On the coupling of analytical and FEM solution in stress analysis around the polygonal hole shape in a finite two-dimensional domain

Stress analysis of finite plates with arbitrary hole shapes is performed using a mixed analytical-FEM approach. The analytical solution for the infinite plate is corrected using the FEM correction for the finite plate. The analytical method uses a modified Muskhelishvili complex variable method for an arbitrary polygonal hole shape utilizing the Schwarz-Christoffel mapping approach. Later, the FEM correction is calculated for the finite two-dimensional domain with appropriate boundary conditions. Coupled solutions accurately solve the problem of stress concentration at the hole corners. It is impossible to solve stress concentrations accurately using only the finite element method (FEM) approach because the solution is mesh dependent. The proposed method rapidly solves for the stress concentrations with arbitrary accuracy irrespective of hole shape and domain geometry.