Analytical stress solution for an infinite plate containing two oval holes

The problem refers to an elastic infinite plate bounded by two oval holes, which is subjected to uniform surface tractions on the boundary of the holes and uniform tension and shear stress at infinity. By looking for a new mapping function, the considered region is conformally mapped onto an annulus, and a complex variable method is used to obtain the stress solution. The problem that an elastic infinite plate contains two circular holes or a circular hole and an oval hole is the special case of this article. The present solution has been validated by both published solutions for special cases and ANSYS software. Some computational examples are given to investigate the effects of the separation distance of the two holes, relative ratio of applied stresses, surface tractions on the boundaries, the size of a hole, shear stress at infinity and the loading orientation angle on the stress distribution of the hole boundaries. Practical significance of the solution is placed in the fact that it could be used as a quick-solver with high accuracy.