This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of -measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that the optimal microstructures are always simple laminates.
Mots-clés : optimal design, $H$-measures, homogenization
@article{M2AN_2007__41_3_543_0,
author = {Allaire, Gr\'egoire and Guti\'errez, Sergio},
title = {Optimal design in small amplitude homogenization},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {543--574},
publisher = {EDP-Sciences},
volume = {41},
number = {3},
year = {2007},
doi = {10.1051/m2an:2007026},
mrnumber = {2355711},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007026/}
}
TY - JOUR AU - Allaire, Grégoire AU - Gutiérrez, Sergio TI - Optimal design in small amplitude homogenization JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 543 EP - 574 VL - 41 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007026/ DO - 10.1051/m2an:2007026 LA - en ID - M2AN_2007__41_3_543_0 ER -
%0 Journal Article %A Allaire, Grégoire %A Gutiérrez, Sergio %T Optimal design in small amplitude homogenization %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 543-574 %V 41 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007026/ %R 10.1051/m2an:2007026 %G en %F M2AN_2007__41_3_543_0
Allaire, Grégoire; Gutiérrez, Sergio. Optimal design in small amplitude homogenization. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 3, pp. 543-574. doi : 10.1051/m2an:2007026. http://www.numdam.org/articles/10.1051/m2an:2007026/
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