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Structural and Multidisciplinary Optimization

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01-06-2011 | Research Paper

Material interpolation schemes for unified topology and multi-material optimization

Authors: Christian Frier Hvejsel, Erik Lund

Published in: Structural and Multidisciplinary Optimization | Issue 6/2011

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Abstract

This paper presents two multi-material interpolation schemes as direct generalizations of the well-known SIMP and RAMP material interpolation schemes originally developed for isotropic mixtures of two isotropic material phases. The new interpolation schemes provide generally applicable interpolation schemes between an arbitrary number of pre-defined materials with given (anisotropic) properties. The method relies on a large number of sparse linear constraints to enforce the selection of at most one material in each design subdomain. Topology and multi-material optimization is formulated within a unified parametrization.

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Ahmad S, Irons B, Zienkiewicz O (1970) Analysis of thick and thin shell structures by curved elements. Int J Numer Methods Eng 2:419–451CrossRef

Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidisc Optim 1(4):193–202

Bendsøe M, Kikuchi N (1988) Generating optimal topologies in optimal design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224CrossRef

Bendsøe M, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654CrossRef

Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer

Bendsøe M, Díaz A, Lipton R, Taylor J (1995) Optimal design of material properties and material distribution for multiple loading conditions. Int J Numer Methods Eng 38(7):1149–1170CrossRef

Bendsøe M, Lund E, Olhoff N, Sigmund O (2005) Topology optimization - broadening the areas of application. Control Cybern 34(1):7–35MATH

Bodnár G (2009) Visualization and interpretation tools for free material optimization results. In: 8th world congress on structural and multidisciplinary optimization, Lisbon, Portugal

Bruyneel M (2011) SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidisc Optim 43:17–27. doi:10.1007/s00158-010-0548-0 CrossRef

Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–390CrossRef

Gibiansky L, Sigmund O (2000) Multiphase composites with extremal bulk modulus. J Mech Phys Solids 48(3):461–498MathSciNetMATHCrossRef

Gill P, Murray W, Saunders M (2005) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev 47(1):99–131MathSciNetMATHCrossRef

Gill P, Murray W, Saunders M (2008) User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming, Report NA 05-2, Department of Mathematics, University of California, San Diego

Hörnlein H, Kočvara M, Werner R (2001) Material optimization: bridging the gap between conceptual and preliminary design. Aerosp Sci Technol 5(8):541–554MATHCrossRef

Hvejsel C, Lund E, Stolpe M (2011) Optimization strategies for discrete multi-material stiffness optimization. Struct Multidisc Optim (submitted)

Lund E, Stegmann J (2005) On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy 8(1):109–124CrossRef

Muñoz E (2010) Global optimization for structural design by generalized benders’ decomposition. PhD thesis, Technical University of Denmark, Department of Mathematics, Kgs. Lyngby, Denmark

Muñoz E, Stolpe M (2010) Generalized benders’ decomposition for topology optimization problems. J Glob Optim. doi:10.1007/s10898-010-9627-4

Panda S, Natarajan R (1981) Analysis of laminated composite shell structures by finite element method. Comput Struct 14(3–4):225–230MATHCrossRef

Setoodeh S, Abdalla M, Gürdal Z (2005) Combined topology and fiber path design of composite layers using cellular automata. Struct Multidisc Optim 30(6):413–421CrossRef

Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45(6):1037–1067MathSciNetCrossRef

Stegmann J (2004) Analysis and optimization of laminated composite shell structures. PhD thesis, Department of Mechanical Engineering, Aalborg University

Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62:2009–2027MATHCrossRef

Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22(2):116–124CrossRef

Stolpe M, Svanberg K (2003) Modelling topology optimization problems as linear mixed 0–1 programs. Int J Numer Methods Eng 57(5):723–739MathSciNetMATHCrossRef

Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetMATHCrossRef

Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12(2):555MathSciNetMATHCrossRef

Wächter A, Biegler L (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57MathSciNetMATHCrossRef

Wang M, Wang X (2005) A level-set based variational method for design and optimization of heterogeneous objects. Comput-Aided Des 37(3):321–337CrossRef

Wang M, Chen S, Wang X, Mei Y (2005) Design of multimaterial compliant mechanisms using level-set methods. J Mech Des 127:941CrossRef

Wang MY, Wang X (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193(6–8):469–496MATHCrossRef

Yin L, Ananthasuresh G (2001) Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Struct Multidisc Optim 23(1):49–62CrossRef

Title: Material interpolation schemes for unified topology and multi-material optimization
Authors: Christian Frier Hvejsel
Erik Lund
Publication date: 01-06-2011
Publisher: Springer-Verlag
Published in: Structural and Multidisciplinary Optimization / Issue 6/2011
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-011-0625-z

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