Reinforcement of a plate weakened by multiple holes with several patches for different types of plate-patch attachment

Abstract

The most general situation of the reinforcement of a plate with multiple holes by several patches is considered. There is no restriction on the number and the location of the patches. Two types of patch attachment are considered: only along the boundary of the patch or both along the boundary of the patch and the boundaries of the holes which this patch covers. The unattached boundaries of the holes may be loaded with given in-plane stresses. The mechanical problem is reduced to a system of singular integral equations which can be further reduced to a system of Fredholm equations. A new numerical procedure for the solution of the system of singular integral equations is proposed in this paper. It is demonstrated on numerical examples that this procedure has advantages in the case of multiple patches and holes and allows achievement of better numerical convergence with less computational effort.