Numerical Solution of 2D Contact Shape Optimization Problems Involving a Solution-Dependent Coefficient of Friction

This contribution deals with numerical solution of shape optimization problems in frictional contact mechanics. The state problem in our case is given by 2D static Signorini problems with Tresca friction and a solution-dependent coefficient of friction. A suitable Lipschitz continuity assumption on the coefficient of friction is made, ensuring unique solvability of the discretized state problems and Lipschitz continuity of the corresponding control-to-state mapping. The discrete shape optimization problem can be transformed into a nonsmooth minimization problem and handled by the bundle trust method. In each step of the method, the state problem is solved by the method of successive approximations and necessary subgradient information is computed using the generalized differential calculus of B. Mordukhovich.