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Mathematical Problems in Engineering
Volume 2018, Article ID 8346891, 16 pages
https://doi.org/10.1155/2018/8346891
Research Article

Variational and Numerical Analysis of a Static Thermo-Electro-Elastic Problem with Friction

1Laboratoire MATIC, Université Hassan 1er, 26000 Settat, Morocco
2Laboratoire LS3M, Université Hassan 1er, 25000 Khouribga, Morocco

Correspondence should be addressed to Rachid Fakhar; rf.oohay@rahkafdihcar

Received 12 August 2017; Revised 21 November 2017; Accepted 27 December 2017; Published 28 January 2018

Academic Editor: Francesco Marotti de Sciarra

Copyright © 2018 Othman Baiz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a mathematical model which describes a static frictional contact between a piezoelectric body and a thermally conductive obstacle. The constitutive law is supposed to be thermo-electro-elastic and the contact is modeled with normal compliance and a version of Coulomb’s friction law. We derive a variational formulation of the problem and we prove the existence and uniqueness of its solution. The proof is based on some results of elliptic variational inequalities and fixed point arguments. Furthermore, a finite element approximation and a priori error estimates are obtained.