Stress analytical solution for an infinite plane containing two holes

Abstract An analytical solution is presented for an elastic infinite plate containing an ellipse hole and a circle hole, which undergoes the internal traction along the holes and uniform tensions and shears at infinity. The solution uses the conformal transformation in complex functions, with the multiple connected region mapping onto a circular ring. The stress distribution solved for the infinite plane containing two unequal circle holes in prior literatures is the special case of this article. And contrast between the results of two unequal circle holes obtained by using the present analytical method and the Hoang's results is made in the article. As there is no analytical solution for two non-circular holes, the results obtained using the present analytical method are compared with the numerical results calculated by ANSYS. Computational examples given in this article has been analyzed to study the effect of distance between two holes, the ratio of stress in two directions at infinity, and the ratio of the major and minor axis, on the stress distribution of the hole boundary.