Journal of Shanghai Jiao Tong University

Journal of Shanghai Jiaotong University >

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

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

Natural Element Method for Biot Plane Consolidation Analysis

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

Received date: 2007-11-28

  Online published: 2008-11-28

Fold

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

Cite this article

CHU Yan-biao, WANG Jian-hua . Natural Element Method for Biot Plane Consolidation Analysis[J]. Journal of Shanghai Jiaotong University, 2008 , 42(11) : 1880 -1883,1887 . DOI: 10.16183/j.cnki.jsjtu.2008.11.028

References

[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.
Options
Outlines

/

〈 〉