An Elastic Frictional Contact Problem with Unilateral Constraint
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We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.
KeywordsElastic material Frictional contact Quasi-variational inequality Weak solution Convergence results Optimization problem
Mathematics Subject Classification74M10 74M15 49J40 49J45 49J20
- 3.Benraouda, A., Couderc, M., Sofonea, M.: Analysis and control of a contact problem with unilateral constraints. J. Appl. Anal. (submitted) Google Scholar