WJM  Vol.3 No.1 , February 2013
Comparative Study of the Effect of the Parameters of Sizing Data on Results by the Meshless Methods (MLPG)

The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain. In this paper, we studied the effect of the configuration parameters of the size of the support or quadrature domain, and the effect of the size of the cells with nodes distribution number on the accuracy of the methods. It also presents a comparison of the results for the Shear stress, the deflections and the error in energy.

Cite this paper
A. Moussaoui and T. Bouziane, "Comparative Study of the Effect of the Parameters of Sizing Data on Results by the Meshless Methods (MLPG)," World Journal of Mechanics, Vol. 3 No. 1, 2013, pp. 82-87. doi: 10.4236/wjm.2013.31006.
[1]   T. Belyschko, Y. Y. Lu and L. Gu, “Element-Free Galerkin methods,” International Journal for Numerical Methods, Vol. 37, No. 2, 1994, pp. 229-256. doi:10.1201/9781420082104.ch2

[2]   S. N. Atluri and S. Shen, “The Meshless Local PetrovGalerkin (MLPG) Method,” Tech Science Press, Forsyth, 2002.

[3]   G. R. Liu, “Mesh Free Methods, Moving beyond the Finite Element Method,” CRC, Boca Raton, 2003.

[4]   S. N. Atluri, “The Meshless Method, (MLPG) for Domain & BIE Discretizations,” Tech Science Press, Forsyth, 2004.

[5]   S. N. Atluri, H. T. Liu and Z. D.Han, “Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems,” Tech Science Press CMES, Vol. 14, No. 3, 2006, pp. 141-152. doi:10.1152/jn.00885.2006

[6]   S. N. Atluri1, Z. D. Hanl and A. M. Rajendran, “A New Implementation of the Meshless Finite Volume Method, through the MLPG ‘Mixed” Approach’,” Tech Science Press CMES, Vol. 6, No. 6, 2004, pp. 491-513.

[7]   J. Sladek, V. Sladek and C. Zhang, “Application of Meshless Local Petrov-Galerkin (MLPG) Method to Elastodynamic Problems in Continuously Non-Homogeneous Solids,” Computer Modeling in Engineering & Sciences, Vol. 4, No. 6, 2003, pp. 637-648.

[8]   S. N. Atluri, J. Y. Cho and H. G. Kim, “Analysis of Thin Beams, Using the Meshless Local Petrov-Galerkin Method, with Generalized Moving Least Squares Interpolations,” Computational Mechanics, Vol. 24, No. 5, 1999, pp. 334-347. doi:10.1007/s004660050456

[9]   Y. T. Gu and G. R. Liu, “A Meshless Local PetrovGalerkin (MLPG) Formulation for Static and Free Vibration Analyses of Thin Plates,” Computer Modeling in Engineering & Sciences, Vol. 2, No. 4, 2001, pp. 463-476.

[10]   J. Sladek, V. Sladek, C. Zhang and M. Schanz, “Meshless Local Petrov-Galerkin Method for Continuously Non-Homogeneous Viscoelastic Solids,” Computational Mechanics, Vol. 37, No. 3, 2006, pp. 279-289. doi:10.1007/s00466-005-0715-0

[11]   G. R. Liu and Y. T. Gu, “Meshless Local Petrov-Galerkin (MLPG) Method in Combination with Finite Element and Boundary Element Approaches,” Computational Mechanics, Vol. 26, No. 6, 2000, pp. 536-546. doi:10.1007/s004660000203

[12]   S. N. Atluri and T. Zhu, “A New Meshless Local PetrovGalerkin (MLPG) Approachs in Computational Mechanics,” Computational Mechanics, Vol. 22, No. 2, 1998, pp. 117-127. doi:10.1007/s004660050346

[13]   T. Belytschko, Y. Krogauz, D. Organ, M. Fleming and P. Krysl, “Meshless Methods: An Overview and Recent Developments,” Computer Methods in Applied Mechanics and Engineering, Vol. 139, No. 1, 1996, pp. 3-47. doi:10.1016/S0045-7825(96)01078-X

[14]   S. Drapier and R. Fortunée, “Méthodes Numériques d’Approximations et de Résolution en Mécaniques,” 2010.

[15]   S. P. Timoshenko and J. N. Goodier, “Theory of Elasticity,” 3rd Edition, McGraw Hill, New York, 1970.