饱和多孔介质动力分析的数值流形单元  

NUMERICAL MANIFOLD ELEMENT FOR DYNAMIC ANALYSIS OF SATURATED POROUS MEDIA

作　　者：周雷[1] 张洪武[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024

出　　处：《工程力学》2006年第9期167-172,共6页Engineering Mechanics

基　　金：国家自然科学基金与创新群体基金(10225212;10421002);长江学者和创新团队发展计划;国家基础性发展规划项目(2005CB321704)

摘　　要：基于数值流形方法中覆盖函数的基本思想,构造了适用于饱和多孔介质动力耦合分析的三节点平面流形单元,该单元满足Babuska-Brezzi稳定性准则与Zienkiewicz-Taylor分片试验条件,对于位移和孔隙压力具有不等阶的插值函数,且所有节点上具有相同自由度。用标准Galerkin法和Newmark法将饱和多孔介质动力基本方程在空间和时间上离散,得到饱和多孔介质动力分析的流形元离散的算法公式。数值结果表明,与传统有限元相比在孔隙流体不可压缩且非渗流的条件下,数值流形单元对于压力场的计算具有良好的数值稳定性。A three nodal plane manifold element is developed based on the technique of cover function of numerical manifold method （NMM） for dynamic analysis of saturated porous media. The advantages of the manifold element developed are that it satisfies the so-called Babuska-Brezzi stability criterion and Zienkiewicz-Taylor patch test. The interpolation of displacement and pressure can be determined independently. All nodes of the manifold element have uniform degrees of freedom. The standard Galerkin method and Newmark scheme are used in the spatial and temporal discretization of the governing equations. Compared with the widely used traditional finite element method （FEM）, the manifold element method （MEM） presents good stability for the coupling problems, particularly in the nearly incompressible pore fluid and undrained conditions.

关 键 词：饱和多孔介质 数值流形方法 稳定性准则 覆盖函数 流固耦合 

分 类 号：TU435[建筑科学—岩土工程]