弹性力学的复变量无网格局部 Petrov-Galerkin 法

杨秀丽; 戴保东; 栗振锋

doi:10.7498/aps.61.050204

摘要

复变量移动最小二乘法构造形函数, 其优点是采用一维基函数建立二维问题的试函数, 使得试函数中所含的待定系数减少, 从而有效提高计算效率. 文章基于复变量移动最小二乘法和局部Petrov-Galerkin弱形式, 采用罚函数法施加边界条件, 推导相应的离散方程, 提出弹性力学的复变量无网格局部Petrov-Galerkin法. 数值算例验证了该方法的有效性.

关键词:

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.

Keywords:

meshless method /
moving least-squares method with complex variables /
meshless local Petrov-Galerkin method /
elasticity

作者及机构信息

1.
太原科技大学工程力学系, 太原 030024;

2.
太原科技大学交通与物流学院, 太原 030024

基金项目: 国家自然科学基金(批准号: 51078250)资助的课题.

Authors and contacts

1.
Department of Engineering Mechanics, Taiyuan University of Science and Technology, Taiyuan 030024, China;

2.
College of Transportation and Logistics, Taiyuan University of Science and Technology, Taiyuan 030024, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51078250).

参考文献

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[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 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 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 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 55 3215]
[15]	Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 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 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 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 57 6047]
[25]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 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

施引文献

[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 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 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 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 55 3215]
[15]	Dai B D, Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese) [戴保东, 程玉民 2007 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 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 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 57 6047]
[25]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese) [陈丽, 程玉民 2008 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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