Abstract
We consider a mathematical model which describes a contact between a deformable body and a foundation. The contact is bilateral and modelled with Tresca’s friction law. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. We also introduce the regularized control problem for which we study the convergence when the regularization parameter tends to zero. Finally, an optimally condition is established for this problem.
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Touzaline, A. Optimal control of a frictional contact problem. Acta Math. Appl. Sin. Engl. Ser. 31, 991–1000 (2015). https://doi.org/10.1007/s10255-015-0519-8
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DOI: https://doi.org/10.1007/s10255-015-0519-8