有限覆盖点插值无网格方法及其应用  

Element-free point-interpolation procedure based on finite covers and its application

作　　者：樊成[1] 栾茂田[1] 杨庆[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室

出　　处：《大连理工大学学报》2007年第4期577-582,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10172022);教育部跨世纪优秀人才培养计划研究基金资助项目(教技函[1999]2号)

摘　　要：数值流形方法能够统一地处理连续与非连续变形问题,有限覆盖技术是这种方法的核心.无网格方法的前处理比较简单,点插值法是其中的一种计算格式.为此,将有限覆盖技术与点插值方法相结合发展了有限覆盖点插值无网格方法,从而综合了数值流形方法与点插值方法的各自优点,能够有效地处理非连续性问题.在简要阐述了该方法基本原理的基础上,对其进行了分片检验和曲线拟合试验,由此证明了这种方法的收敛性,同时表明由这种方法所构造的形函数具有Kroneckerδ-函数属性,曲线拟合精度较高.Numerical manifold method can solve both continuous and discontinuous deformation problems in a unified mathematical formulation. The finite cover is the essential technique in this method. The element-free methods have a relative simple pre-treatment process. The point-interpolation procedure is one of the element-free methods. So the finite cover technique and point-interpolation method are integrated together to develop an element-free point-interpolation procedure based on finite covers which takes both advantages of these two types of numerical methods. The fundamental theory of this procedure is illustrated. Then it is shown that the convergence can be guaranteed by the patch test. As an example, curve-fitting test is conducted and it is shown that the shape functions constructed by the proposed method can display the property of Kronecker δ-function and the curve fitted by the procedure has a higher accuracy.

关 键 词：有限覆盖 无网格 有限覆盖点插值法 Kroneckerδ-函数属性 

分 类 号：TU311.4[建筑科学—结构工程]