摘要
基于滑动最小二乘近似的无单元法摆脱了有限元法节点和单元之间彼此联系的约束,具有只需节点信息而不需单元信息的特点,故信息简单,可以求解复杂边界条件的边值问题,也很适用于岩土工程数值分析.文章对影响无单元法求解精度的关键因素——节点的分布进行了讨论,提出了规则节点与随机节点相结合的节点分布方法;其次,将无单元法与微分方程等价性相结合,导出了用无单元法表示的土体固结方程;最后,利用所提出的节点分布方法对一个一维函数进行了模拟,紧接着又对一受均布局部荷载作用的平面应变二维土体进行了算例分析,验证了该方法的有效性与合理性,同时也说明了无单元法在处理土体固结方面的可行性.
Element - free method(EFM) which is based on the moving least squares method, is not constrained by the connectivity between nodes and elements in the finite element method (FEM) . By this method, only nodal data is required, and no element connectivity is needed. It is well adopted to boundary value problems with complex boundary conditions in geotechnique engineering. In the paper, one of the key factors which affects the precision of the method, and the distribution of nodes are discussed. A new nodal distribution method is proposed based on combing stochastic and regular nodes. After that, EFM combines with equality of the partial differential equation, thus it can be applied to solve equation of consolidation. At last, a one-dimensional function is simulated with the proposed method, then a plane strain two-dimensional consolidation problem under a strip loading is also analyzed, and both prove the validity and efficiency of the method. In the mean time, all prove the feasibility of EFM in treating consolidation problems of soils.
出处
《宁夏工程技术》
CAS
2004年第1期14-17,23,共5页
Ningxia Engineering Technology
基金
宁夏高等学校科研基金资助项目(JY2002109)
宁夏大学科研基金资助项目(032106)
关键词
无单元法
土体
固结方程
滑动最小二乘法
土力学
element-free method
distribution of nodes
equation of consolidation
equality of the partial differential equation