A new special element for stress concentration analysis of a plate with elliptical holes

Special hole elements are presented for analyzing the stress behavior of an isotropic elastic solid containing an elliptical hole. The special hole elements are constructed using the special fundamental solutions for an infinite domain containing a single elliptical hole, which are derived based on complex conformal mapping and Cauchy integrals. During the construction of the special elements, the interior displacement and stress fields are assumed to be the combination of fundamental solutions at a number of source points, and the frame displacement field defined over the element boundary is independently approximated with conventional shape functions. The hybrid finite element model is formulated based on a hybrid functional that provides a link between the two assumed independent fields. Because the fundamental solutions used exactly satisfy both the traction-free boundary conditions of the elliptical hole under consideration and the governing equations of the problems of interest, all integrals can be converted into integrals along the element boundary and there is no need to model the elliptical hole boundary. Thus, the mesh effort near the elliptical hole is significantly reduced. Finally, the numerical model is verified through three examples, and the numerical results obtained for the prediction of stress concentration factors caused by elliptical holes are extremely accurate.