A comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains

As an alternative to domain discretization methods, the boundary element me thod (BEM) provides a powerful tool for the calculation of dynamic structur al response in frequency and rime domain. Field equations of motion and bou ndary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary. Fundamental solutions are used as weight ing functions in the BTE which fulfil the Sommerfeld radiation condition, i .e., the energy radiation into a surrounding medium is modelled correctly. Therefore, infinite and semi-infinite domains can be effectively treated by the method. The soil represents such a semi-finite domain in soil-structur e-interaction problems. The response to vibratory loads superimposed to sta tic pre-loads can often be calculated by linear viscoelastic constitutive e quations. Conventional viscoelastic constitutive equations can be generaliz ed by taking fractional order time derivatives into account. In the present paper two time domain BEM approaches including generalized viscoelastic be haviour are compared with the Laplace domain BEM approach and subsequent nu merical inverse transformation. One of the presented time domain approaches uses an analytical integration of the elastodynamic BIE in a time step. Vi scoelastic constitutive properties are introduced after Laplace transformat ion by means of an elastic-viscoelastic correspondence principle. The trans ient response is obtained by inverse transformation in each rime step. The other rime domain approach is based on the so-called;con volution quadratur e method. In this formulation. the convolution integral in the BIE is numer ically approximated by a quadrature formula whose weights are determined by the same Laplace transformed fundamental solutions used in the first metho d and a linear multistep method. A numerical study of wave propagation prob lems in 3-d viscoelastic continuum is performed for comparing the three BEM formulations. (C) 1999 Elsevier Science S.A. All rights reserved.