A revisit of circular hole problem by the equivalent inclusion method

Abstract

Stress and displacement analysis of an infinite extended isotropic elastic plane with a circular cavity is a classical elasticity problem. To solve this kind of problem, finite element method (FEM) and complex variable function are often used which have their pros and cons to some degree. In classical textbooks of elasticity, the closed-form solutions are usually given for the stresses, but the displacement solutions are seldom listed. In this paper, we revisit the circular hole problem via the equivalent inclusion method (EIM), and attempt to derive both the stress and displacement solutions simultaneously under the combined tensile and shear loading. With the knowledge of Eshelby s inclusion in two dimensional and EIM, the solutions to be sought may be constructed in a straightforward and elegant manner. Several examples are examined to validate the present solutions, demonstrating that the EIM may provide a more concise and convenient way to solve the circular cavity problem.