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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.
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Keywords:
- meshless method /
- moving least-squares method with complex variables /
- meshless local Petrov-Galerkin method /
- elasticity
[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
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[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
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