Soil-structure interaction and wave propagation problems in 2D by a Duhamel integral based approach and the convolution quadrature method

Abstract

In this paper, a new methodology for analyzing wave propagation problems, originally presented and checked by the authors for one-dimensional problems [18], is extended to plane strain elastodynamics. It is based on a Laplace domain boundary element formulation and Duhamel integrals in combination with the convolution quadrature method (CQM) [13], [14]. The CQM is a technique which approximates convolution integrals, in this case the Duhamel integrals, by a quadrature rule whose weights are determined by Laplace transformed fundamental solutions and a multi-step method. In order to investigate the accuracy and the stability of the proposed algorithm, some plane wave propagation and interaction problems are solved and the results are compared to analytical solutions and results from finite element calculations. Very good agreement is obtained. The results are very stable with respect to time step size. In the present work only multi-region boundary element analysis is discussed, but the presented technique can easily be extended to boundary element – finite element coupling as will be shown in subsequent publications.