We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled. By letting the size of the microstructure going to zero and by using the periodic unfolding method combined with the Korn's inequality in perforated domains, we obtain the limit model.
Mots clés : computational solid mechanics, homogenization, perforations, piezoelectricity, shells
@article{M2AN_2007__41_5_875_0,
author = {Ghergu, Marius and Griso, Georges and Mechkour, Houari and Miara, Bernadette},
title = {Homogenization of thin piezoelectric perforated shells},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {875--895},
publisher = {EDP-Sciences},
volume = {41},
number = {5},
year = {2007},
doi = {10.1051/m2an:2007046},
mrnumber = {2363887},
zbl = {1138.74039},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2007046/}
}
TY - JOUR AU - Ghergu, Marius AU - Griso, Georges AU - Mechkour, Houari AU - Miara, Bernadette TI - Homogenization of thin piezoelectric perforated shells JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 875 EP - 895 VL - 41 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2007046/ DO - 10.1051/m2an:2007046 LA - en ID - M2AN_2007__41_5_875_0 ER -
%0 Journal Article %A Ghergu, Marius %A Griso, Georges %A Mechkour, Houari %A Miara, Bernadette %T Homogenization of thin piezoelectric perforated shells %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 875-895 %V 41 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2007046/ %R 10.1051/m2an:2007046 %G en %F M2AN_2007__41_5_875_0
Ghergu, Marius; Griso, Georges; Mechkour, Houari; Miara, Bernadette. Homogenization of thin piezoelectric perforated shells. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 5, pp. 875-895. doi : 10.1051/m2an:2007046. http://archive.numdam.org/articles/10.1051/m2an:2007046/
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