针对砂土应变软化强非线性问题的动态松弛有限元法研究

›› 2012, Vol. 33 ›› Issue (2): 590-596.

针对砂土应变软化强非线性问题的动态松弛有限元法研究

彭芳乐^{1, 2}，李福林^{1, 3}，白晓宇^{1, 2}

1.同济大学地下建筑与工程系，上海 200092；2.同济大学岩土及地下工程教育部重点实验室，上海 200092； 3. 中国矿业大学力学与建筑工程学院，江苏徐州 221116

收稿日期:2010-07-16 出版日期:2012-02-10 发布日期:2012-02-14
作者简介:彭芳乐，男，1965年生，博士，教授，博士生导师，主要从事岩土力学、地下空间与工程等方面的研究工作。
基金资助:
国家自然科学基金（No. 40972176）；教育部长江学者和创新团队发展计划资助（No. IRT1029）；上海市重点学科建设项目（No. B308）。

A dynamic relaxation - finite element method for strong nonlinearity caused by post-peak strain softening of sands

PENG Fang-le^{1, 2}, LI Fu-lin^{1, 3}, BAI Xiao-yu^{1, 2}

1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China; 2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China; 3. School of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China

Received:2010-07-16 Online:2012-02-10 Published:2012-02-14

摘要/Abstract

摘要： 对于密实砂土峰值后应变软化特性引起的材料强非线性问题，利用常规有限元所采用的隐式算法很难求解，而动态松弛法在求解这类非线性问题方面却具有独特的优势。针对砂土应变软化强非线性问题，将动态松弛法与有限单元法相结合，提出了一种新的动态松弛有限元法。该方法根据动态松弛法的显式特性，由中心差分法导出了动态松弛有限元法的基本控制方程，并实现了对应力-应变空间中整个平衡路径的追踪。将动态松弛法嵌入到非线性有限元程序中，即可对砂土材料应变软化引起的强非线性问题进行有限元数值计算。该有限元程序中，应力更新采用回归映射算法。最后通过对砂土平面应变压缩试验进行有限元模拟，验证了动态松弛有限元法在求解材料强非线性问题方面的优越性。

关键词: 砂土, 应变软化, 有限单元法, 强非线性, 动态松弛, 显式算法

Abstract: In the presence of the strong material nonlinearity caused by post-peak strain softening of dense sandy soils, the solution of traditional finite element method (FEM) with implicit algorithm often becomes intractable. The dynamic relaxation (DR) method has a great reputation in solving highly nonlinear equations. A new dynamic relaxation-finite element method (DR-FEM) for strong nonlinearity caused by post-peak strain softening of sands is proposed, which takes into account the advantages of DR and FEM together. According to the explicit nature of DR and the central difference technique, the general governing equations of DR-FEM has been derived. The way of tracing the whole equilibrium curve in the stress-strain space has also been presented; and then the DR method is implemented into a general nonlinear finite element codes. The return mapping algorithm is used for stress updating, which is a first-order approximated Euler backward integration. Therefore, the strong material nonlinearity caused by post-peak strain softening of sandy soils can be simulated by the proposed DR-FEM combined with the corresponding material model. The DR-FEM is validated by simulating the result of physical plane strain compression test performed on sands. It is shown that the DR method has a superiority to solve the material nonlinearity.

Key words: sands, strain softening, finite element method, strong nonlinearity, dynamic relaxation, explicit algorithm

中图分类号:

O 242.21

彭芳乐，李福林，白晓宇. 针对砂土应变软化强非线性问题的动态松弛有限元法研究[J]. , 2012, 33(2): 590-596.

PENG Fang-le , LI Fu-lin , BAI Xiao-yu. A dynamic relaxation - finite element method for strong nonlinearity caused by post-peak strain softening of sands[J]. , 2012, 33(2): 590-596.

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