Optimal control of a bilateral contact with friction
Volume 49 / 2022
Applicationes Mathematicae 49 (2022), 21-34
MSC: 49J40, 74B20, 74M10, 74M15.
DOI: 10.4064/am2405-4-2021
Published online: 30 August 2021
Abstract
We consider a mathematical model which describes a static frictional contact between a nonlinear elastic body and a rigid foundation. The contact is modelled with Tresca’s nonlocal friction law. We derive a variational formulation and prove its unique weak solvability under a certain condition on the friction coefficient. We state an optimal control problem which consists in leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We prove that the optimal control admits a solution, and then we study a regularized control problem and establish a convergence result.
