THE COMPLEX VARIABLE ELEMENT-FREE GALERKIN (CVEFG) METHOD FOR TWO-DIMENSIONAL ELASTODYNAMICS PROBLEMS

被引：82
作者：
Cheng, Yumin [1 ]
Wang, Jianfei [1 ]
Li, Rongxin [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
来源：
INTERNATIONAL JOURNAL OF APPLIED MECHANICS | 2012年 / 4卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Moving least-squares approximation; complex variable moving least-squares approximation; element-free Galerkin method; complex variable element-free Galerkin method; elastodynamics; FREE-METHOD BEFM; FREE METHOD IBEFM; IEFG METHOD;
D O I：
10.1142/S1758825112500421
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The complex variable moving least-squares (CVMLS) approximation is discussed in this paper, and the mathematical and physical meaning of the complex functional in the CVMLS approximation is presented. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. Then combining the CVMLS approximation and the Galerkin weak form, we investigate the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. The penalty method is used to apply the essential boundary conditions, and the implicit time integration method, which is the Newmark method, is used for time history analysis. Then the corresponding formulae of the CVEFG method for two-dimensional elastodynamics problems are obtained. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method. Compared with the EFG method, the CVEFG method has greater precision.
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页数：23
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[21]   An improved boundary element-free method (IBEFM) for two-dimensional potential problems [J].
Ren Hong-Ping ;
Cheng Yu-Min ;
Zhang Wu .
CHINESE PHYSICS B, 2009, 18 (10) :4065-4073
[22]   The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems [J].
Ren, Hongping ;
Cheng, Yumin .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2012, 36 (05) :873-880
[23]   THE INTERPOLATING ELEMENT-FREE GALERKIN (IEFG) METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS [J].
Ren, Hongping ;
Cheng, Yumin .
INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2011, 3 (04) :735-758
[24]   An interpolating boundary element-free method (IBEFM) for elasticity problems [J].
Ren HongPing ;
Cheng YuMin ;
Zhang Wu .
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY, 2010, 53 (04) :758-766
[25]   Analyzing 2D fracture problems with the improved element-free Galerkin method [J].
Zhang, Zan ;
Liew, K. M. ;
Cheng, Yumin ;
Lee, Y. Y. .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2008, 32 (03) :241-250
[26]   Coupling of the improved element-free Galerkin and boundary element methods for two-dimensional elasticity problems [J].
Zhang, Zan ;
Liew, K. M. ;
Cheng, Yumin .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2008, 32 (02) :100-107
[27]   The improved element-free Galerkin method for three-dimensional wave equation [J].
Zhang, Zan ;
Li, Dong-Ming ;
Cheng, Yu-Min ;
Liew, Kim Moew .
ACTA MECHANICA SINICA, 2012, 28 (03) :808-818
[28]   Analyzing three-dimensional potential problems with the improved element-free Galerkin method [J].
Zhang, Zan ;
Zhao, Peng ;
Liew, K. M. .
COMPUTATIONAL MECHANICS, 2009, 44 (02) :273-284
[29]   Improved element-free Galerkin method for two-dimensional potential problems [J].
Zhang, Zan ;
Zhao, Peng ;
Liew, K. M. .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (04) :547-554
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