A 1-D time-domain method for 2-d wave motion in elastic layered half-space by antiplane wave oblique incidence
成层半空间出平面自由波场的一维化时域算法

A 1-D finite element method in time domain is developed in this paper, which can be used to calculate the wave motion of free field in elastic layered half-space by antiplane SH wave oblique incidence. When the layered half-space is discretized, the vertical element size is determined conforming to the simulation accuracy; the horizontal element size is determined automatically by the horizontal apparent wave velocity and the discrete time step in the step-by-step calculation, and then the elements are divided virtually. Artificial boundary is constructed on the bottom of the computational area and the input wave motion is transformed into an equivalent load, which is applied on the nodes of the boundary. Then, the finite element method 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 be represented by that of the adjacent node in the horizontal direction, the 2-D wave motion equations can be transformed into 1-D equations. By solving the 1-D equations, the displacement Of nodes in one vertical line can be obtained. Finally, the wave motion in elastic half-space is obtained based on the propagation characteristics of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method features high accuracy and good stability.