Numerical solution for the stress near a hole with corners in an infinite plate under biaxial loading

We consider the elastic stress near a hole with corners in an infinite plate under biaxial stress. The elasticity problem is formulated using complex Goursat functions, resulting set of singular integro-differential equations on boundary. boundary integral are solved numerically Chebyshev collocation method which augmented by fractional power term, derived asymptotic analysis corner region, to resolve singularities at hole. apply our numerical test case formed two partially-overlapping circles, can include either pointing into solid or out solid. Our results recover exact within relative error $10^{-3}$ for modest computational effort.