Optimal control of a two-dimensional contact problem |
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Authors: | Mircea Sofonea Ahlem Benraouda Hadjer Hechaichi |
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Institution: | 1. Laboratoire de Mathématiques et Physique, University of Perpignan Via Domitia, Perpignan, France. sofonea@univ-perp.fr;3. Laboratoire de Mathématiques et Physique, University of Perpignan Via Domitia, Perpignan, France. |
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Abstract: | We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result. |
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Keywords: | Contact problem unilateral constraint variational inequality weak solution optimal control convergence results |
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