Stationary Dynamic Stress Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full-Space

Abstract

This paper presents stress influence functions for uniformly distributed, time-harmonic rectangular loads within a three-dimensional, viscoelastic, isotropic full-space. The coupled differential equations relating displacements and stresses in the full-space are solved through double Fourier integral transforms in the wave number domain, in which they can be solved algebraically. The final stress fields are expressed in terms of double indefinite integrals arising from the Fourier transforms. The paper presents numerical schemes with which to integrate these functions accurately. The article presents numerical validation of the synthesized stress kernels and their behavior for high frequencies and large distances from the excitation source. The influence of damping ratio on the dynamic results is also investigated. This article is complementary to previous results of the authors in which the corresponding displacement solutions were derived. Stress influence functions, together with their displacement counterparts, are a fundamental part of many numerical methods of discretization such the boundary element method.