二维Biot固结方程的自然单元法求解

doi:10.16183/j.cnki.jsjtu.2008.11.028

上海交通大学学报 ›› 2008, Vol. 42 ›› Issue (11): 1880-1883,1887.doi: 10.16183/j.cnki.jsjtu.2008.11.028

所属专题：王建华教授学报发文专辑

二维Biot固结方程的自然单元法求解

褚衍标, 王建华()

上海交通大学土木工程系，上海　200030

收稿日期:2007-11-28 出版日期:2008-11-01 发布日期:2008-11-28
作者简介: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.
基金资助:
国家自然科学基金资助项目(50679041)

Natural Element Method for Biot Plane Consolidation Analysis

CHU Yan-biao, WANG Jian-hua()

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

Received:2007-11-28 Online:2008-11-01 Published:2008-11-28

摘要/Abstract

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

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

中图分类号:

TU43
O241

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.

CHU Yan-biao, WANG Jian-hua. Natural Element Method for Biot Plane Consolidation Analysis[J]. Journal of Shanghai Jiao Tong University, 2008, 42(11): 1880-1883,1887.

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深度/m	14 d		42 d		70 d		140 d
深度/m	FEM	NEM	FEM	NEM	FEM	NEM	FEM	NEM
-1	-7.86	-1.78	-6.01	-1.09	-4.09	0.22	-0.12	0.01
-2	-3.29	2.78	-3.67	0.29	-3.69	-1.05	3.06	-0.34
-3	-0.26	0.98	-1.17	0.23	-0.98	0.74	-1.83	0.20
-4	0.19	1.75	-0.74	0.49	-0.82	-0.11	0.83	-0.09
-5	0.75	1.27	-0.47	0.59	-0.69	0.50	-0.94	0.11
-6	1.14	0.78	0.24	0.51	-0.05	0.29	-0.27	0.03
-7	0.99	0.64	0.55	0.50	0.25	0.28	-0.02	0.00
-8	0.70	0.59	0.34	0.55	0.09	0.42	-0.35	0.04
-9	0.99	0.84	0.64	0.62	0.37	0.40	-0.03	0.00
-10	0.61	1.01	0.36	0.65	0.23	0.50	-0.11	0.01

二维Biot固结方程的自然单元法求解

Natural Element Method for Biot Plane Consolidation Analysis

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