Frictional contact of an anisotropic piezoelectric plate

¹ Centro de Matemática da Universidade de Coimbra (CMUC), Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal. isabelf@mat.uc.pt
² Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, 1 University Station C0200, Austin, TX 78712, USA. georgst@ices.utexas.edu

Received: 13 April 2007
Revised: 7 November 2007

Abstract

The purpose of this paper is to derive and study a new asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. In the asymptotic process, the thickness of the piezoelectric plate is driven to zero and the convergence of the unknowns is studied. This leads to two-dimensional Kirchhoff-Love plate equations, in which mechanical displacement and electric potential are partly decoupled. Based on this model numerical examples are presented that illustrate the mutual interaction between the mechanical displacement and the electric potential. We observe that, compared to purely elastic materials, piezoelectric bodies yield a significantly different contact behavior.