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.
Mots clés : structural topology optimization, linear elasticity, phase-field method, first order conditions, matched asymptotic expansions, shape calculus, numerical simulations
@article{COCV_2014__20_4_1025_0,
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://www.numdam.org/articles/10.1051/cocv/2014006/}
}
TY - JOUR AU - Blank, Luise AU - Garcke, Harald AU - Hassan Farshbaf-Shaker, M. AU - Styles, Vanessa TI - Relating phase field and sharp interface approaches to structural topology optimization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 1025 EP - 1058 VL - 20 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014006/ DO - 10.1051/cocv/2014006 LA - en ID - COCV_2014__20_4_1025_0 ER -
%0 Journal Article %A Blank, Luise %A Garcke, Harald %A Hassan Farshbaf-Shaker, M. %A Styles, Vanessa %T Relating phase field and sharp interface approaches to structural topology optimization %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 1025-1058 %V 20 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014006/ %R 10.1051/cocv/2014006 %G en %F COCV_2014__20_4_1025_0
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. http://www.numdam.org/articles/10.1051/cocv/2014006/
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