Optimal control of the angle between two rigid inclusions in an inhomogeneous 2D body

A nonlinear mathematical model describing equilibrium of a two-dimensional elastic body with two thin rigid inclusions is investigated. It is assumed that two rigid inclusions have one common connection point. Moreover, a connection between two inclusions at a given point is characterized by a positive damage parameter. Rectilinear inclusions are located at a given angle to each other in an initial state. Nonlinear Signorini conditions are imposed, which describe the contact with the obstacle, as well as a homogeneous Dirichlet condition is set on corresponding parts of the outer boundary of the body. An optimal control problem for the parameter that specifies the angle between inclusions is formulated. The quality functional is given by an arbitrary continuous functional defined on the Sobolev space. The solvability of the optimal control problem is proved. A continuous dependence of solutions on varying angle parameter between the inclusions is established.