The Reissner–Sagoci problem for a transversely isotropic half-space

Abstract

A transversely isotropic linear elastic half-space, z⩾0, with the isotropy axis parallel to the z-axis is considered. The purpose of the paper is to determine displacements and stresses fields in the interior of the half-space when a rigid circular disk of radius a completely bonded to the surface of the half-space is rotated through a constant angle θ0. The region of the surface lying out with the circle r⩽a, is free from stresses. This problem is a type of Reissner–Sagoci mixed boundary value problems. Using cylindrical co-ordinate system and applying Hankel integral transform in the radial direction, the problem may be changed to a system of dual integral equations. The solution of the dual integral equations is obtained by an approach analogous to Sneddon's (J. Appl. Phys. 1947; 18:130–132), so that the circumferential displacement and stress fields inside the medium are obtained analytically. The same problem has already been approached by Hanson and Puja (J. Appl. Mech. 1997; 64:692–694) by the use of integrating the point force potential functions. It is analytically proved that the present solution, although of a quite different form, is equivalent to that given by Hanson and Puja. To illustrate the solution, a few plots are provided. The displacements and the stresses in a soil deposit due to a rotationally symmetric force or boundary displacement may be obtained using the results of this paper. Copyright © 2006 John Wiley & Sons, Ltd.