Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(12): 120203    DOI: 10.1088/1674-1056/22/12/120203
GENERAL Prev   Next  

An improved interpolating element-free Galerkin method for elasticity

Sun Feng-Xin (孙凤欣)a c, Wang Ju-Feng (王聚丰)a b, Cheng Yu-Min (程玉民)a
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Faculty of Science, Ningbo University of Technology, Ningbo 315016, China
Abstract  Based on the improved interpolating moving least-squares (ⅡMLS) method and the Galerkin weak form, an improved interpolating element-free Galerkin (ⅡEFG) method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares (IMLS) method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin (IEFG) method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.
Keywords:  meshless method      improved interpolating moving least-squares (ⅡMLS) method      improved interpolating element-free Galerkin (ⅡEFG) method      elasticity  
Received:  30 March 2013      Revised:  02 May 2013      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.30.Em (Potential theory)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).
Corresponding Authors:  Cheng Yu-Min     E-mail:  ymcheng@shu.edu.cn

Cite this article: 

Sun Feng-Xin (孙凤欣), Wang Ju-Feng (王聚丰), Cheng Yu-Min (程玉民) An improved interpolating element-free Galerkin method for elasticity 2013 Chin. Phys. B 22 120203

[1] Liu Z S, Harsono E and Swaddiwudhipong S 2009 Int. J. Appl. Mech. 1 61
[2] Liu Z S, Hong W, Suo Z G, Swaddiwudhipong S and Zhang Y W 2010 Comput. Mater. Sci. 49 60
[3] Brebbia C A and Wrobel L C 1984 Boundary Element Techniques: Theory and Applications in Engineering (Berlin: Springer-Verlag)
[4] Chen S S, Li Q and Liu Y 2012 Chin. Phys. B 21 110207
[5] Cheng R J and Ge H X 2012 Chin. Phys. B 21 100209
[6] Cheng Y M and Peng M J 2005 Sci. China Ser. G: Phys. Mech. Astron. 48 641
[7] Yang X L, Dai B D and Zhang W W 2012 Chin. Phys. B 21 100208
[8] Cheng Y M, Li R X and Peng M J 2012 Chin. Phys. B 21 090205
[9] Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[10] Liu W K, Jun S and Zhang Y F 1995 Int. J. Numer. Meth. Eng. 20 1081
[11] Liu G R and Gu Y T 2004 Eng. Anal. Bound. Elem. 28 475
[12] Zhang J M and Tanaka M 2004 Int. J. Numer. Meth. Eng. 41 1147
[13] Zhang J M and Tanaka M 2008 Comput. Mech. 41 777
[14] Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[15] Liew K M, Ren J and Reddy J N 2005 Int. J. Numer. Meth. Eng. 63 1014
[16] Shepard D 1968 Proceeding of the 23rd ACM National Conference (New York) p. 517
[17] Lancaster P and Salkauskas K 2007 Math. Comput. 37 141
[18] Kaljevic I and Saigal S 1997 Int. J. Numer. Meth. Eng. 40 2953
[19] Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
[20] Ren H P, Cheng Y M and Zhang W 2010 Sci. China Ser. G: Phys. Mech. Astron. 53 758
[21] Ren H Pand Cheng Y M 2011 Int. J. Appl. Mech. 3 735
[22] Ren H P and Cheng Y M 2012 Eng. Anal. Bound. Elem. 36 873
[23] Netuzhylov H 2008 Eng. Anal. Bound. Elem. 32 512
[24] Thomas M and Christian B 2008 Eng. Anal. Bound. Elem. 32 461
[25] Wang J F, Sun F X and Cheng Y M 2012 Chin. Phys. B 21 090204
[26] Timoshenko S P and Goodier J N 1970 Theory of Elasticity, 3rd edn. (New York: McGraw-Hill)
[27] Liu G R and Gu Y T 2001 Int. J. Numer. Meth. Eng. 50 937
[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!