弹性介质中SH波传播的三角形格子法

目的提出一种不规则边界非均匀弹性介质中反平面剪切(SH)波传播数值模拟方法,研究反平面剪切波入射时地表起伏及软弱层对场地的影响.方法将实际介质计算区域剖分成三角形网格,构造出控制体,给出积分形式的控制体运动方程;交替运用控制体运动方程和SH波的本构方程,在时间域上递推计算给出被研究区域内各节点的加速度、速度、位移和各格子的应力.结果给出了弹性介质中SH波传播数值模拟三角形格子法.数值算例结果与解析解比较,验证了方法的计算精度和有效性.瞬态反平面剪切波入射时,地表起伏、软弱层会引起场地的运动状态量和应力量的放大,有运动状态量和最大剪应力集中现象.结论SH波传播数值模拟三角形格子法计算精度较高,处理不规则边界非均匀介质波动问题的适应性强,算法实现简单、计算量小.是研究大规模、不规则边界非均匀介质中SH波传播问题的一种有力工具,为岩土动力学中的波动研究提供了一种新的数值方法.

Triangular Grid Algorithm for SH Wave Propagation in Elastic Media

A triangular grid algorithm is presented for simulating out-of-plane shear(SH) wave propagation in heterogeneous elastic media with irregular boundary.The control volumes are constructed among the triangular mesh of spatial discretization in the calculating region,and then the dynamic equilibrium equations of control volumes are given.By applying the dynamic equilibrium equations of control volumes and the constitutive equations of SH wave alternately,the nodal accelerations,velocities,displacements,and the shear stresses in every grid can be obtained in time domain.Thus the triangular grid algorithm for SH wave propagation is established.Comparison with analytical solution,it shows that the numerical algorithm is of good accuracy.It is of the characteristics of simple code and less computation.It is very applicable to handle transient SH wave propagation in heterogeneous elastic media with arbitrary irregular boundary.The algorithm is used to investigate the problems of the site effect where exist surface topography and layer of soft soil during SH wave propagates.The concentration phenomena are studied for the maximum shear stress,the displacements and accelerations.The algorithm presents a useful tool for simulating SH wave propagation in a quite large region of complex geologic structures and provides a new approach for the investigations of wave propagations in soil dynamics.