Simplified Approach to Solution of Mixed Boundary Value Problems on Homogeneous Circular Domain in Elasticity

Abstract

This work proposes a novel strategy to render mixed boundary conditions on circular linear elastic homogeneous domain to displacement-based condition all along the surface. With Michell solution as the starting point, the boundary conditions and extent of the domain are used to associate the appropriate type and number of terms in the Airy stress function. Using the orthogonality of sine and cosine functions, the modified boundary conditions lead to a system of linear equations for the unknown coefficients in the Airy stress function. Solution of the system of linear equations provides the Airy stress function and subsequently stresses and displacement. The effectiveness of the present approach in terms of ease of implementation, accuracy, and versatility to model variants of circular domain is demonstrated through excellent comparison of the solution of following problems: (i) annulus with mixed boundary conditions on outer radius and prescribed traction on the inner radius, (ii) cavity surface with mixed boundary conditions in an infinite plane subjected to far-field uniaxial loading, and (iii) circular disc constrained on part of the surface and subjected to uniform pressure on rest of the surface.