On the Neumann Boundary Optimal Control of a Frictional Quasistatic Contact Problem with Dry Friction

This paper deals with boundary optimal control problem of a frictional quasi-static contact problem with dry friction, described by a nonlocal version of Coulomb’s law. We prove the existence of a boundary optimal control for the regularized problem obtained from a quasi-static contact problem with dry friction. For getting the necessary optimality conditions, we use some regularization techniques leading us to a control problem of a variational equality. The minimizing of cost function is a compromise between energy consumption and the finding of a traction force on the Neumann boundary condition, so that the actual displacement field is as close as possible to the desired displacement field, while the density of body force remain constant and small enough.