Author(s)

C. G. Panagiotopoulos & G. D. Manolis

Abstract

Time-domain boundary element method formulations (TD-BEM) are quite versatile in reproducing the transient response of finite and semi-infinite solid media and offer a number of advantages compared to transformed domain (Fourier or Laplace) approaches. They are known, however, to be prone to numerical instability, especially after a very large number of time steps. This seems to be more of a problem with 1D as compared to 3D formulations, although it is present in the latter ones. A careful investigation of the problem reveals that if the conventional BEM formulation using displacement and traction variables is replaced with one using velocity and traction pairs, the problem is ameliorated to a large extent and much better accuracy results. Keywords: elastodynamics, stability, time-marching schemes, reciprocal theorems, convolution integrals. 1 Introduction Although the importance of TD-BEM formulations in studying wave motion problems in elastic continua is indisputable, the conventional formulation in terms of the displacement and traction vectors (DBEM) has a latent problem when a large number of time steps are required. More specifically, unstable behaviour may occur that is known as ‘‘intermittent instability’’ [1]. Various schemes have been proposed in recent years, many of them drawn from finite element methodologies (such as the Wilson-theta integration algorithm) to eliminating or reduce this unstable behaviour of the time convolution integrals associated with the transient BEM. All such methods basically seek to modify

Keywords

elastodynamics, stability, time-marching schemes, reciprocal theorems, convolution integrals