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MODELING AND ANALYSIS OF AN ANTIPLANE PIEZOELECTRIC CONTACT PROBLEM

Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30348 Krakow, Poland

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ANNA OCHAL

Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30348 Krakow, Poland

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, and

MIRCEA SOFONEA

Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France

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https://doi.org/10.1142/S0218202509003796Cited by:19 (Source: Crossref)

Abstract

We study a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is static, the material behavior is described with a linearly electro-elastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is in the form of a system of two coupled hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on an abstract result on operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our results are valid.

Keywords:

AMSC: 74M10, 74F15, 74G25, 49J40

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