|
|
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.
|
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
|
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
|
|
|