Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(9): 090205    DOI: 10.1088/1674-1056/21/9/090205
GENERAL Prev   Next  

Complex variable element-free Galerkin method for viscoelasticity problems

Cheng Yu-Mina, Li Rong-Xinb, Peng Miao-Juanb
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Civil Engineering, Shanghai University, Shanghai 200072, China
Abstract  Based on the complex variable moving least-square (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin (EFG) method, with the same node distribution, the CVEFG method has a higher precision, and to obtain the similar precision, the CVEFG method has a greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method in this paper.
Keywords:  meshless method      complex variable moving least-square approximation      complex variable element-free Galerkin method      viscoelasticity  
Received:  06 April 2012      Revised:  18 April 2012      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  46.35.+z (Viscoelasticity, plasticity, viscoplasticity)  
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: 

Cheng Yu-Min, Li Rong-Xin, Peng Miao-Juan Complex variable element-free Galerkin method for viscoelasticity problems 2012 Chin. Phys. B 21 090205

[1] Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Engin. 139 3
[2] Cheng Y M and Ji X 1997 Acta Mech. Solida Sin. 10 246
[3] Cheng Y M and Peng M J 2005 Sci. Chin. Ser. G: Phys. Mech. Astron. 48 641
[4] Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[5] Cheng R J and Cheng Y M 2007 Acta Phys. Sin. 56 5569 (in Chinese)
[6] Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
[7] Cheng R J and Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese)
[8] Cheng R J and Ge H X 2009 Chin. Phys. B 18 4059
[9] Wang J F, Sun F X and Cheng R J 2010 Chin. Phys. B 19 060201
[10] Cheng R J and Ge H X 2010 Chin. Phys. B 19 090201
[11] Wang J F and Cheng Y M 2011 Chin. Phys. B 20 030206
[12] Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[13] Cheng R J and Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese)
[14] Lancaster P and Salkauskas K 1981 Math. Comput. 37 141
[15] Cheng Y M and Li J H 2006 Sci. Chin. Ser. G: Phys. Mech. Astron. 49 46
[16] Liew K M, Feng C, Cheng Y M and Kitipornchai S 2007 Int. J. Num. Methods Engin. 70 46
[17] Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[18] Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 719
[19] Liew K M and Cheng Y M 2009 Comput. Methods Appl. Mech. Engin. 198 3925
[20] Chen L and Cheng Y M 2010 Sci. Chin. Ser. G: Phys. Mech. Astron. 40 242 (in Chinese)
[21] Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[22] Peng M J, Liu P and Cheng Y M 2009 Int. J. Appl. Mech. 1 367
[23] Peng M J, Li D M and Cheng Y M 2011 Engin. Struct. 33 127
[24] Li D M, Peng M J and Cheng Y M 2011 Sci. Chin. Ser. G: Phys. Mech. Astron. 41 1003 (in Chinese)
[25] Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[26] Yang H T and Liu Y 2003 Int. J. Solids Struct. 40 701
[27] Sladek J, Sladek V and Zhang C 2005 Engin. Anal. Bound. Elem. 29 597
[28] Sladek J, Sladek V, Zhang C and Schanz M 2006 Comput. Mech. 37 279
[29] Guan Y J, Zhao G Q, Wu X and Lu P 2007 J. Mater. Process Tech. 187 412
[30] Canelas A and Sensale B 2010 Engin. Anal. Bound. Elem. 34 845
[31] Flügge W 1975 Viscoelasticity (2nd edn.) (New York: Springer-Verlag) p. 1
[32] Zhang Z, Liew K M and Cheng Y M 2008 Engin. Anal. Bound. Elem. 32 100
[33] Zhang Z, Liew K M, Cheng Y M and Lee Y Y 2008 Engin. Anal. Bound. Elem. 32 241
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] Hybrid natural element method for large deformation elastoplasticity problems
Ma Yong-Qi, Zhou Yan-Kai. Chin. Phys. B, 2015, 24(3): 030204.
[7] Homogenization theory for designing graded viscoelastic sonic crystals
Qu Zhao-Liang, Ren Chun-Yu, Pei Yong-Mao, Fang Dai-Ning. Chin. Phys. B, 2015, 24(2): 024303.
[8] Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method
Cheng Yu-Min, Liu Chao, Bai Fu-Nong, Peng Miao-Juan. Chin. Phys. B, 2015, 24(10): 100202.
[9] Hybrid natural element method for viscoelasticity problems
Zhou Yan-Kai, Ma Yong-Qi, Dong Yi, Feng Wei. Chin. Phys. B, 2015, 24(1): 010204.
[10] A meshless algorithm with moving least square approximations for elliptic Signorini problems
Wang Yan-Chong, Li Xiao-Lin. Chin. Phys. B, 2014, 23(9): 090202.
[11] A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation
Ge Hong-Xia, Cheng Rong-Jun. Chin. Phys. B, 2014, 23(4): 040203.
[12] Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method
Weng Yun-Jie, Cheng Yu-Min. Chin. Phys. B, 2013, 22(9): 090204.
[13] A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems
Wang Qi-Fang, Dai Bao-Dong, Li Zhen-Feng. Chin. Phys. B, 2013, 22(8): 080203.
[14] A meshless Galerkin method with moving least square approximations for infinite elastic solids
Li Xiao-Lin, Li Shu-Ling. Chin. Phys. B, 2013, 22(8): 080204.
[15] Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method
Cheng Rong-Jun, Wei Qi. Chin. Phys. B, 2013, 22(6): 060209.
No Suggested Reading articles found!