基础-饱和土地基耦合系统分析的微分求积单元法  

Differential Quadrature Element Method for Analysis of Foundation-Saturated Soil Coupled System

作　　者：刘静[1] 朱媛媛[1] 胡育佳[2] 

机构地区：[1]上海师范大学计算机科学与技术系,上海200234 [2]上海理工大学机械工程学院,上海200093

出　　处：《力学季刊》2014年第1期54-65,共12页Chinese Quarterly of Mechanics

基　　金：国家自然科学青年基金(11002084);上海市教委创新基金(12YZ074;12YZ092)

摘　　要：研究了基础-饱和土地基耦合系统的动力学特性.首先根据多孔介质理论,在小变形的假设下,分别建立了耦合系统中不可压流体饱和土地基和弹性基础的运动微分方程以及相应的边界条件,连接条件和初始条件;然后在空间域采用微分求积单元法对基础-饱和土地基的控制方程进行离散,并提供了正确处理耦合系统界面之间连接条件和间断性条件的方法,从而得到时间域内的一组代数-微分方程;接着运用隐式二阶向后差分格式处理了代数-微分方程组;最后利用牛顿迭代法数值求解了该方程组,得到了耦合系统的数值解,考察了所布节点数和参数对数值结果的影响.The dynamic characteristic of a foundation-saturated soil coupled system was studied in this paper. Firstly, based on the porous media theory, the governing equations of incompressible fluid-saturated soil and elastic foundation were presented in the case of small deformation respectively, and the corresponding boundary conditions, initial conditions as well as the joint conditions were derived. Then, the differential quadrature element method and the second-order backward difference scheme were used to discretize the governing equations of the coupled system on the spatial and temporal domains respectively, in which, a general method was presented to deal with the continuity and discontinuity conditions on the interface between the foundation and the saturated soil, and a set of nonlinear ordinary differential equations was yielded with respect to time. Finally, the Newton-Raphson method was adopted to solve the discretization equations, the dynamic characteristics of the coupled system were analyzed, and the effects of number of grid points and parameters were considered.

关 键 词：基础-饱和土地基耦合系统 流体饱和多孔介质理论 微分求积单元法(DQEM) 动力学特性 

分 类 号：O342[理学—固体力学]