Application of addition theorems to the solution of the stress concentration problem in multi-connected domain with circular and elliptical boundaries

Abstract

The paper solves a plane elasticity problem for an elastic plane with a circular hole and a semi-infinite cut under uniform load. By applying addition theorems for Lamé equations in mixed coordinate systems, the boundary value problem is reduced to a solvable infinite system of linear algebraic equations. The obtained analytical formulas for stress intensity factors provide a fast, high-accuracy alternative to resource-intensive numerical methods for structural strength assessment.