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

This study proposes a time-discontinuous Galerkin finite element method (FE M) for solving second-order ordinary differential equations in the time dom ain. The equations are formulated using a particular integral boundary elem ent method (BEM) in the space domain for elastodynamic problems. The partic ular integral BEM technique depends only on elastostatic displacement and t raction fundamental solutions, without resorting to commonly used complex f undamental solutions for elastodynamic problems. Based on the time-disconti nuous Galerkin FEM, the unknown displacements and velocities are approximat ed as piecewise linear functions in the time domain, and are permitted to b e discontinuous at the discrete time levels. This leads to stable and third -order accurate solution algorithms for ordinary differential equations. Nu merical results using the time-discontinuous Galerkin FEM are compared with results using a conventional finite difference method (the Houbolt method) . Both methods are employed for a particular integral BEM analysis in elast odynamics. This comparison reveals that the time-discontinuous Galerkin FEM is more stable and more accurate than the traditional finite difference me thods. (C) 2000 Elsevier Science Ltd. FLU rights reserved.