Zhor Lerguet, Meir Shillor, Mircea Sofonea
Abstract:
A mathematical model which describes the quasistatic frictional
contact between a piezoelectric body and a deformable conductive
foundation is studied. A nonlinear electro-viscoelastic
constitutive law is used to model the piezoelectric material.
Contact is described with the normal compliance condition, a
version of Coulomb's law of dry friction, and a regularized
electrical conductivity condition. A variational formulation of
the model, in the form of a coupled system for the displacements
and the electric potential, is derived. The existence of
a unique weak solution of the model is established
under a smallness assumption on the surface conductance. The proof is
based on arguments of evolutionary variational inequalities and
fixed points of operators.
Submitted February 12, 2007. Published December 4, 2007.
Math Subject Classifications: 74M10, 74M15, 74F15, 49J40.
Key Words: Piezoelectric; frictional contact; normal compliance;
fixed point; variational inequality.
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Zhor Lerguet Département de Matématiques, Faculté des Sciences Université Farhat Abbas de Sétif Cité Maabouda, 19000 Sétif, Algérie email: zhorlargot@yahoo.fr |
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Meir Shillor Department of Mathematics and Statistics Oakland University Rochester, MI 48309, USA email: shillor@oakland.edu |
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Mircea Sofonea Laboratoire de Mathématiques et Physique pour les Systémes, University of Perpignan 52 avenue Paul Alduy 66860 Perpignan, France email: sofonea@univ-perp.fr |
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