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Erschienen in: Structural and Multidisciplinary Optimization 2/2017

28.06.2016 | RESEARCH PAPER

Evolutionary topology optimization of elastoplastic structures

verfasst von: Liang Xia, Felix Fritzen, Piotr Breitkopf

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 2/2017

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Abstract

We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106(6):430–453, 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

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Literatur
Zurück zum Zitat Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetCrossRefMATH Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393MathSciNetCrossRefMATH
Zurück zum Zitat Bendsøe M, Sokolowsk J (1987) Sensitivity analysis and optimization of elastic-plastic structures. Eng Optim 11(1-2):31–38CrossRef Bendsøe M, Sokolowsk J (1987) Sensitivity analysis and optimization of elastic-plastic structures. Eng Optim 11(1-2):31–38CrossRef
Zurück zum Zitat Bendsøe M, Guedes J, Plaxton S, Taylor J (1996) Optimization of structure and material properties for solids composed of softening material. Int J Solids Struct 33(12):1799–1813MathSciNetCrossRefMATH Bendsøe M, Guedes J, Plaxton S, Taylor J (1996) Optimization of structure and material properties for solids composed of softening material. Int J Solids Struct 33(12):1799–1813MathSciNetCrossRefMATH
Zurück zum Zitat Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRef Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRef
Zurück zum Zitat Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH
Zurück zum Zitat Bendsøe MP, Sigmund O (2003) Topology optimization: theory methods and applications. Springer, BerlinMATH Bendsøe MP, Sigmund O (2003) Topology optimization: theory methods and applications. Springer, BerlinMATH
Zurück zum Zitat Bogomolny M, Amir O (2012) Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling. Int J Numer Methods Eng 90(13):1578– 1597CrossRefMATH Bogomolny M, Amir O (2012) Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling. Int J Numer Methods Eng 90(13):1578– 1597CrossRefMATH
Zurück zum Zitat Bruns T, Tortorelli D (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 T, Tortorelli D (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 Buhl T, Pedersen C, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19(2):93–104CrossRef Buhl T, Pedersen C, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19(2):93–104CrossRef
Zurück zum Zitat Burger M, Hackl B, Ring W (2004) Incorporating topological derivatives into level set methods. J Comput Phys 194(1):344–362MathSciNetCrossRefMATH Burger M, Hackl B, Ring W (2004) Incorporating topological derivatives into level set methods. J Comput Phys 194(1):344–362MathSciNetCrossRefMATH
Zurück zum Zitat Challis VJ (2010) A discrete level-set topology optimization code written in matlab. Struct Multidiscip Optim 41(3):453–464MathSciNetCrossRefMATH Challis VJ (2010) A discrete level-set topology optimization code written in matlab. Struct Multidiscip Optim 41(3):453–464MathSciNetCrossRefMATH
Zurück zum Zitat Cho S, Jung HS (2003) Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures. Comput Methods Appl Mech Eng 192(22-23):2539–2553CrossRefMATH Cho S, Jung HS (2003) Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures. Comput Methods Appl Mech Eng 192(22-23):2539–2553CrossRefMATH
Zurück zum Zitat Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38MathSciNetCrossRef Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38MathSciNetCrossRef
Zurück zum Zitat Fritzen F, Leuschner M (2013) Reduced basis hybrid computational homogenization based on a mixed incremental formulation. Comput Methods Appl Mech Eng 260:143–154MathSciNetCrossRefMATH Fritzen F, Leuschner M (2013) Reduced basis hybrid computational homogenization based on a mixed incremental formulation. Comput Methods Appl Mech Eng 260:143–154MathSciNetCrossRefMATH
Zurück zum Zitat Fritzen F, Hodapp M, Leuschner M (2014) Gpu accelerated computational homogenization based on a variational approach in a reduced basis framework. Comput Methods Appl Mech Eng 278:186–217MathSciNetCrossRef Fritzen F, Hodapp M, Leuschner M (2014) Gpu accelerated computational homogenization based on a variational approach in a reduced basis framework. Comput Methods Appl Mech Eng 278:186–217MathSciNetCrossRef
Zurück zum Zitat Fritzen F, Xia L, Leuschner M, Breitkopf P (2016) Topology optimization of multiscale elastoviscoplastic structures. Int J Numer Methods Eng 106:430–453MathSciNetCrossRefMATH Fritzen F, Xia L, Leuschner M, Breitkopf P (2016) Topology optimization of multiscale elastoviscoplastic structures. Int J Numer Methods Eng 106:430–453MathSciNetCrossRefMATH
Zurück zum Zitat Gea H, Luo J (2001) Topology optimization of structures with geometrical nonlinearities. Comput Struct 79(20-21):1977–1985CrossRef Gea H, Luo J (2001) Topology optimization of structures with geometrical nonlinearities. Comput Struct 79(20-21):1977–1985CrossRef
Zurück zum Zitat Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically-a new Moving Morphable Components based framework. J Appl Mech Trans ASME 81(8) Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically-a new Moving Morphable Components based framework. J Appl Mech Trans ASME 81(8)
Zurück zum Zitat Huang X, Xie Y (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049CrossRef Huang X, Xie Y (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049CrossRef
Zurück zum Zitat Huang X, Xie Y (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30(7):2057–2068CrossRef Huang X, Xie Y (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30(7):2057–2068CrossRef
Zurück zum Zitat Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401MathSciNetCrossRefMATH Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401MathSciNetCrossRefMATH
Zurück zum Zitat Huang X, Xie YM (2010a) Evolutionary topology optimization of continuum structures: methods and applications. Wiley, ChichesterCrossRefMATH Huang X, Xie YM (2010a) Evolutionary topology optimization of continuum structures: methods and applications. Wiley, ChichesterCrossRefMATH
Zurück zum Zitat Huang X, Xie YM (2010b) A further review of ESO type methods for topology optimization. Struct. Multidiscip. Optim. 41(5):671– 683CrossRef Huang X, Xie YM (2010b) A further review of ESO type methods for topology optimization. Struct. Multidiscip. Optim. 41(5):671– 683CrossRef
Zurück zum Zitat Huang X, Xie Y, Lu G (2007) Topology optimization of energy-absorbing structures. Int J Crashworthiness 12(6):663–675CrossRef Huang X, Xie Y, Lu G (2007) Topology optimization of energy-absorbing structures. Int J Crashworthiness 12(6):663–675CrossRef
Zurück zum Zitat Huang X, Zhou S, Sun G, Li G, Xie Y (2015) Topology optimization for microstructures of viscoelastic composite materials. Comput Methods Appl Mech Eng 283:503–516CrossRef Huang X, Zhou S, Sun G, Li G, Xie Y (2015) Topology optimization for microstructures of viscoelastic composite materials. Comput Methods Appl Mech Eng 283:503–516CrossRef
Zurück zum Zitat Jung D, Gea H (2004) Topology optimization of nonlinear structures. Finite Elem Anal Des 40(11):1417–1427CrossRef Jung D, Gea H (2004) Topology optimization of nonlinear structures. Finite Elem Anal Des 40(11):1417–1427CrossRef
Zurück zum Zitat Kato J, Hoshiba H, Takase S, Terada K, Kyoya T (2015) Analytical sensitivity in topology optimization for elastoplastic composites. Struct Multidiscip Optim. doi:10.1007/s00158-015-1246-8, article in Press Kato J, Hoshiba H, Takase S, Terada K, Kyoya T (2015) Analytical sensitivity in topology optimization for elastoplastic composites. Struct Multidiscip Optim. doi:10.​1007/​s00158-015-1246-8, article in Press
Zurück zum Zitat Luo Y, Wang M, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRef Luo Y, Wang M, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRef
Zurück zum Zitat Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91CrossRef Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91CrossRef
Zurück zum Zitat Michaleris P, Tortorelli D A, Vidal C A (1994) Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. Int J Numer Methods Eng 37(14):2471–2499CrossRefMATH Michaleris P, Tortorelli D A, Vidal C A (1994) Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. Int J Numer Methods Eng 37(14):2471–2499CrossRefMATH
Zurück zum Zitat Pedersen C, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50(12):2683–2705CrossRefMATH Pedersen C, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50(12):2683–2705CrossRefMATH
Zurück zum Zitat Schwarz S, Maute K, Ramm E (2001) Topology and shape optimization for elastoplastic structural response. Comput Methods Appl Mech Eng 190(15-17):2135–2155CrossRefMATH Schwarz S, Maute K, Ramm E (2001) Topology and shape optimization for elastoplastic structural response. Comput Methods Appl Mech Eng 190(15-17):2135–2155CrossRefMATH
Zurück zum Zitat Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefMATH Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528MathSciNetCrossRefMATH
Zurück zum Zitat Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127MathSciNetCrossRef Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21 (2):120–127MathSciNetCrossRef
Zurück zum Zitat Sigmund O, Maute K (2013) Topology optimization approaches - a comparative review. Struct Multidiscip Optim 48(6):1031– 1055MathSciNetCrossRef Sigmund O, Maute K (2013) Topology optimization approaches - a comparative review. Struct Multidiscip Optim 48(6):1031– 1055MathSciNetCrossRef
Zurück zum Zitat Wang F, Lazarov B, Sigmund O, Jensen J (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472MathSciNetCrossRef Wang F, Lazarov B, Sigmund O, Jensen J (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472MathSciNetCrossRef
Zurück zum Zitat Wang M Y, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1-2):227–246MathSciNetCrossRefMATH Wang M Y, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1-2):227–246MathSciNetCrossRefMATH
Zurück zum Zitat Wei P, Wang M, Xing X (2010) A study on x-FEM in continuum structural optimization using a level set model. CAD Comput Aided Des 42(8):708–719CrossRef Wei P, Wang M, Xing X (2010) A study on x-FEM in continuum structural optimization using a level set model. CAD Comput Aided Des 42(8):708–719CrossRef
Zurück zum Zitat Xia L, Breitkopf P (2014a) Concurrent topology optimization design of material and structure within FE 2 nonlinear multiscale analysis framework. Comput. Methods Appl. Mech. Eng. 278:524–542CrossRef Xia L, Breitkopf P (2014a) Concurrent topology optimization design of material and structure within FE 2 nonlinear multiscale analysis framework. Comput. Methods Appl. Mech. Eng. 278:524–542CrossRef
Zurück zum Zitat Xia L, Breitkopf P (2014b) A reduced multiscale model for nonlinear structural topology optimization. Comput. Methods Appl. Mech. Eng. 280:117–134MathSciNetCrossRef Xia L, Breitkopf P (2014b) A reduced multiscale model for nonlinear structural topology optimization. Comput. Methods Appl. Mech. Eng. 280:117–134MathSciNetCrossRef
Zurück zum Zitat Xia L, Breitkopf P (2015) Multiscale structural topology optimization with an approximate constitutive model for local material microstructure. Comput Methods Appl Mech Eng 286:147–167MathSciNetCrossRef Xia L, Breitkopf P (2015) Multiscale structural topology optimization with an approximate constitutive model for local material microstructure. Comput Methods Appl Mech Eng 286:147–167MathSciNetCrossRef
Zurück zum Zitat Xia Q, Shi T (2015) Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization. Comput Methods Appl Mech Eng 295:525–542MathSciNetCrossRef Xia Q, Shi T (2015) Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization. Comput Methods Appl Mech Eng 295:525–542MathSciNetCrossRef
Zurück zum Zitat Xia Q, Shi T, Liu S, Wang M (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90-91:55–64CrossRef Xia Q, Shi T, Liu S, Wang M (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90-91:55–64CrossRef
Zurück zum Zitat Xia Q, Wang M, Shi T (2014) A level set method for shape and topology optimization of both structure and support of continuum structures. Comput Methods Appl Mech Eng 272:340–353MathSciNetCrossRefMATH Xia Q, Wang M, Shi T (2014) A level set method for shape and topology optimization of both structure and support of continuum structures. Comput Methods Appl Mech Eng 272:340–353MathSciNetCrossRefMATH
Zurück zum Zitat Xia Q, Wang M, Shi T (2015) Topology optimization with pressure load through a level set method. Comput Methods Appl Mech Eng 283:177–195MathSciNetCrossRef Xia Q, Wang M, Shi T (2015) Topology optimization with pressure load through a level set method. Comput Methods Appl Mech Eng 283:177–195MathSciNetCrossRef
Zurück zum Zitat Xie Y M, Steven G P (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896CrossRef Xie Y M, Steven G P (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896CrossRef
Zurück zum Zitat Yoon G, Kim Y (2005) Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int J Solids Struct 42(7):1983–2009MathSciNetCrossRefMATH Yoon G, Kim Y (2005) Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int J Solids Struct 42(7):1983–2009MathSciNetCrossRefMATH
Zurück zum Zitat Yoon G, Kim Y (2007) Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization. Int J Numer Methods Eng 69(10):2196–2218MathSciNetCrossRefMATH Yoon G, Kim Y (2007) Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization. Int J Numer Methods Eng 69(10):2196–2218MathSciNetCrossRefMATH
Zurück zum Zitat Yuge K, Kikuchi N (1995) Optimization of a frame structure subjected to a plastic deformation. Struct Optim 10(3-4):197–208CrossRef Yuge K, Kikuchi N (1995) Optimization of a frame structure subjected to a plastic deformation. Struct Optim 10(3-4):197–208CrossRef
Zurück zum Zitat Yuge K, Iwai N, Kikuchi N (1999) Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method. Struct Optim 17(4):286–299CrossRef Yuge K, Iwai N, Kikuchi N (1999) Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method. Struct Optim 17(4):286–299CrossRef
Zurück zum Zitat Zhang W, Yuan J, Zhang J, Guo X (2015) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim. doi:10.1007/s00158-015-1372-3, article in Press Zhang W, Yuan J, Zhang J, Guo X (2015) A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Struct Multidiscip Optim. doi:10.​1007/​s00158-015-1372-3, article in Press
Zurück zum Zitat Zhang W, Zhang J, Guo X (2016) Lagrangian description based topology optimization - a revival of shape optimization. J Appl Mech Trans ASME 83(4) Zhang W, Zhang J, Guo X (2016) Lagrangian description based topology optimization - a revival of shape optimization. J Appl Mech Trans ASME 83(4)
Zurück zum Zitat Zhou M, Rozvany GIN (1991) The COC algorithm, part ii: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1-3):309–336CrossRef Zhou M, Rozvany GIN (1991) The COC algorithm, part ii: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1-3):309–336CrossRef
Zurück zum Zitat Zhu J, Zhang W, Qiu K (2007) Bi-directional evolutionary topology optimization using element replaceable method. Comput Mech 40(1):97–109CrossRefMATH Zhu J, Zhang W, Qiu K (2007) Bi-directional evolutionary topology optimization using element replaceable method. Comput Mech 40(1):97–109CrossRefMATH
Metadaten
Titel
Evolutionary topology optimization of elastoplastic structures
verfasst von
Liang Xia
Felix Fritzen
Piotr Breitkopf
Publikationsdatum
28.06.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 2/2017
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-016-1523-1

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