|
|
Complex variable element-free Galerkin method for viscoelasticity problems |
Cheng Yu-Min (程玉民)a, Li Rong-Xin (李荣鑫)b, Peng Miao-Juan (彭妙娟)b |
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.
|
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 (程玉民), Li Rong-Xin (李荣鑫), Peng Miao-Juan (彭妙娟) 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
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|