Shape Sensitivity Analysis of an Equilibrium Problem for a Body with a Thin Rigid Inclusion

In the paper we consider an equilibrium problem of an elastic body with a thin rigid inclusion. There is a delamination crack between the one side of the inclusion and the elastic body. We investigate the dependence of the solution on the shape perturbation. The main result is the calculation of the material derivative of the solution with respect to the shape perturbation parameter. As an example of the obtained results we calculate the shape derivative of the energy functional. Moreover, we consider the optimization problem of the length of the rigid inclusion. For this problem we get the necessary optimality conditions.