Kriging插值无网格方法及其在力学边值问题中的应用  

A NEW-TYPE ELEMENT-FREE METHOD BASED ON KRIGING INTERPOLATION SCHEME AND ITS APPLICATION TO SOLVING BOUNDARY-VALUE PROBLEM OF MECHANICS

作　　者：樊成[1] 栾茂田[1] 黎勇[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：《岩石力学与工程学报》2007年第1期195-200,共6页Chinese Journal of Rock Mechanics and Engineering

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

摘　　要：在传统的无网格Galerkin法中,采用滑动Kriging插值方法构造形函数,并与无网格方法相结合建立一种新的无网格方法。依此方法所构造的形函数具有Kroneckerδ-函数属性,便于直接施加强制边界条件。结合弹性力学边值问题,阐述该方法的基本原理,进而通过算例计算与分析,考察该方法的计算精度及其效率。　Presented in this paper is a new formulation of the element-free Galerkin method for the boundary-value problems of solid mechanics in which the moving Kriging interpolation procedure is employed instead of moving least squared procedure to construct shape function.The proposed procedure is characterized by the feature that the shape function constructed by moving Kriging procedure possess the property of Kronecker δ-function and the consistency property.At the same time,the specified essential boundary conditions can be easily implemented while displacement boundary conditions are not easily imposed in the conventional element-free methods.The fundamental theory of this procedure is illustrated;and mathematical formulations are given.Then numerical examples are analyzed by the proposed procedure;and the computed results are compared with other solutions to verify the effectiveness and accuracy of the proposed method.

关 键 词：数值分析 无网格方法 KRIGING插值 KRONECKER δ-函数属性 

分 类 号：O241[理学—计算数学]