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Rayleigh wave correction for the BEM analysis of two‐dimensional elastodynamic problems in a half‐space
Author(s) -
Arias I.,
Achenbach J. D.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1039
Subject(s) - boundary element method , boundary (topology) , mathematics , mathematical analysis , isotropy , truncation (statistics) , half space , method of fundamental solutions , displacement field , computation , rayleigh wave , matrix (chemical analysis) , wave propagation , finite element method , singular boundary method , physics , algorithm , statistics , materials science , quantum mechanics , composite material , thermodynamics
A simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two‐dimensional wave propagation problems in elastic half‐spaces. The proposed method exploits the knowledge of the far‐field asymptotic behaviour of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution involving the same boundary integrals that form the original BEM system. The method is formulated for a two‐dimensional homogeneous, isotropic, linearly elastic half‐space and its implementation in a frequency domain boundary element scheme is discussed in some detail. The formulation is then validated for a free Rayleigh pulse travelling on a half‐space and successfully tested for a benchmark problem with a known approximation to the analytical solution. Copyright © 2004 John Wiley & Sons, Ltd.