Singular integral equations for a patch repair problem

Within the scope of linear elasticity, an in-plane problem related to the repair of an infinite thin elastic plate with a hole by a patch is considered. The patch and the plate are joined together only along their boundaries. The plate is subjected to stresses applied at infinity. The problem is reduced to a system of four singular integral equations. Existence and uniqueness of the solution of the system is proved. The proposed solution allows one to evaluate the efficiency of a patch repair with little computational effort.