A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function

International Journal for Numerical Methods in Engineering

Volumn 57, Issue 11, 2003, Pages 1523-1552

  Alves, Marcelo Krajnc ^a   Rossi, Rodrigo ^b  

^a FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

^b UNIVERSITY OF CAXIAS DO SUL   (Brazil)

Author keywords

Damage; Element free Galerkin; Moving least square approximation (MLSA); Partition of unity finite element method (PUFEM); Plasticity

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING;

ELASTIC PROBLEMS;

GALERKIN METHODS;

DAMAGE; FINITE ELEMENT ANALYSIS; PLASTICITY;

EID: 0043132011     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.730     Document Type: Article

References (29)

1. Belytschko T, Lu YY, Gu L. Element free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
2. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158.
3. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1996: 39;923-938.
4. Mukherjee YX, Mukherjee S. On boundary conditions in the element-free Galerkin method. International Journal for Numerical Methods in Engineering 1997; 19:229-256.
5. Zhu T, Atluri N. Modified collocation method and a penalty function for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics 1998; 21:211-222.
6. Lu YY, Belytschko T, Gu L. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:455-471.
7. Belytschko T, Organ D, Krongauz Y. A coupled finite element-element-free Galerkin method. Computational Mechanics 1995; 17(3):186-195.
8. Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering 1996; 131(1-2):133-145.
9. Hegen D. Element-free Galerkin methods in combination with finite element approaches. Computer Methods in Applied Mechanics and Engineering 1996; 135(1 2):143 166.
10. Huerta A, Méndez SF. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering 2000; 48:1615 1636.
11. Duarte AC, Oden JT. An h-p adaptive method using clouds. Computer Methods in Applied Mechanics and Engineering 1996; 139(1-4):237-262.
12. Kaljević I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering 1997; 40(16):2953 2974.
13. Günther FC, Liu WK. Implementation of boundary conditions for meshless methods. Computer Methods in Applied Mechanics and Engineering 1998; 163:205 230.
14. Pannachet T, Askes H. Some observations on the enforcement of constraint equations in the EFG method. Communications in Numerical Methods in Engineering 2000; 16(12):819 930.
15. Gavete L, Benito JJ, Falcón S, Ruiz A. Penalty functions in constrained variational principles for element free Galerkin method. European Journal of Mechanics A Solids 2000; 19(4):699-720.
16. Zhang X, Liu X, Song KZ, Lu MW. Imposition of essential boundaries conditions by displacement constraint equations in meshless methods. Communications in Numerical Methods in Engineering 2001; 17(3):165-178.
17. Ventura G. An augmented Lagrangian approach to essential boundary conditions in meshless methods. International Journal for Numerical Methods in Engineering 2002; 53:825-842.
18. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 1996; 139(1 4):3-47.
19. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 39:289-314.
20. Lemaitre J. A Course on Damage Mechanics. Springer-Verlag: Germany, 1992.
21. Ganghoffer JF, Brillard A, Schultz J. A model of damaged adhesives. European Journal of Mechanics A/Solids 1997; 16(1):19-52.
22. Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1996; 139:49 74.
23. Liu W-K, Li S, Belytschko T. Moving least-square reproducing kernel methods. (1) Methodology and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 147:113 154.
24. Robotnov YN. Creep Rupture, International Congress on Applied Mechanics 1969, Springer: Berlin.
25. Krajcinovic D, Lemaitre J. Continuum Damage Mechanics Theory and Applications, Courses and Lectures. Springer-Verlag: New York, 1971.
26. Lemaitre J, Chaboche JL. Mechanics of Solid Materials. Cambridge University Press: Cambridge, 1994.
27. Benallal A, Comi C, Lemaitre J. Critical damage states at crack initiation. AMD-Vol.142/MD-Vol.34, Damage Mechanics and Localization, ASME 1992.
28. Benallal A, Billanlon R, Doghri I. An integration algorithm and the corresponding consistent tangent operator for fully coupled elastoplastic and damage equations. Communications in Applied Numerical Methods 1988; 4:731-740.
29. Timoshenko SP, Goodier JN. Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970.