Document ESAIM: COCV
DOI: 10.1051/cocv:2008022
Frictional contact of an anisotropic piezoelectric plate
Isabel N. Figueiredo1 and Georg Stadler21 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 April 13, 2007. Revised November 7, 2007. Published online March 6, 2008.)
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.
Mathematics Subject Classification. 74K20, 78M35, 74M15, 74M10, 74F15
Key words: Contact, friction, asymptotic analysis, anisotropic material, piezoelectricity, plate
© EDP Sciences, SMAI 2008