ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 3, p. 543-574

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 $H$-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.

DOI : https://doi.org/10.1051/m2an:2007026
Classification:  15A15,  15A09,  15A23
Keywords: optimal design, $H$-measures, homogenization
@article{M2AN_2007__41_3_543_0,
author = {Allaire, Gr\'egoire and Guti\'errez, Sergio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {41},
number = {3},
year = {2007},
pages = {543-574},
doi = {10.1051/m2an:2007026},
zbl = {pre05289384},
mrnumber = {2355711},
language = {en},
url = {http://www.numdam.org/item/M2AN_2007__41_3_543_0}
}

Allaire, Grégoire; Gutiérrez, Sergio. Optimal design in small amplitude homogenization. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 3, pp. 543-574. doi : 10.1051/m2an:2007026. http://www.numdam.org/item/M2AN_2007__41_3_543_0/

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