Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(8): 080204    DOI: 10.1088/1674-1056/22/8/080204
GENERAL Prev   Next  

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
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.
Keywords:  meshless method      Galerkin boundary node method      error estimates      elasticity  
Received:  15 January 2013      Revised:  04 March 2013      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  46.25.-y (Static elasticity)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11101454) and the Natural Science Foundation of Chongqing CSTC (Grant No. cstc2011jjA30003).
Corresponding Authors:  Li Xiao-Lin     E-mail:  lxlmath@163.com

Cite this article: 

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 2013 Chin. Phys. B 22 080204

[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
[1] Effect of chemical ordering annealing on superelasticity of Ni-Mn-Ga-Fe ferromagnetic shape memory alloy microwires
Yanfen Liu(刘艳芬), Xuexi Zhang(张学习), Hongxian Shen(沈红先), Jianfei Sun(孙剑飞), Qinan Li(李奇楠), Xiaohua Liu(刘晓华), Jianjun Li(李建军), Weidong Cheng(程伟东). Chin. Phys. B, 2020, 29(5): 056202.
[2] Efficiency of collective myosin Ⅱ motors studied with an elastic coupling power-stroke ratchet model
Zi-Qing Wang(汪自庆), Jin-Fang Li(李金芳), Ying-Ge Xie(解迎革), Guo-Dong Wang(王国栋), Yao-Gen Shu(舒咬根). Chin. Phys. B, 2018, 27(12): 128701.
[3] Improved reproducing kernel particle method for piezoelectric materials
Ji-Chao Ma(马吉超), Gao-Feng Wei(魏高峰), Dan-Dan Liu(刘丹丹). Chin. Phys. B, 2018, 27(1): 010201.
[4] Topology optimization using the improved element-free Galerkin method for elasticity
Yi Wu(吴意), Yong-Qi Ma(马永其), Wei Feng(冯伟), Yu-Min Cheng(程玉民). Chin. Phys. B, 2017, 26(8): 080203.
[5] Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems
Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林). Chin. Phys. B, 2017, 26(3): 030203.
[6] First-principles calculations of structure and elasticity of hydrous fayalite under high pressure
Chuan-Yu Zhang(张传瑜), Xu-Ben Wang(王绪本), Xiao-Feng Zhao(赵晓凤), Xing-Run Chen(陈星润), You Yu(虞游), Xiao-Feng Tian(田晓峰). Chin. Phys. B, 2017, 26(12): 126103.
[7] Enhanced effect of dimension of receptor-ligand complex and depletion effect on receptor-mediated endocytosis of nanoparticles
Ye Liu(刘野), Qingqing Gao(高庆庆), Yijun Liu(刘益军), Chuang Zhao(赵闯), Zongliang Mao(毛宗良), Lin Hu(胡林), Yanhui Liu(刘艳辉). Chin. Phys. B, 2017, 26(12): 128704.
[8] Phenomenological description of semi-soft nematic elastomers
Wen-Wen Diao(刁文文), Qing-Tian Meng(孟庆田), Fang-Fu Ye(叶方富). Chin. Phys. B, 2016, 25(6): 066103.
[9] Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method
Shen-Shen Chen(陈莘莘), Juan Wang(王娟), Qing-Hua Li(李庆华). Chin. Phys. B, 2016, 25(4): 040203.
[10] Reflection of thermoelastic wave on the interface of isotropic half-space and tetragonal syngony anisotropic medium of classes 4, 4/m with thermomechanical effect
Nurlybek A Ispulov, Abdul Qadir, M A Shah, Ainur K Seythanova, Tanat G Kissikov, Erkin Arinov. Chin. Phys. B, 2016, 25(3): 038102.
[11] Solving unsteady Schrödinger equation using the improved element-free Galerkin method
Rong-Jun Cheng(程荣军) and Yu-Min Cheng(程玉民). Chin. Phys. B, 2016, 25(2): 020203.
[12] Vibration and buckling analyses of nanobeams embedded in an elastic medium
S Chakraverty, Laxmi Behera. Chin. Phys. B, 2015, 24(9): 097305.
[13] Hybrid natural element method for large deformation elastoplasticity problems
Ma Yong-Qi (马永其), Zhou Yan-Kai (周延凯). Chin. Phys. B, 2015, 24(3): 030204.
[14] Homogenization theory for designing graded viscoelastic sonic crystals
Qu Zhao-Liang (曲兆亮), Ren Chun-Yu (任春雨), Pei Yong-Mao (裴永茂), Fang Dai-Ning (方岱宁). Chin. Phys. B, 2015, 24(2): 024303.
[15] Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method
Cheng Yu-Min (程玉民), Liu Chao (刘超), Bai Fu-Nong (白福浓), Peng Miao-Juan (彭妙娟). Chin. Phys. B, 2015, 24(10): 100202.
No Suggested Reading articles found!