Control in obstacle three-layered plate problem

The problem to find an optimal thickness of a three-layered plate (ignoring shears in the middle plate) in a set of bounded Lipschitz continuous functions is considered. The variable thickness of the exterior layer of the plate is to be optimized to reach the minimal weight under some con-straints for maximal stresses. The cost functionals represent: 1) weight of the three-layered plate, 2) positive distribution (a non-negative Radon measure). The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of ad-missible functions. The existence of the optimal thickness is proved and some convergence analysis for an approximate penalized optimal control problem is presented. We prove the existence of a solution to the weight minimization problem or minimization the work of interaction forces on the basis of a general theorem on the control of variational inequalities.