摘要
鉴于以Goodman单元为代表的界面单元在传统有限元法中取得了广泛而成功的应用,因而采用无网格法进行岩土工程数值分析时,首先考虑引入Goodman单元以模拟不连续面。详细分析将Goodman单元引入无网格法模拟不连续面的可行性和当前研究所存在的问题。研究结果表明,由于Goodman单元最初的应用对象是有限元法,其位移模式实质是为了实现与其相连接的有限单元相协调;而无网格的位移模式是基于离散节点的,对于不同的待插值点,影响域覆盖该插值点的节点及其数量也不相同;因而必然存在着无网格法的位移模式与Goodman单元边界上假定的位移模式不相协调的问题。解决这个问题的关键是在考虑节理单元的刚度对总体刚度矩阵的贡献时,应采用数值积分计算得到节理单元的刚度矩阵而不是简单的将传统解析表达式累加到求解系统的总体刚度矩阵中去;考虑到上述特点,界面单元可以隐式或显式出现在计算模型中。以自然单元法为例详细介绍显式和隐式Goodman单元的具体实现方案,并给出相应的算例进行数值验证和对比;所提出的思路对于一般的无网格方法都是适用的。
Various interface elements are successfully applied in traditional finite element method（FEM） to model discontinuities, in which Goodman element is the most representative one. The paper discusses the feasibility of introducing Goodman element to model geological discontinuities in meshless method in full length, and points out the problems existing in some current studies. The Goodman element is presented in the framework of FEM~ the displacement mode of Goodman element is designed to be compatible with the finite element along the common boundary between finite element and Goodman element. But, in the meshless method, the displacement mode of Goodman element generally is not compatible with the meshless displacement mode which is based on a number of discrete nodes, the number, however, cannot be known beforehand. The key to solve this problem is that the stiffness matrix of the Goodman element must be computed through numerical integration, then the computed matrix but not the analytical stiffness matrix in the traditional FEM is added to the general matrix of the system when the contribution of the Goodman element to the general stiffness matrix is considered. So, discontinuities can be represented by Goodman element in analytical model in implicit or explicit mode. In the framework of the natural element method（NEM）, the implementation scheme of the Goodman element, implicitly and explicitly respectively, is addressed in detail for illustration of the idea. The presented method is general and suitable for all existing meshless methods.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2008年第10期2108-2117,共10页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金重大项目(50539110
50639090)
长江科学院科研基金资助项目"自然单元法在岩土工程中的应用研究"
关键词
岩石力学
数值分析
不连续面
Goodman单元
有限元法
无网格法
自然单元法
rock mechanics
numerical analysis
discontinuities： Goodman element
finite element method（FEM）
meshless method
natural element method（NEM）
