Optimal internal stabilization of the linear system of elasticity

Abstract

We consider the nonlinear optimal design problem which consists in finding the best position and shape of the internal viscous damping set for the stabilization of the linear system of elasticity. Since non-existence of classical designs is usual in this context, a relaxation of the original problem is proposed. Then, the relaxed problem is solved numerically. Finally, a penalization technique to recover quasi-optimal classical designs from the relaxed ones and the over-damping phenomenon are analyzed in several numerical experiments.