1D Time-Domain Method for 2D Wave Motion in Elastic Half-Space by  Antiplane Wave Oblique Incidence
Liu Jingbo,Wang Yan
(Department of Civil Engineering, Tsinghua University, Beijing 100084, China)

Abstract: A 1D finite element method in time domain is developed, where the wave motion of free field in elastic half-space by SH wave oblique incidence is simulated. The horizontal propagation characteristic of plane wave is revealed on t he basis of Snell law, when the elastic half-space is discreted by finite element, the vertical element size is determined according to the demand of simulation accuracy, and the horizontal element size is determined by the propagation cha racteristic and the discrete time step. Therefore, the displacement of any node in finite element model can be represented by that of the adjacent node in horizontal direction to reduce the wave motion equations in 2D finite element model to 1D scheme. Solving the 1D equations, the displacement of nodes in one vertical line is obtained, and the wave motion in half space is sought based on the prop agation characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate the satisfied accuracy and stability.
Keywords: SH wave, oblique incidence, elastic half-space, Snell law, one-dimension computational method.