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Structural and Multidisciplinary Optimization
Published in: Structural and Multidisciplinary Optimization 2/2013

01-08-2013 | RESEARCH PAPER

Stress-constrained topology optimization: a topological level-set approach

Authors: Krishnan Suresh, Meisam Takalloozadeh

Published in: Structural and Multidisciplinary Optimization | Issue 2/2013

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Abstract

The objective of this paper is to introduce and demonstrate an algorithm for stress-constrained topology optimization. The algorithm relies on tracking a level-set defined via the topological derivative. The primary advantages of the proposed method are: (1) the stresses are well-defined at all points within the evolving topology, (2) the finite-element stiffness matrices are well-conditioned, making the analysis robust and efficient, (3) the level-set is tracked through a simple iterative process, and (4) the stress constraint is precisely satisfied at termination. The proposed algorithm is illustrated through numerical experiments in 2D and 3D.
previous article On choice of optimal anisotropy of composite plates against buckling, with special attention to bending-twisting coupling
next article A stress–based approach to the optimal design of structures with unilateral behavior of material or supports

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Literature
Allaire G, Jouve F (2005) A level-set method for vibration and multiple loads structural optimization. Struct Des Optim 194(30–33): 3269–3290MathSciNetMATH
Allaire G, Jouve F (2008) Minimum stress optimal design with the level set method. Eng Anal Bound Elem 32(11): 909–918MATHCrossRef
Allaire G, Jouve F, Toader AM (2002) A level-set method for shape optimization. Comput Rendus Math 334(12): 1125–1130MathSciNetMATH
Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1): 363–393MathSciNetMATHCrossRef
Amstutz S, Novotny AA (2010) Topological optimization of structures subject to Von Mises stress constraints. Struct Multidisc Optim 41(3): 407–420MathSciNetCrossRef
Arbenz P, Hetmaniuk UL, Lehoucq RB, Tuminaro RS (2005) A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods. Int J Numer Methods Eng 64(2): 204–236MATHCrossRef
Augarde CE, Ramage A, Staudacher J (2006) An element-based displacement preconditioner for linear elasticity problems. Comput Struct 84(31–32): 2306–2315CrossRef
Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods and application, 2nd edn. Springer
Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidisc Optim 46: 369–384MathSciNetCrossRef
Bruggi M, Venini P (2008) A mixed FEM approach to stress constrained topology optimization. Int J Numer Methods Eng 73(12): 1693–1714MathSciNetMATHCrossRef
Céa J, Garreau S, Guillaume P, Masmoudi M (2000) The shape and topological optimization connection. Comput Methods Appl Mech Eng 188(4): 713–726MATHCrossRef
Choi KK, Kim NH (2005) Structural sensitivity analysis and optimization I: linear systems. Springer, New York
Duysinx P, Bendsoe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8): 1453–1478MathSciNetMATHCrossRef
Duysinx P, Miegroet LV, Lemaire E, Brüls O, Bruyneel M (2008) Topology and generalized shape optimization: why stress constraints are so important?Int J Simul Multidisc Des Optim 2: 253–258CrossRef
Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4Esch01): 331–389CrossRef
Eschenauer HA, Kobelev VV, Schumacher A (1994) Bubble method for topology and shape optimization of structures. Struct Optim 8: 42–51CrossRef
Feijoo RA, Novotny AA, Taroco E, Padra C (2005) The topological-shape sensitivity method in two-dimensional linear elasticity topology design. In: Applications of computational mechanics in structures and fluids. CIMNE
Gopalakrishnan SH, Suresh K (2008) Feature sensitivity: a generalization of topological sensitivity (This work was partly or wholly funded by the National Science Foundation). Finite Elem Anal Des 44(11): 696–704MathSciNetCrossRef
Guo X, Cheng GD (2004) Epsilon-continuation approach for truss topology optimization. Acta Mech Sin 20(5): 526–533CrossRef
Guo X, Zhang WS, Wang YU, Wei P (2011) Stress-related topology optimization via level set approach. Comput Methods Appl Mech Eng 200: 3439–3452MathSciNetMATHCrossRef
He L, Kao C-Y, Osher S (2007) Incorporating topological derivatives into shape derivatives based level set methods. J Comput Phys 225(1): 891–909MathSciNetMATHCrossRef
James KA, Lee E, Martins JRRA (2012) Stress-based topology optimization using an isoparametric level set method. Finite Elem Anal Des 58: 20–30CrossRef
Kocvara M, Stingl M (2012) Solving stress constrained problems in topology and material optimization. Struct Multidisc Optim 46(1): 1–15MathSciNetCrossRef
Le C (2010) Developments in topology and shape optimization. PhD thesis, University of Illinois at Urbana-Champaign, Urbana-Champaign
Le C, Norato JA, Bruns TE, Ha C, Tortorelli DA (2010) Stress-based topology optimization for continua. Struct Multidisc Optim 41(4): 605–620CrossRef
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface reconstruction algorithm. Comput Graph (Proc. of SIGGRAPH) 21(4): 163–169CrossRef
Norato JA, Bendsøe MP, Haber RB, Tortorelli DA (2007) A topological derivative method for topology optimization. Struct Multidisc Optim 33: 375–386MATHCrossRef
Novotny AA (2006) Topological-shape sensitivity method: theory and applications. Solid Mech Appl 137: 469–478
Novotny AA, Feijóo RA, Padra C, Taroco E (2005) Topological derivative for linear elastic plate bending problems. Control Cybern 34(1): 339–361MATH
Novotny AA, Feijoo RA, Taroco E (2007) Topological sensitivity analysis for three-dimensional linear elasticity problem. Comput Methods Appl Mech Eng 196(41–44): 4354–4364MathSciNetMATHCrossRef
Paris J, Navarrina F, Colominas I, Casteleiro M (2009) Topology optimization of continuum structures with local and global stress constraints. Struct Multidisc Optim 39(4): 419–437MathSciNetCrossRef
Qiu GY, Li XS (2010) A note on the derivation of global stress constraints. Struct Multidisc Optim 40(1–6): 625–628MathSciNetCrossRef
Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidisc Optim 37(3): 217–237MathSciNetCrossRef
Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21(2): 120–127CrossRef
Stump FV, Silva ECN, Paulino G (2007) Optimization of material distribution in functionally graded structures with stress constraints. Commun Numer Methods Eng 23(6): 535–551MathSciNetMATHCrossRef
Suresh K (2010) A 199-line Matlab code for Pareto-optimal tracing in topology optimization. Struct Multidisc Optim 42(5): 665–679MathSciNetCrossRef
Suresh K, Yadav P (2012) Large-scale modal analysis on multi-core architectures. In: Proceedings of the ASME 2012 international design engineering technical conferences & computers and information in engineering conference, Chicago, IL
Svanberg K, Werme M (2007) Sequential integer programming methods for stress constrained topology optimization. Struct Multidisc Optim 34(4): 277–299MathSciNetCrossRef
Turevsky I, Suresh K (2007) Generalization of topological sensitivity and its application to defeaturing (This work was partly or wholly funded by the National Science Foundation). In: ASME IDETC conference, Las Vegas
Turevsky I, Suresh K (2011) Tracing the envelope of the objective-space in multi-objective topology optimization (This work was partly or wholly funded by the National Science Foundation)Presented at the ASME IDETC/CIE conference, Washington, DC
Turevsky I, Gopalakrishnan SH, Suresh K (2009) An efficient numerical method for computing the topological sensitivity of arbitrary shaped features in plate bending (This work was partly or wholly funded by the National Science Foundation). Int J Numer Methods Eng 79: 1683–1702MATHCrossRef
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192: 227–246MATHCrossRef
Wang S, Sturler ED, Paulino G (2007) Large-scale topology optimization using preconditioned Krylov subspace methods with recycling. Int J Numer Methods Eng 69(12): 2441–2468MATHCrossRef
Xia Q, Shi T, Liu S, Wang MY (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90–91: 55–64CrossRef
Yalamanchili VK, Kumar AV (2012) Topology optimization of structures using a global stress measure. In: Proceedings of the ASME 2012 international design engineering technical conferences & computers and information in engineering conference. Chicago, IL
Yang RJ, Chen CJ (1996) Stress-based topology optimization. Struct Optim 12: 98–105CrossRef
Zhang WS, Guo X, Wang MY, Wei P (2012) Optimal topology design of continuum structures with stress concentration alleviation via level set method. Int J Numer Methods Eng. doi:10.​1002/​10.​1002/​nme.​4416
Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics. Elsevier
Metadata
Title
Stress-constrained topology optimization: a topological level-set approach
Authors
Krishnan Suresh
Meisam Takalloozadeh
Publication date
01-08-2013
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 2/2013
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-013-0899-4

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