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A comparison between the improved element-free Galerkin method and the element-free Galerkin method for 2D potential and elasticity problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a comparison between the improved element-free Galerkin (IEFG) method, based on the improved moving least square (IMLS) approximation, and the element-free Galerkin (EFG) method, based on the moving least square (MLS) approximation, is presented. The IMLS approximation is obtained when an orthogonal basis function with a weight function is used. The IMLS approximation has a greater computational efficiency than the existing MLS approximation and does not lead to an ill-conditioned system of equations. The comparison is made for two-dimensional (2D) potential problems and 2D elastic problems. From these problems, the efficiency of the IEFG method is validated by comparing the results obtained with the IEFG method and EFG method with those obtained analytically.
Rocznik
Strony
87--107
Opis fizyczny
Bibliogr. 22 poz., tab., wykr.
Twórcy
autor
  • LGM, ENIM, University of Monastir Monastir, Tunisia
autor
  • LGM, ENIM, University of Monastir Monastir, Tunisia
  • LGM, ENIM, University of Monastir Monastir, Tunisia
Bibliografia
  • [1] Z. Zhang, K.M. Liew, Y. Cheng, Y.Y. Lee. Analyzing 2D fracture problems with the improved element-free Galerkin method. Engineering Analysis with Boundary Elements, 32: 241–250, 2008.
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  • [3] N.F.M. Martins, M. Rebelo. A meshfree method for elasticity problems with interfaces. Applied Mathematics and Computation, 219: 10732–10745, 2013.
  • [4] Y. Cheng, M. Chen. A boundary element-free method for linear elasticity. Acta Mechanica Sinica, 35: 181–186, 2003.
  • [5] A. Karamanli, A. Mugan. Strong form meshless implementation of Taylor series method. Applied Mathematics and Computation, 219: 9069–9080, 2013.
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  • [9] T. Belytschko, Y.Y. Lu, L. Gu. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 37: 229–256, 1994.
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  • [12] Y.Y. Lu, T. Belytschko. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 113: 397–414, 1994.
  • [13] He Zeng, Li Peng. Dispersion and pollution of the improved meshless weighted least-square (IMWLS) solution for the Helmholtz equation. Engineering Analysis with Boundary Elements, 35: 791–801, 2011.
  • [14] R.J. Cheng, K.M. Liew. Analyzing modified equal width (MEW) wave equation using the improved element-free Galerkin method. Engineering Analysis with Boundary Elements, 36: 1322–1330, 2012.
  • [15] Z. Zhang, Peng Zhao, K.M. Liew. Improved element-free Galerkin method for two-dimensional potential problems. Engineering Analysis with Boundary Elements, 33: 547–554, 2009.
  • [16] I. Debbabi, Z. Sendi, H. BelHadj Salah. Element Free and Improved Element Free Galerkin Methods for One and Two-Dimensional Potential Problems. [In:] Design and Modeling of Mechanical Systems – II: 201–212, Springer International Publishing, 2015.
  • [17] P. Lancaster, K. Salkauskas. Surface generated by moving least squares methods. Mathematics of Computation, 37: 141–158, 1981.
  • [18] T. Zhu, S.N. Atluri. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech., 21: 211–222, 1998.
  • [19] G.R. Liu. Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press LLC, 2003.
  • [20] R. Hongping, Cheng Yumin. The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems. Engineering Analysis with Boundary Elements, 36: 873–880, 2012.
  • [21] Prax Christian, Sadat Hamou. Mise en oeuvre d’une methode d’approximation diffuse adaptative pour la résolution des équations de diffusion et de transport. Revue Générale de Thermique, 37: 39–48, 1998.
  • [22] Z. Zhang, K.M. Liew. Coupling of the improved element-free Galerkin and boundary element methods for twodimensional elasticity problems. Engineering Analysis with Boundary Elements, 32: 100–107, 2008.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7deb5a5f-6844-4402-b44b-202825a1233b
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