Homogenization of thin piezoelectric perforated shells

¹ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, PO Box 1-764, RO-014700, Bucharest, Romania. marius.ghergu@imar.ro
² Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris VI), 4 Place Jussieu, 75252 Paris, France. georges.griso@wanadoo.fr
³ École Polytechnique, Centre de Mathématiques Appliquées, CMAP (CNRS UMR 7641), 91128 Palaiseau, France. mechkour@cmap.polytechnique.fr
⁴ Laboratoire de Modélisation et Simulation Numérique, ESIEE, 2 Boulevard Blaise Pascal, 91360 Noisy-Le-Grand, France. miarab@esiee.fr

Received: 21 October 2006
Revised: 18 March 2007

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.