Optimal Size of a Rigid Thin Stiffener Reinforcing a Timoshenko-Type Plate on the Outer Edge

摘要

For a family of variational problems describing equilibrium of cracked elastic plates, we analyze the dependence of solutions on the length parameter of rigid thin stiffeners reinforcing the plates on the outer boundary. We consider the nonlinear crack model providing a mutual non-penetration between crack faces with unknown set of a contact and zero friction. The existence is proved of the solution to the optimal control problem. For this problem the cost functional is defined by an arbitrary continuous functional, while the length parameter of the thin rigid stiffener is chosen as a control parameter