摘要
提出了一种计算出平面SH波斜入射时弹性水平成层半空间中自由波场时域计算的一维化有限元方法．在进行有限元网格划分时,竖向单元取满足有限元模拟精度的任意尺寸,水平向网格尺寸由时间离散步长和水平视波速确定,并自动进行虚拟网格划分．基底设置人工边界,并将波动输入转化为等效荷载施加在边界节点上．然后将集中质量有限元法和中心差分法相结合建立节点运动方程,并将水平方向相邻节点的运动用该节点相邻时刻的运动表示,从而将求解节点运动的二维方程组转化为一维方程组．求解此方程组,即得到自由场中竖向一列节点的运动．最后根据行波传播的特点,可方便地确定全部自由波场．理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性．
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.
出处
《力学学报》
EI
CSCD
北大核心
2006年第2期219-225,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(50478014)国家973计划(2002CB412706)北京市自然科学基金重点项目(8061003)资助.~~
关键词
水平成层半空间
斜入射
显式有限元法
Snell定律
人工边界
虚拟划分
layered half-space, oblique incidence, explicit finite element method, Snell law, artificial boundary,virtual division
