A 1-D time-domain method for 2-d wave motion in elastic layered half-space by antiplane wave oblique incidence

A 1-D finite element method in time domain is developed inthis paper, which can be used to calculate the wave motion of free field inelastic layered half-space by antiplane SH wave oblique incidence. When thelayered half-space is discretized, the vertical element size is determinedconforming to the simulation accuracy; the horizontal element sizeis determined automatically by the horizontal apparent wave velocity and thediscrete time step in the step-by-step calculation, and then the elements aredivided virtually. Artificial boundary is constructed on the bottom ofthe computational area and the input wave motion is transformed into an equivalentload, which is applied on the nodes of the boundary. Then, the finite elementmethod with lumped mass and the central difference method are combined to establish the wave motion equations in 2-D finite element model.Since the displacement of any node in the finite element model can berepresented by that of the adjacent node in the horizontal direction, the 2-Dwave motion equations can be transformed into 1-D equations. By solving the1-D equations, the displacement of nodes in one vertical line can beobtained. Finally, the wave motion in elastic half-space is obtained basedon the propagation characteristics of traveling wave. Both the theoreticalanalysis and the numerical results demonstrate that the proposed methodfeatures high accuracy and good stability.