上海交通大学学报

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2008 , Vol. 42 >Issue 11: 1880 - 1883,1887

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2008.11.028

二维Biot固结方程的自然单元法求解

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  • 上海交通大学土木工程系，上海 　200030
褚衍标（1984-)，男，山东枣庄人，硕士生，主要研究方向为计算岩土力学．|王建华（联系人），男，教授，博士生导师，电话（Tel.):021-62932915; E-mail:wjh417@sjtu.edu.cn.

收稿日期: 2007-11-28

  网络出版日期: 2008-11-28

基金资助

国家自然科学基金资助项目(50679041)

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Natural Element Method for Biot Plane Consolidation Analysis

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  • Department of Civil Engineering, Shanghai Jiaotong University, Shanghai 200030, China

Received date: 2007-11-28

  Online published: 2008-11-28

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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．

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

本文引用格式

褚衍标, 王建华 . 二维Biot固结方程的自然单元法求解[J]. 上海交通大学学报, 2008 , 42(11) : 1880 -1883,1887 . DOI: 10.16183/j.cnki.jsjtu.2008.11.028

Abstract

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.

Key words： natural element method (NEM); Biot consolidation equation; natural neighbor interpolation; classical variation principle

参考文献

[1] Braun J, Sambridge M. A numerical method for solving partial differential equations on highly irregular evolving grids[J]. Nature, 1995, 376: 655-660.
[2] Sukumar N, Moran B, Belytschko T.The nature element method in solid mechanics[J]. International Journal of Numerical Method in Engineering, 1998, 43: 839-887.
[3] 戴斌, 王建华.自然单元法原理与三维算法实现[J]. 上海交通大学学报, 2004, 38(7): 1222-1224.
[3] DAI Bin, WANG Jian-hua. The natural element method and its computational algorithms in three dimensions[J]. Journal of Shanghai Jiaotong University, 2004, 38(7): 1222-1224.
[4] 王建华, 张英新, 高绍武.三维弹塑性自然单元法算法实现[J]. 计算力学学报, 2006, 23(5): 594-598.
[4] WANG Jian-hua, ZHANG Ying-xin, GAO Shao-wu. The computational methods of natural element method in three dimensional elasto-plastic analysis[J]. Chinese Journal of Computational Mechanics, 2006, 23(5): 594-598.
[5] 朱怀球, 吴江航.一种基于Voronoi Cells的C∞插值基函数及其在计算流体力学中的若干应用[J]. 北京大学学报(自然科学版), 2001, 37(5): 669-678.
[5] ZHU Huai-qiu, WU Jiang-hang. A Voronoi cells based C∞ interpolation basis function and its application in CFD[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2001, 37(5): 669-678.
[6] Sukumar N.Voronoi cell finite diference method for the difusion operator on arbitrary unstructured grids[J]. International Journal for Numerical Methods in Engineering, 2003, 57: 1-34.
[7] Sibson R. A brief description of natural neighbor interpolation [C]//Barnett V.Interpreting Multivariate Data, Chichester: Wiley, 1981: 21-36.
[8] 郑家栋, 胡慧智, 徐鸿江, 等.解Biot固结方程的有限元方法[J]. 应用数学和力学, 1982, 3(6): 793-805.
[8] ZHENG Jia-dong, HU Hui-zhi, XU Hong-jiang, et al. The application of the finite element method to solve Biot′s consolidation equation[J]. Applied Mathematics and Mechanics, 1982, 3(6): 793-805.
[9] 龚晓南.土工计算机分析[M]. 北京: 中国建筑工业出版社, 2000.
[10] 黄传志, 肖原.二维固结问题的解析解[J]. 岩土工程学报, 1996, 18(3): 47-54.
[10] HUANG Chuan-zhi, XIAO Yuan. Analytical solution of a two dimensional consolidation problems[J]. Chinese Journal of Geotechnical Engineering, 1996, 18(3): 47-54.
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