Analyzing nonlinear large deformation with an improved element-free Galerkin method via the interpolating moving least-squares method

被引:47
作者
Cheng, Yumin [1 ]
Bai, Funong [1 ]
Liu, Chao [1 ]
Peng, Miaojuan [2 ]
机构
[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
[2] Shanghai Univ, Dept Civil Engn, Shanghai 200072, Peoples R China
基金
中国国家自然科学基金;
关键词
Meshless method; moving least-squares approximation; interpolating moving least-squares method; improved element-free Galerkin method; elastic large deformation;
D O I
10.1142/S2047684116500238
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Using the interpolating moving least-squares (IMLS) method to form the shape function, a novel improved element-free Galerkin (IEFG) method is presented for solving nonlinear elastic large deformation problems. To obtain the formulae of the IEFG method for elastic large deformation problems, we use the Galerkin weak form to obtain the discretized system equation, and use the penalty method to apply the displacement boundary conditions. Some selected numerical examples of two-dimensional elastic large deformation problems are given, and the numerical results are analyzed. From the examples, it is shown that the IEFG method in this paper has higher computational precision than the element-free Galerkin (EFG) method presented before.
引用
收藏
页数:22
相关论文
共 47 条
[1]   ELEMENT-FREE GALERKIN METHODS [J].
BELYTSCHKO, T ;
LU, YY ;
GU, L .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1994, 37 (02) :229-256
[2]   Meshless methods: An overview and recent developments [J].
Belytschko, T ;
Krongauz, Y ;
Organ, D ;
Fleming, M ;
Krysl, P .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :3-47
[3]   Reproducing kernel particle methods for large deformation analysis of non-linear structures [J].
Chen, JS ;
Pan, CH ;
Wu, CT ;
Liu, WK .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :195-227
[4]   AN INTERPOLATING LOCAL PETROV-GALERKIN METHOD FOR POTENTIAL PROBLEMS [J].
Chen, L. ;
Liu, C. ;
Ma, H. P. ;
Cheng, Y. M. .
INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2014, 6 (01)
[5]   Lower-bound limit analysis by using the EFG method and non-linear programming [J].
Chen, Shenshen ;
Liu, Yinghua ;
Cen, Zhangzhi .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 74 (03) :391-415
[6]   A complex variable meshless method for fracture problems [J].
Cheng, YM ;
Li, JH .
SCIENCE IN CHINA SERIES G-PHYSICS MECHANICS & ASTRONOMY, 2006, 49 (01) :46-59
[7]   Boundary element-free method for elastodynamics [J].
Cheng, YM ;
Peng, MJ .
SCIENCE IN CHINA SERIES G-PHYSICS MECHANICS & ASTRONOMY, 2005, 48 (06) :641-657
[8]  
Cheng Yumin, 2003, Acta Mechanica Sinica, V35, P181
[9]   Mathematical Aspects of Meshless Methods [J].
Cheng, Yumin ;
Wang, Wenqing ;
Peng, Miaojuan ;
Zhang, Zan .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
[10]   THE COMPLEX VARIABLE ELEMENT-FREE GALERKIN (CVEFG) METHOD FOR TWO-DIMENSIONAL ELASTODYNAMICS PROBLEMS [J].
Cheng, Yumin ;
Wang, Jianfei ;
Li, Rongxin .
INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2012, 4 (04)