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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 limithomogeneous constitutive law of a piezoelectric composite made of periodicallyperforated microstructures and whose reference configuration is athin shell with fixed thickness. We deal with an extension of theKoiter shell model in which the three curvilinear coordinates ofthe elastic displacement field and the electric potential arecoupled. By letting the size of themicrostructure going to zero and by using the periodicunfolding method combined with the Korn's inequality in perforateddomains, we obtain the limit model.

Keywords

Computational solid mechanicshomogenizationperforationspiezoelectricityshells.

Information

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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