A meshless Galerkin method with moving least square approximations for infinite elastic solids

doi:10.1088/1674-1056/22/8/080204

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80204-080204.doi: 10.1088/1674-1056/22/8/080204

A meshless Galerkin method with moving least square approximations for infinite elastic solids

李小林, 李淑玲

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

收稿日期:2013-01-15 修回日期:2013-03-04 出版日期:2013-06-27 发布日期:2013-06-27
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11101454) and the Natural Science Foundation of Chongqing CSTC (Grant No. cstc2011jjA30003).

A meshless Galerkin method with moving least square approximations for infinite elastic solids

Li Xiao-Lin (李小林), Li Shu-Ling (李淑玲)

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received:2013-01-15 Revised:2013-03-04 Online:2013-06-27 Published:2013-06-27
Contact: Li Xiao-Lin E-mail:lxlmath@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11101454) and the Natural Science Foundation of Chongqing CSTC (Grant No. cstc2011jjA30003).

摘要/Abstract

摘要： Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method (GBNM), for two-and three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.

关键词: meshless method, Galerkin boundary node method, error estimates, elasticity

Abstract: Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method (GBNM), for two-and three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.

Key words: meshless method, Galerkin boundary node method, error estimates, elasticity

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 46.25.-y (Static elasticity)

李小林, 李淑玲. A meshless Galerkin method with moving least square approximations for infinite elastic solids[J]. 中国物理B, 2013, 22(8): 80204-080204.

Li Xiao-Lin (李小林), Li Shu-Ling (李淑玲). A meshless Galerkin method with moving least square approximations for infinite elastic solids[J]. Chin. Phys. B, 2013, 22(8): 80204-080204.

参考文献 31

[1]	Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Methods Eng. 37 229
[2]	Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[3]	Wang J F, Sun F X and Cheng R J 2012 Chin. Phys. B 21 090204
[4]	Xia M H and Li J 2007 Chin. Phys. 16 3067
[5]	Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[6]	Li Z H, Qin Y X and Cui X C 2012 Acta Phys. Sin. 61 080205 (in Chinese)
[7]	Liu M B and Chang J F 2010 Acta Phys. Sin. 59 3654 (in Chinese)
[8]	Zheng B J and Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese)
[9]	Shirron J J and Babuska I 1998 Comput. Methods Appl. Mech. Eng. 164 121
[10]	Hsiao G C and Wendland W L 2008 Boundary Integral Equations (Berlin: Springer) pp. 45-75
[11]	Zhu J and Yuan Z 2009 Boundary Element Analysis (Beijing: Science Press) p. 282 (in Chinese)
[12]	Mukherjee Y X and Mukherjee S 1997 Int. J. Numer. Methods Eng. 40 797
[13]	Zhang J, Qin X, Han X and Li G 2009 Int. J. Numer. Methods Eng. 80 320
[14]	Cheng Y M and Peng M J 2005 Sci. China: Phys. Mech. Astron. 48 641 (in Chinese)
[15]	Ren H P, Cheng Y M and Zhang W 2010 Sci. China: Phys. Mech. Astron. 53 758 (in Chinese)
[16]	Chen S S, Li Q H and Liu Y H 2012 Chin. Phys. B 21 110207
[17]	Li X and Zhu J 2009 J. Comput. Appl. Math. 230 314
[18]	Li X and Zhu J 2009 Comput. Methods Appl. Mech. Engrg. 198 2874
[19]	Li X 2011 Appl. Numer. Math. 61 1237
[20]	Li X 2011 Int. J. Numer. Methods Eng. 88 442
[21]	Li X and Zhu J 2009 CMES: Comput. Model. Eng. Sci. 45 1
[22]	Li X 2012 Eng. Anal. Bound. Elem. 36 993
[23]	Cheng R J and Cheng Y M 2008 Appl. Numer. Math. 58 884
[24]	Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[25]	Cheng Y M and Li J H 2006 Sci. China: Phys. Mech. Astron. 49 46 (in Chinese)
[26]	Li D M, Peng M J and Cheng Y M 2011 Sci. China: Phys. Mech. Astron. 41 1003
[27]	Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[28]	Yang X L, Dai B D and Zhang W W 2012 Chin. Phys. B 21 100208
[29]	Cheng Y M, Li R X and Peng M J 2012 Chin. Phys. B 21 090205
[30]	Cheng Y M, Wang J F and Bai F N 2012 Chin. Phys. B 21 090203
[31]	Liew K M and Cheng Y M 2009 Comput. Methods Appl. Mech. Eng. 198 3925

A meshless Galerkin method with moving least square approximations for infinite elastic solids

A meshless Galerkin method with moving least square approximations for infinite elastic solids

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