Boundary optimal control for antiplane contact problems with power-law friction

Abstract

• A variational inequality models the antiplane shear deformation of a body in frictional contact with a foundation. • The distance between the solution of the variational inequality and a given target can be minimized by acting with a boundary control force. • The boundary control can be approximated by using linearization and fixed point method. We consider a contact model with power-law friction in the antiplane context. Our study focuses on the boundary optimal control, paying special attention to optimality conditions and computational methods. Depending on the exponent of the power-law friction, we are able to deduce an optimality condition for the original problem or for a regularized version of it. Furthermore, we introduce and analyze a computational technique based on linearization, saddle point theory and a fixed point method. For a slightly modified optimal control problem, some numerical experiments are presented.