An improved interpolating element-free Galerkin method for elasticity

doi:10.1088/1674-1056/22/12/120203

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (12): 120203-120203.doi: 10.1088/1674-1056/22/12/120203

An improved interpolating element-free Galerkin method for elasticity

孙凤欣^{a c}, 王聚丰^{a b}, 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

收稿日期:2013-03-30 修回日期:2013-05-02 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).

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

Received:2013-03-30 Revised:2013-05-02 Online:2013-10-25 Published:2013-10-25
Contact: Cheng Yu-Min E-mail:ymcheng@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).

摘要/Abstract

摘要： 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.

关键词: meshless method, improved interpolating moving least-squares (ⅡMLS) method, improved interpolating element-free Galerkin (ⅡEFG) method, elasticity

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.

Key words: meshless method, improved interpolating moving least-squares (ⅡMLS) method, improved interpolating element-free Galerkin (ⅡEFG) method, elasticity

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Em (Potential theory)

孙凤欣, 王聚丰, 程玉民. An improved interpolating element-free Galerkin method for elasticity[J]. Chin. Phys. B, 2013, 22(12): 120203-120203.

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[J]. Chin. Phys. B, 2013, 22(12): 120203-120203.

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An improved interpolating element-free Galerkin method for elasticity

An improved interpolating element-free Galerkin method for elasticity

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