The Displacements Produced in an Elastic Half-space by a Suddenly Applied Surface Force

Abstract

The problem considered here is that of the sudden application of a constant force to the surface of a homogeneous, isotropic elastic half-space. The case of a normally applied force is considered under axially-symmetric conditions. This force is assumed to be either concentrated at a point or distributed over a circular disc. The method of solution is based on the use of integral transforms and differs in some respects from methods previously used for this type of problem. The displacements at all points of the solid are calculated in terms of finite integrals. These integrals are evaluated numerically for selected interior points of the half-space for point loading, and for points on the axis of symmetry in the case of distributed loading. An expansion of the integrals which is valid for large values of the time is also obtained.