Numerical implementation of the symmetric Galerkin boundary element method in 2D elastodynamics

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 twodimensional 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 Gpu and Gpp, arti cial 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 arti cial body force scheme is proposed to evaluate the body force term e ectively. 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