Chien-Hsun Lin This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Chan-Ping Pan1

1Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 106, R.O.C.


 

Received: February 15, 2006
Accepted: April 19, 2006
Publication Date: March 1, 2007

Download Citation: ||https://doi.org/10.6180/jase.2007.10.1.05  


ABSTRACT


A principle weakness of the element free Galerkin method, a method widely discussed over the past decade, has been its computation efficiency. This paper describes a new simple and efficient method that overcomes this weakness by combining together the finite element and element free Galerkin methods. No transmission zones are required in this new method. The new method introduced differs from methods such as Lagrange multipliers or the penalty method in that so-called “virtual particles” are defined to approach the compatibility between two displacement fields. Virtual particles are derived from the finite element formulation and used as the particles in the element free Galerkin formulation.


Keywords: Element Free Galerkin Method, Finite Element Method, Compatibility, Displacement Fields


REFERENCES


  1. [1] Belytschko, T., Lu, Y. Y. and Gu, L., “Element-Free Galerkin Methods,” International Journal for Numerical Methods in Engineering, Vol. 37, pp. 229256 (1994).
  2. [2] Belytschko, T., Organ, D. and Krongauz, Y., “A Coupled Finite Element-Element Free Galerkin Method,” Computational Mechanics, Vol. 17, pp. 186195 (1995).
  3. [3] Hegen, D., “Element-free Galerkin Methods in Combination with Finite Element Approaches,” Computer Methods in Applied Mechanics Engineering, Vol. 135, pp. 143166 (1996).
  4. [4] Rao, B. N. and Rahman, S., “A Coupled MeshlessFinite Element Method for Fracture Analysis ofCracks,” International Journal of Pressure Vessels and Piping, Vol. 78, pp. 647657 (2001).
  5. [5] Ho, S. L., Yang, S., Ni, G., Wong, H. C and Wang, Y., “Numerical Analysis of Thin Skin Depths of 3-D Eddy-Current Problems Using a Combination of Finite Element and Meshless Methods,” IEEE Transactions on Magnetics, Vol. 40, pp. 13541357 (2004).
  6. [6] Huerta, A. and Fernandez-Mendex, S., “Enrichment and Coupling of the Finite Element and Meshless Methods,” International Journal for Numerical Methods in Engineering, Vol. 48, pp. 16151636 (2000).
  7. [7] Lu, Y. Y., Belytschko, T. and Gu, L., “A New Implementation of the Element Free Galerkin Method,” Computer Methods in Applied Mechanics Engineering, Vol. 113, pp. 397414 (1994).
  8. [8] Belytschko, T., Lu, Y. Y. and Gu, L., “Crack Propagation by Element-Free Galerkin Methods,” Engineering Fracture Mechanics, Vol. 51, pp. 295315 (1995).
  9. [9] Krysl, P. and Belytschko, T., “Analysis of Thin Plates by the Element-Free Galerkin Methods,” Computational Mechanics, Vol. 17, pp. 2635 (1995).
  10. [10] Fleming, M., Chu, Y. A., Moran, B. and Belytschko, T., “Enriched Element-Free Galerkin Methods for Crack Tip Fields,” International Journal for Numerical Methods in Engineering, Vol. 40, pp. 14831504 (1997).
  11. [11] Krongauz, Y. and Belytschko, T., “Enforcement of Essential Boundary Condition in Meshless Approximation Using Finite Elements,” Computer Methods in Applied Mechanics Engineering, Vol. 131, pp. 133 145 (1996).
  12. [12] Zhu, T. and Atluri, S. N., “A Modified Collocation Method and a Penalty Formulation for Enforcing the Essential Boundary Conditions in the Element Free Galerkin Method,” Computational Mechanics, Vol. 21, pp. 211222 (1998).
  13. [13] Mukherjee, Y. X. and Mukherjee, S., “On Boundary Conditions in the Element-Free Galerkin Method,” Computational Mechanics, Vol. 19, pp. 264270 (1997).
  14. [14] Gavete, L., Benito, J. J., Falcon, S. and Ruiz, A., “Implementation of Essential Boundary Conditions in a Meshless Method,” Communications in Numerical Methods in Engineering, Vol. 16, pp. 409421 (2000).
  15. [15] Fernandez-Mendez, S. and Huerta, A., “Imposing Essential Boundary Conditions in Mesh-free Methods,” Computer Methods in Applied Mechanics Engineering, Vol. 193, pp. 12571275 (2004).
  16. [16] Lee, S. H. and Yoon, Y. C., “Numerical Prediction of Crack Propagation by an Enhanced Element-Free Galerkin Method,” Nuclear Engineering and Design, Vol. 227, pp. 257271 (2004).
  17. [17] Gu, Y. T. and Liu, G. R., “A Coupled Element Eree Galerkin/Boundary Element Method for Stress Analysis of Two-Dimension Solids,” Computer Methods in Applied Mechanics Engineering, Vol. 190, pp. 4405 4419 (2001).
  18. [18] Rao, B. N. and Rahman, S., “An Enriched Meshless Method for Non-Linear Fracture Mechanics,” International Journal for Numerical Methods in Engineering, Vol. 59, pp. 197223 (2004).
  19. [19] Cook, R. D., Malkus, D. S. and Plesha, M. E., Concepts and Applications of Finite Element Analysis, Third edition, John Wiley & Sons, New York (1989).
  20. [20] Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, Third edition, McGraw-Hill, New York (1986).