Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 216297, 20 pages
Research Article

Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

Department of Computational Mechanics (DMC), School of Mechanical Engineering (FEM), University of Campinas (UNICAMP), Rua Mendeleyev 200, Cidade Universitária “Zeferino Vaz”, 13083-860 Campinas, SP, Brazil

Received 9 August 2011; Accepted 18 October 2011

Academic Editor: Kwok W. Wong

Copyright © 2012 Euclides Mesquita et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full space is presented. The solution is obtained within the frame of a double Fourier integral transform. Closed-form solutions for general loadings within the full space are furnished in the transformed wave number domain. Expressions for three boundary value problems, associated to a normal and two tangential rectangular loadings in the original physical space, are given in terms of a double inverse Fourier integral. These inverse integral transforms must be evaluated numerically. In the second part of the present paper a strategy to evaluate these integrals is described, the procedure validated and a number of original results are reported.