# Shape Optimization in Discretized Contact Problems with Coulomb Friction and a Solution-Dependent Coefficient of Friction

Robert Patho^{*}, Jaroslav Haslinger and Jiri Outrata

The following contribution deals with shape optimization of elastic bodies in unilateral contact. Our aim is to extend existing results to contact problems, where the coefficient of friction depends on the solution. To this end, we will consider the two-dimensional Signorini problem coupled with the local Coulomb law of friction and involving a solution-dependent coefficient of friction. After formulating the discrete shape optimization problem in the form of a Mathematical Program with Equilibrium Constraints (MPEC), main focus shall be on its numerical solution. This latter task will be based on the so-called implicit programming approach and necessary subgradient information will be derived using the generalized differential calculus of B.$~$Mordukhovich.

Mathematics Subject Classification: 49Q10 74M10 90C33 90C90

Keywords: shape optimization; contact problems; Coulomb friction; solution-dependent coefficient of friction; mathematical programs with equilibrium constraints

Minisymposion: Nonsmooth and Unilateral Problems - Modelling, Analysis and Optimization Methods