The Transient Stress in an Elastic Half-space Subjected to a Semi-infinite Line Load varying as Unit Step Function on Its Surface

Abstract

This paper presents an exact solution for the transient response in the interior of an elastic half space subjected to a normal or a tangential semi-infinite line load varying with time as a Heaviside unit step function on its surface. The solution is based on the stress function approach, the Laplace transform and the double Fourier transform method applied to a non-axisymmetric dynamical problem. The Laplace inverse transform which is performed by the three-dimensional Cagniard's technique gives an exact solution for the stress wave propagations. The results of numerical evaluation are shown graphically for the stress variation versus time in the interior of a half space.