Geodesic
Relating phase field and sharp interface approaches to structural topology optimization
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1025-1058

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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.

DOI : 10.1051/cocv/2014006
Classification : 49Q10, 74P10, 49Q20, 74P05, 65M60
Keywords: structural topology optimization, linear elasticity, phase-field method, first order conditions, matched asymptotic expansions, shape calculus, numerical simulations 
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     author = {Blank, Luise and Garcke, Harald and Hassan Farshbaf-Shaker, M. and Styles, Vanessa},
     title = {Relating phase field and sharp interface approaches to structural topology optimization},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1025--1058},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {4},
     year = {2014},
     doi = {10.1051/cocv/2014006},
     mrnumber = {3264233},
     zbl = {1301.49113},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014006/}
}
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Blank, Luise; Garcke, Harald; Hassan Farshbaf-Shaker, M.; Styles, Vanessa. Relating phase field and sharp interface approaches to structural topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1025-1058. doi: 10.1051/cocv/2014006

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