A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

作     者：Xu, X. Liu, G. R. Gu, Y. T. Zhang, G. Y. Luo, J. W. Peng, J. X. 

作者机构：Jilin Univ Coll Math Changchun 130012 Peoples R China Singapore MIT Alliance SMA Singapore 117576 Singapore Queensland Univ Technol Sch Engn Syst Brisbane Qld 4001 Australia Natl Univ Singapore Dept Mech Engn Ctr Adv Computat Engn Sci ACES Singapore 117576 Singapore 

出 版 物：《FINITE ELEMENTS IN ANALYSIS AND DESIGN》 (分析与设计用有限元法)

年 卷 期：2010年第46卷第10期

页      面：862-874页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Program for New Century Excellent Talents in University (NCET) 985 program Jilin University A*Star, Singapore State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body, Hunan University, PR China 

主　　题：Finite element method Meshfree methods Point interpolation method Solution bounds Extended Galerkin Softening effect 

摘      要：A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM-LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very tight lower and upper bound solutions can be obtained using PIM-LS2. (C) 2010 Elsevier B.V. All rights reserved.