A point interpolation method with least square strain field (PIM-LSS) for solution bounds and ultra-accurate solutions using triangular mesh

作     者：Xu, X. Liu, G. R. Zhang, G. Y. 

作者机构：Jilin Univ Coll Math Changchun 130012 Peoples R China Singapore MIT Alliance SMA Singapore 117576 Singapore Natl Univ Singapore Ctr Adv Computat Engn Sci ACES Dept Mech Engn Singapore 117576 Singapore 

出 版 物：《COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING》 (应用力学和工程技术中的计算机方法)

年 卷 期：2009年第198卷第17-20期

页      面：1486-1499页

核心收录：

学科分类：08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [10532050, 10501017, 60673023] Jilin University, China ACES Singapore-MIT Alliance (SMA) National University of Singapore 

主　　题：Numerical methods Finite element method Meshfree method Point interpolation method Solution bound Strain constructed Galerkin weak form Least square method 

摘      要：A point interpolation method with least square strain field (PIM-LSS) is developed for solid mechanics problems using triangular background mesh. In the PIM-LSS, PIM shape functions are used for displacement field construction that may or may not be compatible, and a least square fitting technique is adopted to construct the strain field. A strain constructed Galerkin (SC-Galerkin) weak formulation is then proposed for establishing discretized PIM-LSS models that have a number of special properties. We proved theoretically (1) the PIM-LSS provides a softening effect to the FEM model. and a stiffing effect to the node-based smoothed point interpolation method (NS-PIM) model;(2) the exact solution is bounded from both by PIM-LSS solutions with strain field of zero-order fitting and that with higher order fitting: (3) There exists a preferred order of fitting for the strain field such that ultra-accurate (one order higher accuracy) solution can be obtained using the PIM-LSS. These theorems and properties have been confirmed in numerical examples. (C) 2009 Elsevier B.V. All rights reserved.