Optimal control for elasto-orthotropic plate

The optimal control problems and a weight minimization problem are considered for elastic three-layered plate with inner obstacle and friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. The author proves the existence of a solution to the above-mentioned problem on the basis of a general theorem on the control of variational inequalities. Next, the approximate optimization problem is proved on the basis of the general theorem for the continuous problem.