Meshless local boundary integral equation method for 2D elastodynamic problems

A new meshless method for solving transient elastodynamic boundary value problems, based on the local boundary integral equation (LBIE) method and the moving least squares approximation (MLS), is proposed in this paper. The LBIE with the MLS is applied to both transient and steady-state (Laplace transformed) elastodynamics. Applying the MLS approximation for spatially dependent terms in the rst approach, the LBIEs are transformed into a system of ordinary di erential equations for nodal unknowns. This system of ordinary di erential equations is solved by the Houbolt nite di erence scheme. In the second formulation, the time variable is eliminated by using the Laplace transformation. Unknown Laplace transforms of displacements and traction vectors are computed from the LBIEs with the MLS approximation. The time-dependent values are obtained by the Durbin inversion technique