Axisymmetric Body Force Problems of an Elastic Half-Space

Abstract

This paper is concerned with axisymmetric problems of an elastic half-space with body forces acting in the interior of the elastic solid expressed in cylindrical co-ordinates. General solutions for the problems mentioned above are shown separately: (a) the boundary is assumed to be free from applied forces; (b) the boundary is kept fixed. Employing the general solutions shown, exact solutions for the stresses and displacements of an elastic half-space subjected to radial forces, which act on a finite line vertical to the boundary surface, are obtained. As simple examples of application of the general solutions shown in the paper, solutions for problems of (i) a radial force acting at a point, (ii) a torsion force acting on the circumference of a circle and (iii) a single force acting at a point, are also presented.