RESEARCH ARTICLE

A MATLAB code for the material-field series-expansion topology optimization method

  • Pai LIU 1 ,
  • Yi YAN 2 ,
  • Xiaopeng ZHANG 1 ,
  • Yangjun LUO , 1,2
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  • 1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
  • 2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

Received date: 06 Nov 2020

Accepted date: 04 Mar 2021

Published date: 15 Sep 2021

Copyright

2021 Higher Education Press

Abstract

This paper presents a MATLAB implementation of the material-field series-expansion (MFSE) topo-logy optimization method. The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology. With the series-expansion method for bounded fields, this material field is described with the characteristic base functions and the corresponding coefficients. Compared with the conventional density-based method, the MFSE method decouples the topological description and the finite element discretization, and greatly reduces the number of design variables after dimensionality reduction. Other features of this method include inherent control on structural topological complexity, crisp structural boundary description, mesh independence, and being free from the checkerboard pattern. With the focus on the implementation of the MFSE method, the present MATLAB code uses the maximum stiffness optimization problems solved with a gradient-based optimizer as examples. The MATLAB code consists of three parts, namely, the main program and two subroutines (one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer). The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail. The code is intended for researchers who are interested in this method and want to get started with it quickly. It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.

Cite this article

Pai LIU , Yi YAN , Xiaopeng ZHANG , Yangjun LUO . A MATLAB code for the material-field series-expansion topology optimization method[J]. Frontiers of Mechanical Engineering, 2021 , 16(3) : 607 -622 . DOI: 10.1007/s11465-021-0637-3

Acknowledgements

The authors acknowledge the support of the National Key R&D Program of China (Grant No. 2017YFB0203604), the National Natural Science Foundation of China (Grant Nos. 11902064 and 11772077), and the Liaoning Revitalization Talents Program, China (Grant No. XLYC1807187). The authors are grateful to members of the iDEAS group for their testing of the code.

Electronic Supplementary Materials

The supplementary materials can be found in the online version of this article at https://doi.org/10.1007/s11465-021-0637-3 and is accessible to authorized users.
1
Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224

DOI

2
Bendsøe M P. Optimal shape design as a material distribution problem. Structural Optimization, 1989, 1(4): 193–202

DOI

3
Rozvany G I N, Zhou M, Birker T. Generalized shape optimization without homogenization. Structural Optimization, 1992, 4(3–4): 250–252

DOI

4
Wang M Y, Wang X, Guo D. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1–2): 227–246

DOI

5
Allaire G, Jouve F, Toader A. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, 2004, 194(1): 363–393

DOI

6
Xie Y M, Steven G P. A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885–896

DOI

7
Huang X, Xie Y M. Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Computational Mechanics, 2009, 43(3): 393–401

DOI

8
Sigmund O, Maute K. Topology optimization approaches. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031–1055

DOI

9
van Dijk N P, Maute K, Langelaar M, . Level-set methods for structural topology optimization: A review. Structural and Multidisciplinary Optimization, 2013, 48(3): 437–472

DOI

10
Huang X, Xie Y M. A further review of ESO type methods for topology optimization. Structural and Multidisciplinary Optimization, 2010, 41(5): 671–683

DOI

11
Sigmund O A. 99 line topology optimization code written in MATLAB. Structural and Multidisciplinary Optimization, 2001, 21(2): 120–127

DOI

12
Andreassen E, Clausen A, Schevenels M, . Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 2011, 43(1): 1–16

DOI

13
Suresh K. A 199-line MATLAB code for Pareto-optimal tracing in topology optimization. Structural and Multidisciplinary Optimization, 2010, 42(5): 665–679

DOI

14
Otomori M, Yamada T, Izui K, . MATLAB code for a level set-based topology optimization method using a reaction diffusion equation. Structural and Multidisciplinary Optimization, 2015, 51(5): 1159–1172

DOI

15
Xia L, Breitkopf P. Design of materials using topology optimization and energy-based homogenization approach in MATLAB. Structural and Multidisciplinary Optimization, 2015, 52(6): 1229–1241

DOI

16
Challis V J. A discrete level-set topology optimization code written in MATLAB. Structural and Multidisciplinary Optimization, 2010, 41(3): 453–464

DOI

17
Liu K, Tovar A. An efficient 3D topology optimization code written in MATLAB. Structural and Multidisciplinary Optimization, 2014, 50(6): 1175–1196

DOI

18
Talischi C, Paulino G H, Pereira A, . PolyTop: A MATLAB implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Structural and Multidisciplinary Optimization, 2012, 45(3): 329–357

DOI

19
Wei P, Li Z Y, Li X P, . An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions. Structural and Multidisciplinary Optimization, 2018, 58(2): 831–849

DOI

20
Luo Y, Bao J. A material-field series-expansion method for topology optimization of continuum structures. Computers & Structures, 2019, 225: 106122

DOI

21
Luo Y, Xing J, Kang Z. Topology optimization using material-field series expansion and Kriging-based algorithm: An effective non-gradient method. Computer Methods in Applied Mechanics and Engineering, 2020, 364: 112966

DOI

22
Svanberg K. The method of moving asymptotes—A new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359–373

DOI

23
Luo Y J, Zhan J J, Xing J, . Non-probabilistic uncertainty quantification and response analysis of structures with a bounded field model. Computer Methods in Applied Mechanics and Engineering, 2019, 347: 663–678

DOI

24
Guest J K, Prevost J, Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering, 2004, 61(2): 238–254

DOI

25
Knyazev A V, Argentati M E, Lashuk I, . Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in HYPRE and PETSc. SIAM Journal on Scientific Computing, 2007, 29(5): 2224–2239

DOI

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