Numerical solution of a three-part mixed boundary value problem of linear elastostatics

Abstract

A three-part mixed boundary value problem for the half-space z ⩾ 0 (with Neumann conditions prescribed over a finite doubly connected region S2 and Dirichlet conditions prescribed over the remaining of the z = 0 plane) is formulated to result into a system of two coupled integral equations. A procedure is outlined for the approximate solution of the problem under consideration for an arbitrary shape of the region S2. For the special axisymmetric case when the region S2 is a circular annulus of inner and outer radii a and b, respectively, the system of integral equations is reduced to a Fredholm integral equation of the second kind with a continuous non-symmetric kernel. The resulting integral equation is solved numerically and the results are found to be in good agreement with those previously published.