Two‐dimensional models for geometrically nonlinear thin piezoelectric shells

Article type: Research Article

Authors: Collard, Christophe | Miara, Bernadette^;

Affiliations: Laboratoire d'Analyse Numérique, Tour no 55, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France E‐mail: christophe.collard@metz.ensam.fr, ccollard@club‐internet.fr | Laboratoire de Modélisation et de Simulation Numérique, École Supérieure d'Ingénieurs en Électrotechnique et Électronique, cité Descartes, 2, boulevard Blaise‐Pascal, 93160 Noisy‐le‐Grand, France E‐mail: miarab@esiee.fr

Note: [] Corresponding author.

Abstract: In this paper, we apply the asymptotic analysis to thin piezoelectric shells in the framework of geometrically exact formulation. The formal mathematical approach used here is based neither on geometrical nor on mechanical assumptions and rigorously justifies the limiting constitutive nonlinear two‐dimensional equations. More precisely, we formally obtain two‐dimensional membrane and flexural models written on the middle surface of the shell. We show that the coupling between the limit displacement field and the limit electric potential inherent to piezoelectricity appears in the membrane model but not in the flexural model. Finally, we suggest a “full” new model for piezoelectric shells using membrane and flexural effects.

Journal: Asymptotic Analysis, vol. 31, no. 2, pp. 113-151, 2002