An optimal design problem for an anisotropic elastic plate in a dynamic contact with an obstacle

Abstract

We deal with an optimal design problem governed by an initial‐boundary value problem for a hyperbolic variational inequality describing the perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The admissible set of states for the design problem contains solutions of a state problem gained as limits of the sequences of functions solving penalized problems. We verify the existence of the optimal thickness function using the optimal controls achieved as solutions of optimal design problems connected with penalized state problems.