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Adv. Appl. Math. Mech., 2 (2010), pp. 355-378. |
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Analysis and Numerical Approximation of an El-H. Essoufi 1, El-H. Benkhira 1, R. Fakhar 1* 1 Universit\'{e} Hassan I Facult\'{e} des Sciences et T\'{e}chniques, D\'{e}partement de Math\'{e}matiques et Informatique B.P. 577, Settat, Route de Casablanca, Settat, MarocReceived 24 August 2009; Accepted (in revised version) 29 January 2010 doi: 10.4208/aamm.09-m0980 Abstract 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 material. The unilateral contact is modelled using the Signorini condition, nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition. Existence 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. AMS subject classifications: 35J85, 47J20, 49J40, 74F15, 74G30, 74M10, 74M15, 74S05Key words: Electro-elastic static problem, piezoelectric materials, unilateral contact, nonlocal Coulomb's friction, variational inequality, fixed point, finite element approximation, iterative method, error estimates. *Corresponding author. Email: essoufi@gmail.com (El-H. Essoufi), benkhirahassan@yahoo.fr (El-H. Benkhira), rachidfakhar@yahoo.fr (R. Fakhar) |