A new extension of the natural element method for non-convex and discontinuous problems: The constrained natural element method (C-NEM)

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 8, 2004, Pages 1451-1474

  Yvonnet, J ^a   Ryckelynck, D ^a   Lorong, P ^a   Chinesta, F ^a  

^a CNRS   (France)

Author keywords

C NEM; Constrained Voronoi diagram; Non convex domains; Visibility criterion

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; ELASTICITY; FUNCTIONS;

NATURAL ELEMENT METHOD (NEM); NON-CONVEX GEOMETRIES;

FINITE ELEMENT METHOD;

CRACK; MATHEMATICAL METHOD;

EID: 3142640827     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1016     Document Type: Article

References (35)

1. Lucy LB. A numerical approach to the testing of fusion process. The Astronomic Journal 1977; 88:1013-1024.
2. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
3. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
4. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
5. Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 21:1081-1106.
6. Duarte CA, Oden JT. An H-p adaptative method using clouds. Computer Methods in Applied Mechanics and Engineering 1996; 139:237-262.
7. Chen JS, Pan C, Wu CT, Liu WK. Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Computer Methods in Applied Mechanics and Engineering 1996; 139:195-229.
8. Günther FC, Liu WK. Implementation of boundary conditions for meshless methods. Computer Methods in Applied Mechanics and Engineering 1997; 163:205-230.
9. Kaljevic I, Saigal S. An improved element free Galerkin formulation. International Journal for Numerical Methods in Engineering 1997; 40:2953-2974.
10. Zhu T, Altruni SN. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin methods. International Journal for Numerical Methods in Engineering 1998; 21:211-222.
11. Chen JS, Wang HP. New boundary conditions treatments in meshfree computation of contact problems. Computer Methods in Applied Mechanics and Engineering 2000; 187:441-468.
12. Sambridge M, Braun J, McQueen M. Geophysical parameterization and interpolation of irregular data using natural neighbours. Geophysical Journal International 1995; 122:837-857.
13. Sukumar N, Moran B, Belytschko T. The natural elements method in solid mechanics. International Journal for Numerical Methods in Engineering 1998; 43:839-887.
14. Cueto E, Cegonino J, Calvo B, Doblaré M. On the imposition of essential boundary conditions in natural neighbour Galerkin methods. Communications in Numerical Methods in Engineering 2003; 19:361-376.
15. Sibson R. A vector identity for the Dirichlet tesselations. Mathematical Proceedings of the Cambridge Philosophical Society 1980; 87:151-155.
16. Yvonnet J, Ryckelynck D, Lorong P, Chinesta P. Interpolation naturelle sur les domaines non convexes par l'utilisation du diagramme de Voronoi contraint-Méthode des éléments C-Naturels. Revue Européenne des éléments Finis 2003; 12(4):482-509.
17. Krysl P, Belytschko T. Element-free Galerkin: convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering 1997; 148:257-277.
18. Chen JS, Wu CT, Yoon Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
19. Gonzalez D, Cueto E, Martinez MA, Doblaré M. Numerical integration in natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering 2004; accepted for publication.
20. Voronoi GM. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire: recherhes sur les parallélloèdres primitifs. Journal fur die Reine und Angewandte Mathematik 1908; 134:198-287.
21. Delaunay B. Sur la sphère vide. A la memoire de Georges Voronoi Izvestiya Akademic Nauk SSSR, Otdelenie Matematicheskih i Estestvennyh Nau 1934; 7:793-800.
22. Hiyoshi H, Sugura K. Improving continuity of Voronoi-based interpolation over Delaunay spheres. Computational Geometry 2002; 22:167-183.
23. Sukumar N, Moran B, Semenov Y, Belikov VV. Natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering 2001; 50:207-219.
24. Cueto E, Doblaré M, Gracia L. Imposing essential boundary conditions in the natural elements method by means of density-scaled alpha-shapes'. International Journal for Numerical Methods in Engineering 2000; 49:519-546.
25. Organ D, Fleming M, Terry T, Belytschlo T. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. New Advances in Adaptive Computational Mechanics 1996; 19:1-11.
26. Edelsbrunner H. Geometry and Topology for Mesh Generation. Cambridge University Press: Cambridge, 2001; p30.
27. Seidel R. Constrained Delaunay triangulations and Voronoi diagrams with obstacles. In 1978-1988 Ten Years 11G, 1988; 178-191.
28. Schönhardt E. Uber die zerlegung von dreieckspolyedern in tetraeder. Mathematische Annalen 1928; 98: 309-312.
29. Shewchuck JR. Tetrahedral mesh generation by Delaunay refinement. Proceedings of the 14th Annual Symposium on Computational Geometry, Minneapolis, Minnesota, Association for Computing Machinery, June, 1998; 86-95.
30. Shewchuck JR. Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations. Proceedings of the 16th Annual Symposium on Computational Geometry, Hong-Kong, Association for Computing Machinery, June, 2000; 350-359.
31. Sambridge M, Braun J, McQueen M. Computational methods for natural neighbour interpolation in two and three dimensions. Proceedings of the Seventh Biennial Conference on Computational Techniques and Applications (CTAC 95). Melbourne, Australia, R. L. May, A. K. Easton (eds). 1996; 685-692.
32. Dolbow J. Belytschko T. Numerical integration of the Galerkin weak forme in meshfree methods. Computational Mechanics 1999; 23:219-230.
33. Perrone N, Liebowitz H, Mulville D, Plikey W. Fracture Mechanics. University Press of Virginia: Charlottesville, 1978.
34. Lemaitre J, Chaboche JL. Mechanics of Solid Materials. Cambridge University Press: Cambridge, UK, 1990.
35. Yau J-F, Wang S-S, Corten HT. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 1980; 47:335-341.