Time discontinuous linear traction approximation in time-domain BEM: 2-D elastodynamics

This paper presents a further improvement of the standard time-domain BEM formulation for 2-D elas- todynamics. Linear-time interpolation is assumed for both boundary displacements and tractions. As this assumption implies time continuity for the variables, a procedure to consider tractions time discontinuities must be worked out. The initial step of this procedure consists of adding to the basic BEM integral equation the integral equation for velocities: after discretization is accomplished, this is done only for nodes with pre- scribed values of displacements. Additional equations are then incorporated to the nal system of algebraic equations, providing the means for the determination of the extra unknowns (represented by the tractions at the beginning of each time interval). The integral equations are presented by employing the concept of nite part of integrals, and the kernels are integrated analitically on time: complete time-integrated expressions are included in an appendix. Three numerical examples are presented in order to assess the accuracy of the proposed formulation.