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Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 201-219页

作者： Othman Baiz el-hassan benkhira Rachid Fakhar University Ibn Zohr Lab.ESERFP of OuarzazateMorocco University Moulay Ismail Faculty of SciencesLaboratory MACSESTMBP 3103Toulal-MeknesMorocco University Sultan Moulay Slimane Laboratory LS2MEPolydisciplary Faculty of Khouribga25000 KhouribgaMorocco

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is *** contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the *** addition,the effects of the electrical conductivity of the foundation are taken into *** model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric *** existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point ***,a finite element approximation of the problem is *** some regularity conditions,an optimal order error estimate of the approximate solution is ***,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

关键词： piezoelectric material frictional contact variational Inequality fixed point process finite element method error estimation iteration method

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Analysis and Numerical Approximation of an electro-elastic Frictional Contact Problem

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Advances in Applied Mathematics and Mechanics 2010年第3期2卷 355-378页

作者： el-H.Essoufi el-H.benkhira R.Fakhar Universitéhassan I Facultédes Sciences et Téchniques Département de Mathématiques et Informatique B.P.577SettatRoute de CasablancaSettatMaroc

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric *** unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity *** and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.

关键词： electro-elastic static problem piezoelectric materials unilateral contact nonlocal Coulomb’s friction variational inequality fixed point finite element approximation iterative method error estimates

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