材料非线性分析的自然单元法  

ANALYSIS FOR MATERIAL NONLINEARITY WITH NATURAL ELEMENT METHOD

作　　者：丁道红[1,2] 章青[1,2] 

机构地区：[1]河海大学水文水资源与水利工程科学国家重点实验室,江苏南京210098 [2]河海大学工程力学系,江苏南京210098

出　　处：《工程力学》2012年第A02期97-100,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(10972072;51179064;11132003);国家重点基础研究发展计划资助项目(2007CB714104);河海大学水文水资源与水利工程科学国家重点实验室专项基金项目(2009585912)

摘　　要：自然单元法主要是基于给定结点的Voronoi图,利用自然相邻插值进行形函数的构造,其形函数满足Kronecker delta性质,便于施加本质边界条件,这使得自然单元法同时兼有有限单元法和无网格法的优点。在材料非线性本构关系的基础上,推导了考虑材料非线性问题的自然单元法模型。算例表明:该模型在处理材料非线性问题时,具有一定的合理性和可行性,是一种有效的数值方法。Based on the Voronoi diagram of some nodes, the natural element method constructs a shape function by the natural neighbor interpolation, and its shape functions satisfy the Kronecker delta property, which makes it impose essential boundary conditions easily. From the advantages of a natural element method, we can see the natural element method owns the advantages of both finite element and meshless methods. Based on the material nonlinear constitutive relation, we derived the model of the natural element method for the problem of material nonlinearity. The result of numerical example shows that it is rationality and feasibility for the model in dealing with the material nonlinear problem, and it is an effective numerical method for solving the material nonlinear problem.

关 键 词：自然单元法 材料非线性 自然相邻插值 Sibson插值法 数值方法 

分 类 号：O241.8[理学—计算数学]