An optimal size of an external rigid thin inclusion for a nonlinear problem describing equilibrium of a three-dimensional cracked cylindrical body

A mathematical model describing equilibrium of cracked three-dimensional bodies with rigid thin stiffener on the outer boundary is studied. Inequality type boundary condition is imposed at the crack faces providing a mutual non-penetration between crack faces. We analyze the dependence of solutions on the size of the thin rigid stiffener reinforcing the cracked body on the outer edge. Existence of the solution to the optimal control problem is proved. For this problem the cost functional is defined by an arbitrary continuous functional, while the size parameter of the thin rigid stiffener is chosen as a control parameter.