Homogenization of thin piezoelectric perforated shells
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 5, p. 875-895

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.

DOI : https://doi.org/10.1051/m2an:2007046
Classification:  74K25,  74Q05,  35B27
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {5},
     year = {2007},
     pages = {875-895},
     doi = {10.1051/m2an:2007046},
     zbl = {1138.74039},
     mrnumber = {2363887},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_5_875_0}
}
Ghergu, Marius; Griso, Georges; Mechkour, Houari; Miara, Bernadette. Homogenization of thin piezoelectric perforated shells. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 5, pp. 875-895. doi : 10.1051/m2an:2007046. http://www.numdam.org/item/M2AN_2007__41_5_875_0/

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