Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Meshless local Petrov-Galerkin method with complex variables for elasticity

Yang Xiu-Li Dai Bao-Dong Li Zhen-Feng

Yang Xiu-Li, Dai Bao-Dong, Li Zhen-Feng. Meshless local Petrov-Galerkin method with complex variables for elasticity. Acta Phys. Sin., 2012, 61(5): 050204. doi: 10.7498/aps.61.050204
Citation: Yang Xiu-Li, Dai Bao-Dong, Li Zhen-Feng. Meshless local Petrov-Galerkin method with complex variables for elasticity. Acta Phys. Sin., 2012, 61(5): 050204. doi: 10.7498/aps.61.050204

Meshless local Petrov-Galerkin method with complex variables for elasticity

Yang Xiu-Li, Dai Bao-Dong, Li Zhen-Feng
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • In this paper, the shape functions are obtained by the moving least-squares method with complex variable (MLSCV). The advantages of MLSCV are that the approximation function of a two-dimensional (2D) problem is formed with one-dimensional (1D) basis function, and the number of the undetermined coefficients is reduced, so it effectively improves the computational efficiency. Based on the MLSCV and meshless local Petrov-Galerkin method, the essential boundary conditions are imposed by the penalty method and the corresponding discrete equations are derived, then a meshless local Petrov-Galerkin method with complex variables is presented for 2D elasticity problems. Some examples given in this paper demonstrate the effictiveness of the present method.
      PACS:
      02.60.-x(Numerical approximation and analysis)
      02.70.Pt(Boundary-integral methods)
      02.70.-c(Computational techniques; simulations)
      46.25.-y(Static elasticity)
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51078250).
    [1]

    Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3

    [2]

    Belytscko T, Lu Y Y, Gu L 1994 Int. J. Numer. Meth. Eng. 37 229

    [3]

    Cheng R J, Ge H X 2009 Chin. Phys. B 18 4059

    [4]

    Atluri S N, Zhu T L 1998 Comput. Mech. 22 117

    [5]

    Zheng B J, Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese) [郑保敬, 戴保东 2010 物理学报 59 5182]

    [6]

    Chen L, Liew K M 2010 Comput. Mech. 47 455

    [7]

    Liu W K, Jun S, Zhang Y F 1995 Int. J. Numer. Meth. Fluids 20 1081

    [8]

    Cheng R J, Liew K M 2009 Comput. Mech. 45 1

    [9]

    Onate E, Idelsohn S, Zienkiewicz O Z, Taylor R L 1996 Inter. J. Num. Meth. Eng. 39 3839

    [10]

    Cheng R J, ChengYM2007 Acta Phys. Sin. 56 5569 (in Chinese) [程荣军, 程玉民 2007 物理学报 56 5569]

    [11]

    Liu G R, Gu Y T 2001 Int. J. Numer. Meth. Eng. 50 937

    [12]

    Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 物理学报 54 4463]

    [13]

    Zhu T, Zhang J, Atluri S N 1999 Eng. Anal. Bound. Elem. 23 375

    [14]

    Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3215]

    [15]

    Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 物理学报 56 597]

    [16]

    Li X G, Dai B D, Wang L H 2010 Chin. Phys. B 19 120202

    [17]

    Lancaster P, Salkauskas K 1981 Math. Comput. 37 141

    [18]

    Cheng R J, ChengY M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 物理学报 57 6037]

    [19]

    Wang J F, Bai F N, Cheng Y M 2011 Chin. Phys. B 20 030206

    [20]

    Atluri S N 2004 The Meshless Method for Domain & BIE Discretizations (Irvine: University of California)

    [21]

    Cheng Y M, Peng M J, Li J H 2005 Acta Mech. Sin. 37 719 (in Chinese) [程玉民, 彭妙娟, 李九红 2005 力学学报 37 719]

    [22]

    Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 物理学报 54 4463]

    [23]

    Cheng Y M, Li J H 2005 Science in China Ser. G 35 548 (in Chinese) [程玉民, 李九红 2005 中国科学 (G辑) 35 548]

    [24]

    Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]

    [25]

    Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 1]

    [26]

    Chen L, Cheng Y M 2010 Chin. Phys. B 19 090204

    [27]

    Liew K M, Cheng Y M 2009 Comput. Meth. Appl. Mech. Eng. 198 3925

    [28]

    Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258

  • [1]

    Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3

    [2]

    Belytscko T, Lu Y Y, Gu L 1994 Int. J. Numer. Meth. Eng. 37 229

    [3]

    Cheng R J, Ge H X 2009 Chin. Phys. B 18 4059

    [4]

    Atluri S N, Zhu T L 1998 Comput. Mech. 22 117

    [5]

    Zheng B J, Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese) [郑保敬, 戴保东 2010 物理学报 59 5182]

    [6]

    Chen L, Liew K M 2010 Comput. Mech. 47 455

    [7]

    Liu W K, Jun S, Zhang Y F 1995 Int. J. Numer. Meth. Fluids 20 1081

    [8]

    Cheng R J, Liew K M 2009 Comput. Mech. 45 1

    [9]

    Onate E, Idelsohn S, Zienkiewicz O Z, Taylor R L 1996 Inter. J. Num. Meth. Eng. 39 3839

    [10]

    Cheng R J, ChengYM2007 Acta Phys. Sin. 56 5569 (in Chinese) [程荣军, 程玉民 2007 物理学报 56 5569]

    [11]

    Liu G R, Gu Y T 2001 Int. J. Numer. Meth. Eng. 50 937

    [12]

    Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 物理学报 54 4463]

    [13]

    Zhu T, Zhang J, Atluri S N 1999 Eng. Anal. Bound. Elem. 23 375

    [14]

    Qin Y X, Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese) [秦义校, 程玉民 2006 物理学报 55 3215]

    [15]

    Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 物理学报 56 597]

    [16]

    Li X G, Dai B D, Wang L H 2010 Chin. Phys. B 19 120202

    [17]

    Lancaster P, Salkauskas K 1981 Math. Comput. 37 141

    [18]

    Cheng R J, ChengY M 2008 Acta Phys. Sin. 57 6037 (in Chinese) [程荣军, 程玉民 2008 物理学报 57 6037]

    [19]

    Wang J F, Bai F N, Cheng Y M 2011 Chin. Phys. B 20 030206

    [20]

    Atluri S N 2004 The Meshless Method for Domain & BIE Discretizations (Irvine: University of California)

    [21]

    Cheng Y M, Peng M J, Li J H 2005 Acta Mech. Sin. 37 719 (in Chinese) [程玉民, 彭妙娟, 李九红 2005 力学学报 37 719]

    [22]

    Cheng Y M, Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese) [程玉民, 李九红 2005 物理学报 54 4463]

    [23]

    Cheng Y M, Li J H 2005 Science in China Ser. G 35 548 (in Chinese) [程玉民, 李九红 2005 中国科学 (G辑) 35 548]

    [24]

    Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]

    [25]

    Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 1]

    [26]

    Chen L, Cheng Y M 2010 Chin. Phys. B 19 090204

    [27]

    Liew K M, Cheng Y M 2009 Comput. Meth. Appl. Mech. Eng. 198 3925

    [28]

    Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258

Metrics
  • Abstract views:  8257
  • PDF Downloads:  658
Publishing process
  • Received Date:  05 May 2011
  • Accepted Date:  25 June 2012
  • Published Online:  05 March 2012

/

返回文章
返回