有限覆盖Kriging插值无网格法在裂纹扩展中的应用  

KRIGING INTERPOLATION MESHLESS METHOD BASED ON FINITE COVERS AND ITS APPLICATION TO CRACK PROPAGATION

作　　者：樊成[1] 栾茂田[2] 

机构地区：[1]大连大学材料破坏力学数值试验研究中心,辽宁大连116622 [2]大连理工大学岩土工程研究所,辽宁大连116024

出　　处：《岩石力学与工程学报》2008年第4期743-748,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项目

摘　　要：无网格法前处理过程比较简单,Kriging插值无网格法是其中的一种格式。数值流形方法能够统一处理连续与非连续变形问题,有限覆盖技术是该方法的核心。将有限覆盖技术与Kriging插值无网格法相结合发展有限覆盖Kriging插值无网格法,综合数值流形方法与Kriging插值无网格法各自优点,能够有效地处理连续与非连续性问题,而且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处理奇异问题和非连续问题的能力。The meshless methods have a relative simple pretreatment process. The Kriging interpolation procedure is one of the meshless methods. 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. Both the finite cover technique and Kriging interpolation method are integrated to develop a Kriging interpolation procedure based on finite covers which take advantages of these two types of numerical methods. The merit of the proposed method is that the shape functions constructed using this method have the properties of Kronecker δ-function, which will make the essential boundary conditions be easily implemented. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method for singular and discontinuous problems.

关 键 词：数值分析 无网格法 KRIGING插值 有限覆盖 Kroneckerδ–函数属性 

分 类 号：O241[理学—计算数学]