Solution of an orthotropic elliptic plate with an elliptic hole or crack

Based on the complex variable method, the problem of an elliptic plate with an elliptic hole or a crack is addressed under uniform tension or pressure imposed on the boundary of the hole and on the edge of the plate. A series solution for the stress field inside the plate is derived using conformal mapping techniques, Faber series and Fourier expansion method. The stress fields around the hole or crack relative to the distance between the hole or crack and the edge of the plate are discussed in several examples. It is found that the hoop stress around the hole and the stress intensity factors at the crack tips increase steeply with deceasing distance between the hole or crack and the edge of the plate.