Optimal control of tilt angles in equilibrium problems for the Timoshenko plate with a oblique crack

We consider an equilibrium problem of an elastic plate with a flat oblique crack (cut). Nonpenetration conditions on the crack faces are given in the form of inequalities. We investigate the dependence of the solution and energy functional with respect to variations of the crack's tilt angle. The existence of the solution to the optimal control problem is proved. For that problem the cost functional is defined by derivatives of a energy functional along the crack perturbation parameter and the crack's tilt angle is chosen as the control function.