An efficient hybrid time-Laplace domain method for elastodynamic analysis based on the explicit Green’s approach

This work aims at presenting a novel hybrid method applied to the numerical solution of elastodynamic problems. The formulation is based on the so-called Explicit Green’s Approach (ExGA), recently developed by Mansur et al. [Mansur, W.J., Loureiro, F.S., Soares Jr., D., Dors, C., 2007. Explicit time-domain approaches based on numerical Green’s functions computed by finite differences – the ExGA family. Journal of Computational Physics 227, 851–870.] in which a recursive time integration procedure based on Green’s function is adopted. Here, the finite element method is employed to calculate the Green’s function in the Laplace domain; afterwards, the Zakian’s Laplace inversion algorithm is employed to compute numerically the Green’s function in the time domain, only at time t=Δtt=Δt. Time integration is then carried out by employing the standard ExGA procedure and another where the convolution integral is replaced by a particular solution that is directly related to the applied load. Finally, some numerical problems are solved to demonstrate the computational efficiency and reliability of the proposed hybrid method.