Transient Analysis of Shear Impact of an Elastic Half Space

Abstract

This paper presents a transient analysis of the propagation of stress waves arising in an elastic half-space subjected to concentrated tangential force varying with as the Heaviside unit step function on the surface. The solution of such a non-axisymmetric problem is obtained from the three dimensional elasto-dynamic theory. The wave motion equations can be obtained by introducing the stress functions ψ₀, λ₂ and λ₃. The boundary conditions of the external force are satisfied with the aid of the Hankel transform method and the Laplace transform theorem. The Laplace inverse transfomrs are accomplished by procceding with the integration along Bromwich integral path. The results of numerical evaluation are shown graphically as the relation of the displacement and the stress variations versus time in elastic half-space.