Three-dimensional BEM for transient elastodynamics based on the velocity reciprocal theorem

The conventional way for formulating a time domain boundary element method (TD-BEM) in linear elastodynamics is to utilize Graffiʹs reciprocal theorem. This theorem may either be the starting point in formulating a numerical methodology or the endpoint, if one starts directly from the governing equations of motion and follows various manipulations. The literature abounds with evidence of serious instability problems that accompany these formulations. Thus, research effort has been devoted on reducing this undesirable behavior. In this paper, we utilize a reciprocal theorem that relates velocities and tractions of two different elastodynamic states of the same body, in order to establish a well behaved TD-BEM formulation for 3D transient problems. It is shown that regarding stability, this straightforward formulation is capable of not only reducing instabilities compared to the conventional formulation, but also seems to eliminate the “intermittent” as well as the “sudden” instability problem.