Green's Functions for Axisymmetric Body Force Problems of an Elastic Thick Infinite Plate and Their Application. Compression of a Thick Plate with a Spherical Cavity.

Abstract

Green's functions are shown for axisymmetric body force problems of an elastic thick infinite plate. The Green's functions are defined as solutions to the problem of an elastic thick infinite plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. The axisymmetric body forces considered here are a radial force and an axial force in cylindrical coordinates. Green's functions for torsional body force problems have been shown in a previous paper. In order to obtain the Green's functions, we apply stress functions for axisymmetric problems of elasticity. As an example of application of the Green's functions shown, we consider a stress concentration problem of a thick plate with a spherical cavity. It is assumed that a uniform pressure acts on the plane surfaces of the plate with a spherical cavity. The problem is formulated by an integral equation with unknown body forces. By numerical calculations, stress distributions around the cavity are shown. The results are compared with the exact solution for an infinite elastic solid with a spherical cavity.