The problem of the reinforcement of a plate with a cutout by a two-dimensional patch

The problem of the reinforcement of an elastic plate with a cutout by means of a two-dimensional patch, which completely covers the cutout and is rigidly fixed to the plate along its boundary, is considered. The cutout and the patch can be of arbitrary shape. The problem is reduced to a system of three singular integral equations using of special integral representations which describe the stress state in the plate and in the patch. The unique solvability of the system is proved. Examples are presented.