流体饱和多孔弹性柱体动力响应的微分求积法

基于多孔介质混合物理论,在小变形的假设下,建立了两相不可压流体饱和多孔介质弹性空间轴对称问题的控制方程。在空间域和时间域内分别采用微分求积方法和二阶向后差分格式来离散控制方程,给出了处理对称轴处奇异性条件的方法,并在空间离散后采用消元法来缩减未知量,提高计算速度。作为应用,分析了流体饱和弹性多孔介质圆柱体的动力响应,考察了所布节点数对数值结果的影响。

DQM for dynamic responses of fluid-saturated porous elastic column

Based on the porous media theory (PMT), governing equations of space-axisymmetrical problem for incompressible fluid-saturated porous elastic media is presented in the case of small deformation. The differential quadrature method (DQM) and the second-order backward difference scheme are used to discretize the governing equations in the spatial and temporal domains respectively. A method is proposed to deal with the singularity condition at points located on the symmetry axis. In order to improve the computing speed, the elimination method is applied to reduce the number of unknowns after discretization in the spatial domain. As application, the dynamic behaviors of a column of fluid-saturated elastic porous media are analyzed, the effect of number of grid points on the numerical results is considered.