摘要
为了使自然单元法能够应用于土体等多孔介质的流固耦合计算,通过结合Biot固结理论及自然单元法自身特点,利用经典变分原理推导了固结微分方程的离散形式,并针对二维问题编制了相应的计算程序.算例结果表明,自然单元法的结果与解析解吻合良好,其精度高于有限单元法.从而验证了自然单元法在固结分析中的正确性,拓展了自然单元法的适用范围.
The natural element method （NEM） is a novel numerical computational method for solving partial differential equation. It is built upon the notion of the natural neighbor interpolation, which is based on Voronoi diagram and Delaunay triangulation. This paper focused on its application in solving Biot consolidation equation. The discrete form of control equation was obtained with classical variation principle; the algorithm routine for 2D condition was also elaborated. The results of numerical examples show that the results of NEM are in concordance with the analytical solution and the precision is higher than that of FEM.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
2008年第11期1880-1883,1887,共5页
Journal of Shanghai Jiaotong University
基金
国家自然科学基金资助项目(50679041)
关键词
自然单元法
BIOT固结方程
自然相邻插值
经典变分原理
natural element method （NEM）
Biot consolidation equation
natural neighbor interpolation
classical variation principle
