A simple and compact Python code for complex 3D topology optimization

This paper presents a 100-line Python code for general 3D topology optimization. The code adopts the Abaqus Scripting Interface that provides convenient access to advanced finite element analysis (FEA). It is developed for the compliance minimization with a volume constraint using the Bi-directional...

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Published inAdvances in engineering software (1992) Vol. 85; pp. 1 - 11
Main Authors Zuo, Zhi Hao, Xie, Yi Min
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2015
Subjects
Online AccessGet full text
ISSN0965-9978
DOI10.1016/j.advengsoft.2015.02.006

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Abstract This paper presents a 100-line Python code for general 3D topology optimization. The code adopts the Abaqus Scripting Interface that provides convenient access to advanced finite element analysis (FEA). It is developed for the compliance minimization with a volume constraint using the Bi-directional Evolutionary Structural Optimization (BESO) method. The source code is composed of a main program controlling the iterative procedure and five independent functions realizing input model preparation, FEA, mesh-independent filter and BESO algorithm. The code reads the initial design from a model database (.cae file) that can be of arbitrary 3D geometries generated in Abaqus/CAE or converted from various widely used CAD modelling packages. This well-structured code can be conveniently extended to various other topology optimization problems. As examples of easy modifications to the code, extensions to multiple load cases and nonlinearities are presented. This code is useful for researchers in the topology optimization field and for practicing engineers seeking automated conceptual design tools. With further extensions, the code could solve sophisticated 3D conceptual design problems in structural engineering, mechanical engineering and architecture practice. The complete code is given in the appendix section and can also be downloaded from the website: www.rmit.edu.au/research/cism/.
AbstractList This paper presents a 100-line Python code for general 3D topology optimization. The code adopts the Abaqus Scripting Interface that provides convenient access to advanced finite element analysis (FEA). It is developed for the compliance minimization with a volume constraint using the Bi-directional Evolutionary Structural Optimization (BESO) method. The source code is composed of a main program controlling the iterative procedure and five independent functions realizing input model preparation, FEA, mesh-independent filter and BESO algorithm. The code reads the initial design from a model database (.cae file) that can be of arbitrary 3D geometries generated in Abaqus/CAE or converted from various widely used CAD modelling packages. This well-structured code can be conveniently extended to various other topology optimization problems. As examples of easy modifications to the code, extensions to multiple load cases and nonlinearities are presented. This code is useful for researchers in the topology optimization field and for practicing engineers seeking automated conceptual design tools. With further extensions, the code could solve sophisticated 3D conceptual design problems in structural engineering, mechanical engineering and architecture practice. The complete code is given in the appendix section and can also be downloaded from the website: www.rmit.edu.au/research/cism/.
Author Xie, Yi Min
Zuo, Zhi Hao
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Cites_doi 10.1016/j.commatsci.2012.09.018
10.1007/s00158-014-1107-x
10.1007/s00158-009-0430-0
10.1007/s001580050176
10.1016/j.finel.2007.06.006
10.1007/s00158-010-0594-7
10.1016/0045-7825(91)90046-9
10.1016/j.compstruc.2009.11.011
10.1007/s00158-010-0487-9
10.1007/s00466-008-0312-0
10.1016/S0045-7825(02)00559-5
10.1007/s001580050089
10.1007/BF01214002
10.1016/0167-6636(94)00069-7
10.1016/j.commatsci.2013.10.024
10.1016/j.matdes.2013.05.014
10.1007/BF01650949
10.1016/0045-7949(93)90035-C
10.1260/1369-4332.15.2.359
10.1016/j.commatsci.2012.08.043
10.2514/1.25046
10.1007/s00158-009-0382-4
10.1016/0021-9991(88)90002-2
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Keywords BESO
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Large deflection
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References Huang, Zhou, Xie, Li (b0065) 2013; 67
Huang, Xie (b0060) 2010; 40
Andreassen, Clausen, Schevenels, Lazarov, Sigmund (b0005) 2011; 43
Bendsøe (b0010) 1989; 1
Huang, Xie (b0035) 2007; 43
Huang, Xie (b0140) 2010
Wang, Wang, Guo (b0105) 2003; 192
Sigmund (b0095) 2001; 21
Challis (b0025) 2010; 41
Liu, Tovar (b0075) 2014
Zuo, Xie, Huang (b0135) 2012; 15
Huang, Xie (b0050) 2010; 41
Huang, Xie (b0040) 2007; 45
Osher, Sethian (b0080) 1988; 79
Yang, Huang, Rong, Xie (b0120) 2013; 67
Sigmund (b0090) 1995; 20
Huang, Zuo, Xie (b0070) 2010; 88
Dassault Systemes; 2014.
.
Xie, Steven (b0110) 1993; 49
Radman, Huang, Xie (b0085) 2014; 82
Buhl, Pedersen, Sigmund (b0020) 2000; 19
Huang, Xie (b0045) 2009; 43
Sigmund, Peterson (b0100) 1998; 16
Xie, Steven (b0115) 1997
Bendsøe, Sigmund (b0015) 2003
Zuo, Huang, Rong, Xie (b0130) 2013; 51
Zhou, Rozvany (b0125) 1991; 89
Sigmund (10.1016/j.advengsoft.2015.02.006_b0095) 2001; 21
Xie (10.1016/j.advengsoft.2015.02.006_b0110) 1993; 49
Huang (10.1016/j.advengsoft.2015.02.006_b0050) 2010; 41
Wang (10.1016/j.advengsoft.2015.02.006_b0105) 2003; 192
Radman (10.1016/j.advengsoft.2015.02.006_b0085) 2014; 82
Zuo (10.1016/j.advengsoft.2015.02.006_b0135) 2012; 15
Huang (10.1016/j.advengsoft.2015.02.006_b0045) 2009; 43
Challis (10.1016/j.advengsoft.2015.02.006_b0025) 2010; 41
Huang (10.1016/j.advengsoft.2015.02.006_b0140) 2010
Andreassen (10.1016/j.advengsoft.2015.02.006_b0005) 2011; 43
Huang (10.1016/j.advengsoft.2015.02.006_b0060) 2010; 40
Buhl (10.1016/j.advengsoft.2015.02.006_b0020) 2000; 19
Huang (10.1016/j.advengsoft.2015.02.006_b0070) 2010; 88
Huang (10.1016/j.advengsoft.2015.02.006_b0065) 2013; 67
Yang (10.1016/j.advengsoft.2015.02.006_b0120) 2013; 67
Bendsøe (10.1016/j.advengsoft.2015.02.006_b0010) 1989; 1
Osher (10.1016/j.advengsoft.2015.02.006_b0080) 1988; 79
Liu (10.1016/j.advengsoft.2015.02.006_b0075) 2014
Huang (10.1016/j.advengsoft.2015.02.006_b0040) 2007; 45
Sigmund (10.1016/j.advengsoft.2015.02.006_b0090) 1995; 20
Sigmund (10.1016/j.advengsoft.2015.02.006_b0100) 1998; 16
Bendsøe (10.1016/j.advengsoft.2015.02.006_b0015) 2003
Huang (10.1016/j.advengsoft.2015.02.006_b0035) 2007; 43
Xie (10.1016/j.advengsoft.2015.02.006_b0115) 1997
Zhou (10.1016/j.advengsoft.2015.02.006_b0125) 1991; 89
10.1016/j.advengsoft.2015.02.006_b0030
Zuo (10.1016/j.advengsoft.2015.02.006_b0130) 2013; 51
References_xml – volume: 19
  start-page: 93
  year: 2000
  end-page: 104
  ident: b0020
  article-title: Stiffness design of geometrically nonlinear structures using topology optimization
  publication-title: Struct Multidisc Optim
– volume: 67
  start-page: 397
  year: 2013
  end-page: 407
  ident: b0065
  article-title: Topology optimization of microstructures of cellular materials and composites for macrostructures
  publication-title: Comput Mater Sci
– volume: 82
  start-page: 457
  year: 2014
  end-page: 463
  ident: b0085
  article-title: Maximizing stiffness of functionally graded materials with prescribed variation of thermal conductivity
  publication-title: Comput Mater Sci
– volume: 89
  start-page: 197
  year: 1991
  end-page: 224
  ident: b0125
  article-title: The COC algorithm, Part II: topological, geometry and generalized shape optimization
  publication-title: Comp Methods Appl Mech Eng
– volume: 40
  start-page: 409
  year: 2010
  end-page: 416
  ident: b0060
  article-title: Evolutionary topology optimization of continuum structures with an additional displacement constraint
  publication-title: Struct Multidisc Optim
– volume: 43
  start-page: 1
  year: 2011
  end-page: 16
  ident: b0005
  article-title: Efficient topology optimization in Matlab using 88 lines of code
  publication-title: Struct Multidisc Optim
– volume: 20
  start-page: 351
  year: 1995
  end-page: 368
  ident: b0090
  article-title: Tailoring materials with prescribed elastic properties
  publication-title: Mech Mater
– year: 2003
  ident: b0015
  article-title: Topology optimization: theory, methods and applications
– volume: 41
  start-page: 453
  year: 2010
  end-page: 464
  ident: b0025
  article-title: A discrete level-set topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim
– volume: 16
  start-page: 68
  year: 1998
  end-page: 75
  ident: b0100
  article-title: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima
  publication-title: Struct Optim
– volume: 88
  start-page: 357
  year: 2010
  end-page: 364
  ident: b0070
  article-title: Evolutionary topological optimization of vibrating continuum structures for natural frequencies
  publication-title: Comput Struct
– volume: 41
  start-page: 671
  year: 2010
  end-page: 683
  ident: b0050
  article-title: A further review of ESO type methods for topology optimization
  publication-title: Struct Multidisc Optim
– year: 1997
  ident: b0115
  article-title: Evolutionary structural optimization
– reference: >.
– volume: 43
  start-page: 1039
  year: 2007
  end-page: 1049
  ident: b0035
  article-title: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method
  publication-title: Finite Elem Anal Des
– volume: 21
  start-page: 120
  year: 2001
  end-page: 127
  ident: b0095
  article-title: A 99 line topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim
– volume: 192
  start-page: 227
  year: 2003
  end-page: 246
  ident: b0105
  article-title: A level set method for structural topology optimization
  publication-title: Comput Methods Appl Mech Eng
– volume: 67
  start-page: 229
  year: 2013
  end-page: 237
  ident: b0120
  article-title: Design of 3D orthotropic materials with prescribed ratios for effective Young’s moduli
  publication-title: Comput Mater Sci
– volume: 45
  start-page: 308
  year: 2007
  end-page: 313
  ident: b0040
  article-title: Bidirectional evolutionary topology optimization for structures with geometrical and material nonlinearities
  publication-title: AIAA J
– reference: Dassault Systemes; 2014. <
– volume: 51
  start-page: 1023
  year: 2013
  end-page: 1034
  ident: b0130
  article-title: Multi-scale design of composite materials and structures for maximum natural frequencies
  publication-title: Mater Des
– volume: 49
  start-page: 885
  year: 1993
  end-page: 896
  ident: b0110
  article-title: A simple evolutionary procedure for structural optimization
  publication-title: Comput Struct
– volume: 43
  start-page: 393
  year: 2009
  end-page: 401
  ident: b0045
  article-title: Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials
  publication-title: Comput Mech
– volume: 79
  start-page: 12
  year: 1988
  end-page: 49
  ident: b0080
  article-title: Fronts propagating with curvature dependent speed: algorithms based on the Hamilton-Jacobi formulation
  publication-title: J Comput Phys
– volume: 1
  start-page: 193
  year: 1989
  end-page: 202
  ident: b0010
  article-title: Optimal shape design as a material distribution problem
  publication-title: Struct Optim
– volume: 15
  start-page: 385
  year: 2012
  end-page: 398
  ident: b0135
  article-title: Evolutionary topology optimization of structures with multiple displacement and frequency constraints
  publication-title: Adv Struct Eng
– year: 2014
  ident: b0075
  article-title: An efficient 3D topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim (online)
– year: 2010
  ident: b0140
  article-title: Evolutionary topology optimization of continuum structures: methods and applications
– volume: 67
  start-page: 397
  year: 2013
  ident: 10.1016/j.advengsoft.2015.02.006_b0065
  article-title: Topology optimization of microstructures of cellular materials and composites for macrostructures
  publication-title: Comput Mater Sci
  doi: 10.1016/j.commatsci.2012.09.018
– year: 2014
  ident: 10.1016/j.advengsoft.2015.02.006_b0075
  article-title: An efficient 3D topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim (online)
  doi: 10.1007/s00158-014-1107-x
– volume: 41
  start-page: 453
  year: 2010
  ident: 10.1016/j.advengsoft.2015.02.006_b0025
  article-title: A discrete level-set topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0430-0
– year: 2010
  ident: 10.1016/j.advengsoft.2015.02.006_b0140
– volume: 21
  start-page: 120
  year: 2001
  ident: 10.1016/j.advengsoft.2015.02.006_b0095
  article-title: A 99 line topology optimization code written in Matlab
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s001580050176
– volume: 43
  start-page: 1039
  year: 2007
  ident: 10.1016/j.advengsoft.2015.02.006_b0035
  article-title: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method
  publication-title: Finite Elem Anal Des
  doi: 10.1016/j.finel.2007.06.006
– volume: 43
  start-page: 1
  issue: 1
  year: 2011
  ident: 10.1016/j.advengsoft.2015.02.006_b0005
  article-title: Efficient topology optimization in Matlab using 88 lines of code
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-010-0594-7
– volume: 89
  start-page: 197
  year: 1991
  ident: 10.1016/j.advengsoft.2015.02.006_b0125
  article-title: The COC algorithm, Part II: topological, geometry and generalized shape optimization
  publication-title: Comp Methods Appl Mech Eng
  doi: 10.1016/0045-7825(91)90046-9
– volume: 88
  start-page: 357
  year: 2010
  ident: 10.1016/j.advengsoft.2015.02.006_b0070
  article-title: Evolutionary topological optimization of vibrating continuum structures for natural frequencies
  publication-title: Comput Struct
  doi: 10.1016/j.compstruc.2009.11.011
– volume: 41
  start-page: 671
  year: 2010
  ident: 10.1016/j.advengsoft.2015.02.006_b0050
  article-title: A further review of ESO type methods for topology optimization
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-010-0487-9
– volume: 43
  start-page: 393
  year: 2009
  ident: 10.1016/j.advengsoft.2015.02.006_b0045
  article-title: Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials
  publication-title: Comput Mech
  doi: 10.1007/s00466-008-0312-0
– year: 1997
  ident: 10.1016/j.advengsoft.2015.02.006_b0115
– volume: 192
  start-page: 227
  year: 2003
  ident: 10.1016/j.advengsoft.2015.02.006_b0105
  article-title: A level set method for structural topology optimization
  publication-title: Comput Methods Appl Mech Eng
  doi: 10.1016/S0045-7825(02)00559-5
– volume: 19
  start-page: 93
  year: 2000
  ident: 10.1016/j.advengsoft.2015.02.006_b0020
  article-title: Stiffness design of geometrically nonlinear structures using topology optimization
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s001580050089
– volume: 16
  start-page: 68
  year: 1998
  ident: 10.1016/j.advengsoft.2015.02.006_b0100
  article-title: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima
  publication-title: Struct Optim
  doi: 10.1007/BF01214002
– volume: 20
  start-page: 351
  year: 1995
  ident: 10.1016/j.advengsoft.2015.02.006_b0090
  article-title: Tailoring materials with prescribed elastic properties
  publication-title: Mech Mater
  doi: 10.1016/0167-6636(94)00069-7
– volume: 82
  start-page: 457
  year: 2014
  ident: 10.1016/j.advengsoft.2015.02.006_b0085
  article-title: Maximizing stiffness of functionally graded materials with prescribed variation of thermal conductivity
  publication-title: Comput Mater Sci
  doi: 10.1016/j.commatsci.2013.10.024
– volume: 51
  start-page: 1023
  year: 2013
  ident: 10.1016/j.advengsoft.2015.02.006_b0130
  article-title: Multi-scale design of composite materials and structures for maximum natural frequencies
  publication-title: Mater Des
  doi: 10.1016/j.matdes.2013.05.014
– year: 2003
  ident: 10.1016/j.advengsoft.2015.02.006_b0015
– ident: 10.1016/j.advengsoft.2015.02.006_b0030
– volume: 1
  start-page: 193
  year: 1989
  ident: 10.1016/j.advengsoft.2015.02.006_b0010
  article-title: Optimal shape design as a material distribution problem
  publication-title: Struct Optim
  doi: 10.1007/BF01650949
– volume: 49
  start-page: 885
  issue: 5
  year: 1993
  ident: 10.1016/j.advengsoft.2015.02.006_b0110
  article-title: A simple evolutionary procedure for structural optimization
  publication-title: Comput Struct
  doi: 10.1016/0045-7949(93)90035-C
– volume: 15
  start-page: 385
  issue: 2
  year: 2012
  ident: 10.1016/j.advengsoft.2015.02.006_b0135
  article-title: Evolutionary topology optimization of structures with multiple displacement and frequency constraints
  publication-title: Adv Struct Eng
  doi: 10.1260/1369-4332.15.2.359
– volume: 67
  start-page: 229
  year: 2013
  ident: 10.1016/j.advengsoft.2015.02.006_b0120
  article-title: Design of 3D orthotropic materials with prescribed ratios for effective Young’s moduli
  publication-title: Comput Mater Sci
  doi: 10.1016/j.commatsci.2012.08.043
– volume: 45
  start-page: 308
  issue: 1
  year: 2007
  ident: 10.1016/j.advengsoft.2015.02.006_b0040
  article-title: Bidirectional evolutionary topology optimization for structures with geometrical and material nonlinearities
  publication-title: AIAA J
  doi: 10.2514/1.25046
– volume: 40
  start-page: 409
  year: 2010
  ident: 10.1016/j.advengsoft.2015.02.006_b0060
  article-title: Evolutionary topology optimization of continuum structures with an additional displacement constraint
  publication-title: Struct Multidisc Optim
  doi: 10.1007/s00158-009-0382-4
– volume: 79
  start-page: 12
  year: 1988
  ident: 10.1016/j.advengsoft.2015.02.006_b0080
  article-title: Fronts propagating with curvature dependent speed: algorithms based on the Hamilton-Jacobi formulation
  publication-title: J Comput Phys
  doi: 10.1016/0021-9991(88)90002-2
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Snippet This paper presents a 100-line Python code for general 3D topology optimization. The code adopts the Abaqus Scripting Interface that provides convenient access...
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SubjectTerms Abaqus
BESO
Computer simulation
Design engineering
Finite element method
Large deflection
Mathematical models
NumPy
Optimization
Python
Three dimensional
Topology optimization
Title A simple and compact Python code for complex 3D topology optimization
URI https://dx.doi.org/10.1016/j.advengsoft.2015.02.006
https://www.proquest.com/docview/1770291984
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