Optimal control of the rigid layer size of the construction

The equilibrium problems of two-layer construction consisting of elastic and rigid layers are investigated. It is assumed that the elastic plate has a crack extending along the line which is the connection line of the construction parts. Passage to the limit on the size parameter of the construction rigid layer has been done. We consider the optimal control problem for the construction in which the cost functional is a derivative of the energy functional with respect to the length of the crack; control parameter is the parameter characterizing the size of the rigid layer.