Enrichissement des interpolations d'éléments finis en utilisant des méthodes sans maillage

Mathematical Modelling and Numerical Analysis

Volumn 36, Issue 6, 2002, Pages 1027-1042

  Huerta, Antonio ^a   Fernández Méndez, Sonia ^a   Díez, Pedro ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Adaptivit ; Convergence; l ments finis; Interpolation mixte; M thodes particulaires; M thodes sans maillage; Raffinement h p

Indexed keywords

EID: 0036880524     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2003004     Document Type: Article

References (21)

1. T. Belytschko, Y.Y. Lu et L. Gu, Element-free Galerkin methods. Internat. J. Numer. Methods Engrg. 37 (1994) 229-256.
2. T. Belytschko et D. Organ, Element-free Galerkin methods for dynamic fracture in concrete. D.R.J. Owen, E. Oñate and E. Hilton Eds., Comp. Plasticity. Fundamentals and Applications (1997) 304-321.
3. T. Belytschko, D. Organ et Y. Krongauz, A coupled finite element-free Galerkin method. Comput. Mech. 17 (1995) 186-195.
4. T. Belytschko et M. Tabbara, Dynamic fracture using element-free Galerkin methods. Internat. J. Numer. Methods Engrg. 39 (1996) 923-938.
5. P. Breitkopf, G. Touzot et P. Villon, Consistency approach and diffuse derivation in element-free methods based on moving least squares approximation. Comput. Assist. Mech. Eng. Sci. 5 (1998) 479-501.
6. P. Breitkopf, A. Rassineux, G. Touzon et P. Villon, Explicit form and efficient computation of MLS shape functions and their derivatives. Internat. J. Numer. Methods Engrg. 48 (2000) 451-466.
7. P. Díez, M. Arroyo et A. Huerta, Adaptivity based on error estimation for viscoplastic softening materials. Mechanics of Cohesive-Frictional Materials 5 (2000) 87-112.
8. D. Hegen, Element-free Galerkin methods in combination with finite element approaches. Comput. Methods Appl. Mech. Engrg. 135 (1996) 143-166.
9. A. Huerta et P. Díez, Error estimation including pollution assessment for nonlinear finite element analysis. Comput. Methods Appl. Mech. Engrg. 180 (2000) 21-41.
10. A. Huerta, A. Rodríguez-Ferran, P. Díez et J. Sarrate, Adaptive finite element strategies based on error analysis. Internat. J. Numer. Meth. Engrg. 46 (1999) 1803-1818.
11. A. Huerta et S. Fernández-Méndez, Enrichment and coupling of the finite element and meshless methods. Internat. J. Numer. Methods Engrg. 48 (2000) 1615-1636.
12. S. Kulasegaram et J. Bonet, Corrected smooth particle hydrodynamics method for metal forming simulations. J. Huétink and F.P.T. Baaijens Eds., Simulation of Materials Processing: Theory, Methods and Applications (1998) 137-142.
13. W.K. Liu et Y. Chen, Wavelet and multiple scale reproducing kernel methods. Internat. J. Numer. Methods Fluids 21 (1995) 901-931.
14. W.K. Liu, S. Jun et Y.F. Zhang, Reproducing kernel particle methods. Internat. J. Numer. Methods Fluids 20 (1995) 1081-1106.
15. W.K. Liu, S. Li et T. Belytschko, Moving least square reproducing kernel methods. (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143 (1996) 113-154.
16. W.K. Liu, R.A. Uras et Y. Chen, Enrichment of the finite element method with reproducing kernel particle method. J. Appl. Mech. 64 (1997) 861-870.
17. Y.Y. Lu, T. Belytschko et L. Gu, A new implementation of the element free Galerkin method. Comput. Methods Appl. Mech. Engrg. 113 (1994) 397-414.
18. B. Nayroles, G. Touzot et P. Villon, Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10 (1992) 307-318.
19. D. Organ, M. Fleming, T. Terry et T. Belytschko, Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Comput. Mech. 18 (1996) 225-235.
20. J.P. Vila, On particle weighted methods and smooth particle hydrodynamics. Math. Models Methods Appl. Sci. 9 (1999) 161-209.
21. P. Villon, Contribution à l'optimisation. Thèse d'état, Université Technologique de Compiègne (1991).