Skip to main content
Erschienen in: Structural and Multidisciplinary Optimization 5/2019

23.11.2018 | Educational Article

A 213-line topology optimization code for geometrically nonlinear structures

verfasst von: Qi Chen, Xianmin Zhang, Benliang Zhu

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 5/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper presents a 213-line MATLAB code for topology optimization of geometrically nonlinear structures. It is developed based on the density method. The code adopts the ANSYS parametric design language (APDL) that provides convenient access to advanced finite element analysis (FEA). An additive hyperelasticity technique is employed to circumvent numerical difficulties in solving the material density-based topology optimization of elastic structures undergoing large displacements. The sensitivity information is obtained by extracting the increment of the element strain energy. The validity of the code is demonstrated by the minimum compliance problem and the compliant inverter problem.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
Zurück zum Zitat 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):1–16CrossRefMATH 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):1–16CrossRefMATH
Zurück zum Zitat Bruns T E, Sigmund O, Tortorelli DA (2002) Numerical methods for the topology optimization of structures that exhibit snap-through. Int J Numer Methods Eng 55(10):1215–1237CrossRefMATH Bruns T E, Sigmund O, Tortorelli DA (2002) Numerical methods for the topology optimization of structures that exhibit snap-through. Int J Numer Methods Eng 55(10):1215–1237CrossRefMATH
Zurück zum Zitat Bruns TE, Tortorelli DA (2003) An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int J Numer Methods Eng 57(10):1413–1430CrossRefMATH Bruns TE, Tortorelli DA (2003) An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int J Numer Methods Eng 57(10):1413–1430CrossRefMATH
Zurück zum Zitat Bruns T E, Sigmund Ole (2004) Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng 193(36-38):3973–4000MathSciNetCrossRefMATH Bruns T E, Sigmund Ole (2004) Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng 193(36-38):3973–4000MathSciNetCrossRefMATH
Zurück zum Zitat Buhl T, Pedersen C BW, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19(2):93–104CrossRef Buhl T, Pedersen C BW, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19(2):93–104CrossRef
Zurück zum Zitat Chen F, Wang Y, Wang MY, Zhang YF (2017) Topology optimization of hyperelastic structures using a level set method. J Comput Phys 351:437–454MathSciNetCrossRef Chen F, Wang Y, Wang MY, Zhang YF (2017) Topology optimization of hyperelastic structures using a level set method. J Comput Phys 351:437–454MathSciNetCrossRef
Zurück zum Zitat Cho S, Jung H-S (2003) Design sensitivity analysis and topology optimization of displacement–loaded non-linear structures. Comput Methods Appl Mech Eng 192(22-24):2539–2553CrossRefMATH Cho S, Jung H-S (2003) Design sensitivity analysis and topology optimization of displacement–loaded non-linear structures. Comput Methods Appl Mech Eng 192(22-24):2539–2553CrossRefMATH
Zurück zum Zitat Huang X, Xie Y M (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30(7):2057–2068CrossRef Huang X, Xie Y M (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30(7):2057–2068CrossRef
Zurück zum Zitat Huang XH, Xie Y (2007) Bidirectional evolutionary topology optimization for structures with geometrical and material nonlinearities. AIAA J 45(1):308–313CrossRef Huang XH, Xie Y (2007) Bidirectional evolutionary topology optimization for structures with geometrical and material nonlinearities. AIAA J 45(1):308–313CrossRef
Zurück zum Zitat Huang X, Xie Y-M (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683CrossRef Huang X, Xie Y-M (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683CrossRef
Zurück zum Zitat James KA, Waisman H (2016) Layout design of a bi-stable cardiovascular stent using topology optimization. Comput Methods Appl Mech Eng 305:869–890MathSciNetCrossRef James KA, Waisman H (2016) Layout design of a bi-stable cardiovascular stent using topology optimization. Comput Methods Appl Mech Eng 305:869–890MathSciNetCrossRef
Zurück zum Zitat Klarbring A, Strömberg N (2013) Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidiscip Optim 47(1):37–48MathSciNetCrossRefMATH Klarbring A, Strömberg N (2013) Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidiscip Optim 47(1):37–48MathSciNetCrossRefMATH
Zurück zum Zitat Kuhl E, Askes H, Steinmann P (2006) An illustration of the equivalence of the loss of ellipticity conditions in spatial and material settings of hyperelasticity. Eur J Mech-A/Solids 25(2):199–214MathSciNetCrossRefMATH Kuhl E, Askes H, Steinmann P (2006) An illustration of the equivalence of the loss of ellipticity conditions in spatial and material settings of hyperelasticity. Eur J Mech-A/Solids 25(2):199–214MathSciNetCrossRefMATH
Zurück zum Zitat Lahuerta RD, Simões ET, Campello EMB, Pimenta PM, Silva ECN (2013) Towards the stabilization of the low density elements in topology optimization with large deformation. Comput Mech 52(4):779–797MathSciNetCrossRefMATH Lahuerta RD, Simões ET, Campello EMB, Pimenta PM, Silva ECN (2013) Towards the stabilization of the low density elements in topology optimization with large deformation. Comput Mech 52(4):779–797MathSciNetCrossRefMATH
Zurück zum Zitat Lee H-A, Park G-J (2012) Topology optimization for structures with nonlinear behavior using the equivalent static loads method. J Mech Des 134(3):031004CrossRef Lee H-A, Park G-J (2012) Topology optimization for structures with nonlinear behavior using the equivalent static loads method. J Mech Des 134(3):031004CrossRef
Zurück zum Zitat Liu K, Tovar A (2014) An efficient 3D topology optimization code written in Matlab. Struct Multidiscip Optim 50(6):1175–1196MathSciNetCrossRef Liu K, Tovar A (2014) An efficient 3D topology optimization code written in Matlab. Struct Multidiscip Optim 50(6):1175–1196MathSciNetCrossRef
Zurück zum Zitat Luo Y, Wang MY, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRefMATH Luo Y, Wang MY, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRefMATH
Zurück zum Zitat Qi C, Zhang X, Zhu B (2018a) Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization. Struct Multidiscip Optim 58(4):1395–1410MathSciNetCrossRef Qi C, Zhang X, Zhu B (2018a) Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization. Struct Multidiscip Optim 58(4):1395–1410MathSciNetCrossRef
Zurück zum Zitat Qi C, Zhang X, Zhu B (2018b) Topology optimization of fusiform muscles with a maximum contraction. Int J Numer Meth Biomed Engng 34:e3096MathSciNetCrossRef Qi C, Zhang X, Zhu B (2018b) Topology optimization of fusiform muscles with a maximum contraction. Int J Numer Meth Biomed Engng 34:e3096MathSciNetCrossRef
Zurück zum Zitat Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127CrossRef Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127CrossRef
Zurück zum Zitat Svanberg K (1987) The method of moving asymptotes<aa new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH Svanberg K (1987) The method of moving asymptotes<aa new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATH
Zurück zum Zitat 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):329–357MathSciNetCrossRefMATH 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):329–357MathSciNetCrossRefMATH
Zurück zum Zitat Tavakoli R, Mohseni SM (2014) Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line Matlab implementation. Struct Multidiscip Optim 49(4):621–642MathSciNetCrossRef Tavakoli R, Mohseni SM (2014) Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line Matlab implementation. Struct Multidiscip Optim 49(4):621–642MathSciNetCrossRef
Zurück zum Zitat Tran AV, Zhang X, Zhu B (2018) The development of a new piezoresistive pressure sensor for low pressures. IEEE Trans Ind Electron 65(8):6487–6496CrossRef Tran AV, Zhang X, Zhu B (2018) The development of a new piezoresistive pressure sensor for low pressures. IEEE Trans Ind Electron 65(8):6487–6496CrossRef
Zurück zum Zitat van Dijk NP , Langelaar M, van Keulen F (2014) Element deformation scaling for robust geometrically nonlinear analyses in topology optimization. Struct Multidiscip Optim 50(4):537–560MathSciNetCrossRef van Dijk NP , Langelaar M, van Keulen F (2014) Element deformation scaling for robust geometrically nonlinear analyses in topology optimization. Struct Multidiscip Optim 50(4):537–560MathSciNetCrossRef
Zurück zum Zitat Vivien J (2010) Challis. a discrete level-set topology optimization code written in Matlab. Struct Multidiscip Optim 41(3):453–464MathSciNetCrossRefMATH Vivien J (2010) Challis. a discrete level-set topology optimization code written in Matlab. Struct Multidiscip Optim 41(3):453–464MathSciNetCrossRefMATH
Zurück zum Zitat Wallin M, Ivarsson N, Tortorelli D (2018) Stiffness optimization of non-linear elastic structures. Comput Methods Appl Mech Eng 330:292–307MathSciNetCrossRef Wallin M, Ivarsson N, Tortorelli D (2018) Stiffness optimization of non-linear elastic structures. Comput Methods Appl Mech Eng 330:292–307MathSciNetCrossRef
Zurück zum Zitat Wang F, Lazarov BS, Sigmund O, Jensen JS (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472MathSciNetCrossRefMATH Wang F, Lazarov BS, Sigmund O, Jensen JS (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472MathSciNetCrossRefMATH
Zurück zum Zitat Wang N, Guo H, Chen B, Cui C, Zhang X (2018) Design of a rotary dielectric elastomer actuator using a topology optimization method based on pairs of curves. Smart Mater Struct 27(5):055011CrossRef Wang N, Guo H, Chen B, Cui C, Zhang X (2018) Design of a rotary dielectric elastomer actuator using a topology optimization method based on pairs of curves. Smart Mater Struct 27(5):055011CrossRef
Zurück zum Zitat 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(2):831–849MathSciNetCrossRef 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(2):831–849MathSciNetCrossRef
Zurück zum Zitat Yoon GH, Kim YY (2005) Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int J Solids Struct 42(7):1983–2009MathSciNetCrossRefMATH Yoon GH, Kim YY (2005) Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int J Solids Struct 42(7):1983–2009MathSciNetCrossRefMATH
Zurück zum Zitat Yoon GH, Joung YS, Kim YY (2007) Optimal layout design of three-dimensional geometrically non-linear structures using the element connectivity parameterization method. Int J Numer Methods Eng 69(6):1278–1304CrossRefMATH Yoon GH, Joung YS, Kim YY (2007) Optimal layout design of three-dimensional geometrically non-linear structures using the element connectivity parameterization method. Int J Numer Methods Eng 69(6):1278–1304CrossRefMATH
Zurück zum Zitat Zhang W, Yuan J, Zhang J, Xu G (2016) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim 53(6):1243–1260MathSciNetCrossRef Zhang W, Yuan J, Zhang J, Xu G (2016) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim 53(6):1243–1260MathSciNetCrossRef
Zurück zum Zitat Zhu B, Zhang X, Zhang Y, Fatikow S (2017) Design of diaphragm structure for piezoresistive pressure sensor using topology optimization. Struct Multidiscip Optim 55(1):317–329MathSciNetCrossRef Zhu B, Zhang X, Zhang Y, Fatikow S (2017) Design of diaphragm structure for piezoresistive pressure sensor using topology optimization. Struct Multidiscip Optim 55(1):317–329MathSciNetCrossRef
Zurück zum Zitat Zuo ZH, Yi MX (2015) A simple and compact python code for complex 3D topology optimization. Adv Eng Softw 85:1–11CrossRef Zuo ZH, Yi MX (2015) A simple and compact python code for complex 3D topology optimization. Adv Eng Softw 85:1–11CrossRef
Metadaten
Titel
A 213-line topology optimization code for geometrically nonlinear structures
verfasst von
Qi Chen
Xianmin Zhang
Benliang Zhu
Publikationsdatum
23.11.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 5/2019
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-018-2138-5

Weitere Artikel der Ausgabe 5/2019

Structural and Multidisciplinary Optimization 5/2019 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.