Transient Stress of an Elastic Half Space Subjected to a Uniform Impulsive Load in a Rectangular Region of Its Surface

Abstract

This paper presents a solution of transient stress in the interior of an elastic half space under a uniform normal or tangential impulsive load acting on a semi-infinite strip and a rectangular region of its surface. First, the response of a half space loaded over a semi-infinite strip, finite in width is obtained by superimposing the solution which has been derived to the problem of one quarter. Subsequently, the solution to a half space loaded on a rectangular region is obtained by the superposition of response of the semi-infinite strip. The response of one quarter pressure may be derived by using double Fourier transforms on space, Laplace transform on time and Cagniard's method. The solution has singularities on the real axis of Fourier transform plane. We must take notice of the problem of Whether the singularities are inside the closed curve of Cagniard's path in the super position or not.