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Volume 18,     Number 2,     Summer 2010

 

ANALYSIS AND NUMERICAL
APPROXIMATION OF A FRICTIONAL
UNILATERAL CONTACT PROBLEM WITH
NORMAL COMPLIANCE
AREZKI TOUZALINE

Abstract. We consider a static contact problem between a linear elastic body and an obstacle, the so-called foundation. The contact is frictional and is modelled with a normal compliance condition such that the penetration is restricted with unilateral constraint, and the associated version of Coulomb's law of dry friction. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element approximation of the problem and obtain an error estimate. Finally, we introduce an iterative method to solve the discrete problem.

 

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