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Numerical implementation of the symmetric Galerkin boundary element method in 2D elastodynamics
Author(s) -
Yuan Weifeng,
Zhao Zhiye,
Lie Seng Tjhen,
Yu Guoyou
Publication year - 2003
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.811
Subject(s) - boundary element method , galerkin method , mathematics , mathematical analysis , singular integral , numerical analysis , domain (mathematical analysis) , traction (geology) , integral equation , finite element method , boundary (topology) , displacement (psychology) , physics , psychology , psychotherapist , geomorphology , geology , thermodynamics
The symmetric Galerkin boundary element method (SGBEM) employs both the displacement integral equation and the traction integral equation which lead to a symmetric system of equations. A two‐dimensional SGBEM is implemented in this paper, with emphasis on the special treatments of singular integrals. The integrals in the time domain are carried out by an analytical method. In order to evaluate the strong singular double integrals and the hypersingular double integrals in the space domain which are associated with the fundamental solutions G pu and G pp , artificial body forces are introduced which can be used to indirectly derive the singular terms. Thus, those singular integrals which behave like 1/ r and 1/ r 2 are all avoided in the proposed SGEBM implementation. An artificial body force scheme is proposed to evaluate the body force term effectively. Two numerical examples are presented to assess the accuracy of the numerical implementation, and show similar accuracy when compared with the FEM and the analytical solutions. Copyright © 2003 John Wiley & Sons, Ltd.