The stress distribution due to a force in the interior of a semi-infinite elastic medium

Abstract

1. In this paper an analysis is given of the distribution of stress in a semi-infinite elastic medium due to the action of an external force applied to the interior of the medium. It will be assumed throughout that the force acts in a direction perpendicular to that of the boundary of the solid; the analysis is similar when the line of action of the force is parallel to the boundary and is therefore not given here. The equations of plane strain parallel to the x-y plane are employed; physically this is equivalent to assuming that there is no component of the displacement vector in a direction normal to the x-y plane or, what is the same thing, that the external force is applied along are infinite line parallel to the axis of z.