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Homogenization of thin piezoelectric perforated shells

Published online by Cambridge University Press:  23 October 2007

Marius Ghergu ,
Georges Griso ,
Houari Mechkour  and
Bernadette Miara
Marius Ghergu
Affiliation:
Institute of Mathematics “Simion Stoilow” of the Romanian Academy, PO Box 1-764, RO-014700, Bucharest, Romania. marius.ghergu@imar.ro
Georges Griso
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris VI), 4 Place Jussieu, 75252 Paris, France. georges.griso@wanadoo.fr
Houari Mechkour
Affiliation:
École Polytechnique, Centre de Mathématiques Appliquées, CMAP (CNRS UMR 7641), 91128 Palaiseau, France. mechkour@cmap.polytechnique.fr
Bernadette Miara
Affiliation:
Laboratoire de Modélisation et Simulation Numérique, ESIEE, 2 Boulevard Blaise Pascal, 91360 Noisy-Le-Grand, France. miarab@esiee.fr
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Abstract

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.

Keywords

Computational solid mechanicshomogenizationperforationspiezoelectricityshells.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 5 , September 2007 , pp. 875 - 895
Copyright
© EDP Sciences, SMAI, 2007

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