A particular integral BEM/time-discontinuous FEM methodology for solving 2-D elastodynamic problems

This study proposes a time-discontinuous Galerkin ®nite element method (FEM) for solving second-order ordinary di€erential equations in the time domain. The equations are formulated using a particular integral boundary element method (BEM) in the space domain for elastodynamic problems. The particular integral BEM technique depends only on elastostatic displacement and traction fundamental solutions, without resorting to commonly used complex fundamental solutions for elastodynamic problems. Based on the time-discontinuous Galerkin FEM, the unknown displacements and velocities are approximated as piecewise linear functions in the time domain, and are permitted to be discontinuous at the discrete time levels. This leads to stable and third-order accurate solution algorithms for ordinary di€erential equations. Numerical results using the time-discontinuous Galerkin FEM are compared with results using a conventional ®nite di€erence method (the Houbolt method). Both methods are employed for a particular integral BEM analysis in elastodynamics. This comparison reveals that the time-discontinuous Galerkin FEM is more stable and more accurate than the traditional ®nite di€erence methods