Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy

C. Y. Wang*, J. D. Achenbach, S. Hirose

*Corresponding author for this work

Research output: Contribution to journalArticle

62 Scopus citations

Abstract

An efficient two-dimensional time-domain application of the Boundary Element Method is presented to solve elastodynamic boundary initial-value problems in solids of general anisotropy. The method is based on the use of integral expressions for the Green's functions derived by Wang and Achenbach (1994) [Elastodynamic fundamental solutions for anisotropic solids. Geophys. J. Int. 118, 384-392]. and on the partition of these Green's functions into singular static and regular dynamic parts. The singular static parts are the elastostatic Green's functions, which have relatively simple explicit expressions in closed form. The regular dynamic parts are given in terms of line integrals over a unit circle, whose integrands have a simple structure which physically corresponds to a superposition of plane waves. The partition of the Green's functions leads to the decomposition of the singular elastodynamic boundary integral equation into terms corresponding to a singular elastostatic integral equation plus regular dynamic terms. The calculation effort is reduced by analytically evaluating both the integration over each boundary element and the time-convolution over each time-step. As a result only regular line integrals over the unit circle have to be computed numerically. Applications are discussed for scattering of elastic waves by cavities. The method has been checked by comparing numerical results against existing analytical solutions for an isotropic solid. Numerical results for scattering of elastic waves in a transversely isotropic material by a circular cylindrical cavity have also been obtained.

Original languageEnglish (US)
Pages (from-to)3843-3864
Number of pages22
JournalInternational Journal of Solids and Structures
Volume33
Issue number26
DOIs
StatePublished - Nov 1996

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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