossRef

Guo X, Zhang W, Zhang J, Yuan J (2016) Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons. Comput Methods Appl Mech Eng 310:711–748. https://doi.org/10.1016/j.cma.2016.07.018MathSciNetCrossRefMATH

Han YS, Xu B, Zhao L, Xie YM (2019) Topology optimization of continuum structures under hybrid additive-subtractive manufacturing constraints. Struct Multidiscip Optim 60(6):2571–2595. https://doi.org/10.1007/s00158-019-02334-3CrossRef

Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049. https://doi.org/10.1016/j.finel.2007.06.006CrossRef

Huang X, Xie YM (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30:2057–2068. https://doi.org/10.1016/j.engstruct.2008.01.009CrossRef

Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401. https://doi.org/10.1007/s00466-008-0312-0MathSciNetCrossRefMATH

Huang X, Xie YM (2010a) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683. https://doi.org/10.1007/s00158-010-0487-9CrossRef

Huang X, Xie YM (2010b) Topology optimization of continuum structures: methods and applications. Wiley, Chichester. https://doi.org/10.1002/9780470689486CrossRefMATH

Kim C, Jung M, Yamada T et al (2020) Freefem++ code for reaction-diffusion equation–based topology optimization: for high-resolution boundary representation using adaptive mesh refinement. Struct Multidiscip Optim 62:439–455. https://doi.org/10.1007/s00158-020-02498-3MathSciNetCrossRef

Lagaros ND, Vasileiou N, Kazakis G (2019) Ac# code for solving 3d topology optimization problems using sap2000. Optim Eng 20(1):1–35. https://doi.org/10.1007/s11081-018-9384-7CrossRefMATH

Laurain A (2018) A level set-based structural optimization code using FEniCS. Struct Multidiscip Optim 58(3):1311–1334. https://doi.org/10.1007/s00158-018-1950-2MathSciNetCrossRef

Liang Y, Cheng G (2020) Further elaborations on topology optimization via sequential integer programming and canonical relaxation algorithm and 128-line MATLAB code. Struct Multidiscip Optim 61(1):411–431. https://doi.org/10.1007/s00158-019-02396-3CrossRef

Liu K, Tovar A (2014) An efficient 3d topology optimization code written in Matlab. Struct Multidiscip Optim 50(6):1175–1196. https://doi.org/10.1007/s00158-014-1107-xMathSciNetCrossRef

Loyola RA, Querin OM, Jiménez AG et al (2018) A sequential element rejection and admission (SERA) topology optimization code written in Matlab. Struct Multidiscip Optim 58(3):1297–1310. https://doi.org/10.1007/s00158-018-1939-xMathSciNetCrossRef

Luo Z, Tong L, Wang MY, Wang S (2007) Shape and topology optimization of compliant mechanisms using a parameterization level set method. J Comput Phys 227(1):680–705. https://doi.org/10.1016/j.jcp.2007.08.011MathSciNetCrossRefMATH

Picelli R, Sivapuram R, Xie YM (2020) A 101-line MATLAB code for topology optimization using binary variables and integer programming. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-020-02719-9

Qian X (2013) Topology optimization in B-spline space. Comput Methods Appl Mech Eng 265:15–35. https://doi.org/10.1016/j.cma.2013.06.001MathSciNetCrossRefMATH

Rong JH, Xie YM, Yang XY (2001) An improved method for evolutionary structural optimisation against buckling. Comput Struct 79(3):253–263. https://doi.org/10.1016/S0045-7949(00)00145-0CrossRef

Rozvany GIN (2001) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Multidiscip Optim 21(2):90–108. https://doi.org/10.1007/s001580050174MathSciNetCrossRef

Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. Int J Numer Methods Eng 163(2):489–528. https://doi.org/10.1006/jcph.2000.6581MathSciNetCrossRefMATH

Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21(2):120–127. https://doi.org/10.1007/s001580050176CrossRef

Sigmund O, Maute K (2013a) Topology optimization approaches-a comparative review. Struct Multidiscip Optim 48(6):1031–1055. https://doi.org/10.1007/s00158-013-0978-6MathSciNetCrossRef

Sigmund O, Maute K (2013b) Topology optimization approaches-a comparative review. Struct Multidiscip Optim 48(6):1031–1055. https://doi.org/10.1007/s00158-013-0978-6MathSciNetCrossRef

Suzuki K, Kikuchi N (1991) A homogenization method for shape and topology optimization. Comput Methods Appl Mech Eng 93(3):291–318. https://doi.org/10.1016/0045-7825(91)90245-2CrossRefMATH

Talischi C, Paulino GH, Pereira A, Menezes IFM (2012) Polytop: a matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Struct Multidiscip Optim 45(3):329–357. https://doi.org/10.1007/s00158-011-0696-xMathSciNetCrossRefMATH

Tavakoli R, Mohseni SM (2014) Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line Matlab implementation. Struct Multidiscip Optim 49(4):621–642. https://doi.org/10.1007/s00158-013-0999-1MathSciNetCrossRef

Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246. https://doi.org/10.1016/S0045-7825(02)00559-5MathSciNetCrossRefMATH

Wang R, Zhang X, Zhu B (2019) Imposing minimum length scale in moving morphable component (mmc)-based topology optimization using an effective connection status (ecs) control method. Comput Methods Appl Mech Eng 351:667–693. https://doi.org/10.1016/j.cma.2019.04.007MathSciNetCrossRefMATH

Wei P, Li Z, Li X, Wang MY (2018) An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Struct Multidiscip Optim 58:831–849. https://doi.org/10.1007/s00158-018-1904-8MathSciNetCrossRef

Xia L, Breitkopf P (2015) Design of materials using topology optimization and energy-based homogenization approach in Matlab. Struct Multidiscip Optim 52:1229–1241. https://doi.org/10.1007/s00158-015-1294-0MathSciNetCrossRef

Xia L, Xia Q, Huang X, Xie YM (2018) Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch Comput Methods Eng 25:437–478. https://doi.org/10.1007/s11831-016-9203-2MathSciNetCrossRefMATH

Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896. https://doi.org/10.1016/0045-7949(93)90035-CCrossRef

Xie YM, Steven GP (1994) Optimal design of multiple load case structures using an evolutionary procedure. Eng Comput 11(4):295–302. https://doi.org/10.1108/02644409410799290CrossRefMATH

Xu B, Han YS, Zhao L (2020) Bi-directional evolutionary topology optimization of geometrically nonlinear continuum structures with stress constraints. Appl Math Model 80:771–791. https://doi.org/10.1016/j.apm.2019.12.009MathSciNetCrossRefMATH

Yaghmaei M, Ghoddosian A, Khatibi MM (2020) A filter-based level set topology optimization method using a 62-line Matlab code. Struct Multidiscip Optim 62:1001–1018. https://doi.org/10.1007/s00158-020-02540-4MathSciNetCrossRef

Zhang W, Yuan J, Zhang J, Guo X (2016) A new topology optimization approach based on moving morphable components (mmc) and the ersatz material model. Struct Multidiscip Optim 53(6):1243–1260. https://doi.org/10.1007/s00158-015-1372-3MathSciNetCrossRef

Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1):309–336. https://doi.org/10.1016/0045-7825(91)90046-9CrossRef

Zhu J, Zhang W, Xia L (2016) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng 23(4):595–622. https://doi.org/10.1007/s11831-015-9151-2MathSciNetCrossRefMATH

Zhu B, Zhang X, Zhang H, Liang J, Zang H, Li H, Wang R (2020a) Design of compliant mechanisms using continuum topology optimization: a review. Mech Mach Theory 143:103622. https://doi.org/10.1016/j.mechmachtheory.2019.103622CrossRef

Zhu B, Zhang X, Li H, Liang J, Wang R, Li H, Nishiwaki S (2020b) An 89-line code for geometrically nonlinear topology optimization written in FreeFEM. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-020-02733-x

Zuo ZH, Xie YM (2015) A simple and compact python code for complex 3d topology optimization. Adv Eng Softw 85:1–11. https://doi.org/10.1016/j.advengsoft.2015.02.006CrossRef

Titel: An efficient 137-line MATLAB code for geometrically nonlinear topology optimization using bi-directional evolutionary structural optimization method
verfasst von: Yongsheng Han
Bin Xu
Yuanhao Liu
Publikationsdatum: 15.02.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Structural and Multidisciplinary Optimization / Ausgabe 5/2021
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-020-02816-9

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