Optimal control of the size of rigid inclusion in equilibrium problem for inhomogeneous Timoshenko-type plate with crack

The equilibrium problems for non-homogeneous plates with a rigid delaminated inclusion are considered. In this case, there is a crack between the rigid inclusion and an elastic part of the plate. Nonpenetration conditions on the crack faces are given in the form of inequalities. We analyze the dependence of solutions and derivatives of the energy functionals on the size of rigid inclusion. The existence of the solution to an optimal control problem is proved. For that problem the cost functional is defined by derivatives of the energy functional with respect to a crack perturbation parameter while the size parameter of rigid inclusion is chosen as the control function.