Analytical Solution for Elastic Analysis around an Ellipse with Displacement-Controlled Boundary

Abstract

This paper presents novel analytical solutions for the analysis of an elliptical cavity within an infinite plane under plane strain conditions, considering typical displacement-controlled boundaries at the inner cavity and biaxial stresses at infinity. The problem is investigated by the plane theory of elasticity using Muskhelishvili’s complex variable method. The complex displacement boundary conditions are represented using the conformal mapping technique and Fourier series, and stress functions are evaluated using Cauchy’s integral formula. The proposed solutions are validated at first by comparing them with other existing solutions and then used to show the influences of displacement vectors on the distributions of induced stresses and displacements. The new solutions may provide useful analytical tools for stress and displacement analysis of an elliptical hole/opening in linear elastic materials which are common in many engineering problems.