Volume 20, Number 4, October-December 2014
|Page(s)||1025 - 1058|
|Published online||05 August 2014|
Relating phase field and sharp interface approaches to structural topology optimization
Fakultät für Mathematik, Universität Regensburg,
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
3 Department of Mathematics, University of Sussex, Brighton, BN1 9QH, UK
Revised: 10 January 2014
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.
Mathematics Subject Classification: 49Q10 / 74P10 / 49Q20 / 74P05 / 65M60
Key words: Structural topology optimization / linear elasticity / phase-field method / first order conditions / matched asymptotic expansions / shape calculus / numerical simulations
© EDP Sciences, SMAI, 2014
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