An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

Complex structure with circular boundaries is commonly used in engineering practice, and it is essential to conduct a detailed analysis of the interior stress field of the structure. The Michell stress function is a well-known general solution for plane elasticity problems in the polar coordinates, particularly when circular boundaries are involved. This work presents an analytical method with the assistance of the Michell solution, which could be seamlessly combined with Fourier analysis. Using the expansion of Fourier series, problems with arbitrarily distributed loads can be handled via a standard procedure. A complete analytical solution is elaborated for an arbitrarily loaded circular ring, and a classical elastic solution is provided for verification. (paper)