Viscoelastic solids may be effectively treated by the boundary element meth
od (BEM) in the Laplace domain. However, calculation of transient response
via the Laplace domain requires the inverse transform. Since all numerical
inversion formulas depend heavily on a proper choice of their parameters, a
direct evaluation in the time domain seems to be preferable. On the other
hand, direct calculation of viscoelastic solids in the time domain requires
the knowledge of viscoelastic fundamental solutions.
Such solutions are simply obtained in the Laplace domain with the elastic-v
iscoelastic correspondence principle, but not in the time domain. Due to th
is, a quadrature rule for convolution integrals, the 'convolution quadratur
e method' proposed by Lubich, is applied. This numerical quadrature formula
determines their integration weights from the Laplace transformed fundamen
tal solution and a linear multistep method. Finally, a boundary element for
mulation in the time domain using all the advantages of the Laplace domain
formulation is obtained. Even materials with complex Poisson ratio, leading
to time-dependent integral free terms in the boundary integral equation, c
an be treated by this formulation.
Two numerical examples, a 3D rod and an elastic concrete slab resting on a
viscoelastic halfspace, are presented in order to assess the accuracy and t
he parameter choice of the proposed method. Copyright (C) 1999 John Wiley &
Sons, Ltd.