Optimal Control of the Obstacle Inclination Angle in the Contact Problem for a Kirchhoff–Love Plate

A family of contact problems depending on a parameter which determines an obstacle inclination angle for a Kirchhoff–Love plate is studied. Namely, we assume that in the initial state a given part of the boundary of the plate top surface touches a nondeformable obstacle. Furthermore, we assume that the obstacle shape composed by rectilinear segments and each segment (generatrix) forms an angle with the plane of the plate corresponding to its front surface. A boundary condition of Signorini’s type is imposed in the form of inequality, which depends on a slope coefficient or the obstacle inclination angle. The parameter varies in a given closed interval and determines variation of the angles between generatrices and the plate front surface. Taking the mentioned parameter as a control, we formulate an optimal control problem for a cost functional that characterizes the deviation of the solution from the specified displacements. We prove existence of a solution for the optimal control problem. The continuous dependence of solutions on the parameter is also established.