A natural neighbour method for linear elastic problems based on Fraeijs de Veubeke variational principle

International Journal for Numerical Methods in Engineering

Volumn 71, Issue 9, 2007, Pages 1081-1101

  Cescotto, Serge ^a   Li, Xiang ^a,b  

^a UNIVERSITY OF LIÈGE   (Belgium)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Fraeijs de Veubeke variational principle; Meshless; Natural neighbour method; Voronoi cell

Indexed keywords

INTEGRAL EQUATIONS; INTERPOLATION; LAPLACE EQUATION; LINEAR EQUATIONS; STRAIN; STRESS CONCENTRATION;

MESHLESS EMTHOD; NATURAL NEIGHBOUR METHOD; PATCH TEST; VORONOI CELL;

VARIATIONAL TECHNIQUES;

INTEGRAL EQUATIONS; INTERPOLATION; LAPLACE EQUATION; LINEAR EQUATIONS; STRAIN; STRESS CONCENTRATION; VARIATIONAL TECHNIQUES;

EID: 34548364088     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1982     Document Type: Article

References (31)

1. Cueto E, Sukumar N, Calvo B, Cegonino J, Doblare M. Overview and recent advances in natural neighbour Galerkin methods. Archives of Computational Methods in Engineering 2003; 10(4):307-384.
2. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Journal of Computational Mechanics 1992; 10:307-318.
3. 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; 139:3-47.
4. Li K, Liu WK. Meshfree and particle methods and their applications. Applied Mechanics Review 2002; 55(1): 1-34.
5. Lancaster P, Salkauskas K. Curve and Surface Fitting: An Introduction. Academic Press: London, 1990.
6. Atluri SN, Kim HG, Cho JY. A critical assessment of the truly meshless local Petrov-Galerkin and local boundary integral equation methods. Computational Mechanics 1999; 24:348-372.
7. Atluri SN, Zhu T. New concepts in meshless methods. International Journal for Numerical Methods in Engineering 2000; 47:537-556.
8. Chen JS, Wu CT, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering 2001; 50:435-466.
9. Yoo J, Moran B, Chen JS. Stabilized conforming nodal integration in the natural-element methods. International Journal for Numerical Methods in Engineering 2004; 60:861-890.
10. Yvonnet J, Ryckelynck D, Lorong PH, Chinesta F. A new extension of the natural element method for non convex and discontinuous domains: the constrained natural element method (c-nem). International Journal for Numerical Methods in Engineering 2004; 60:1451-1474.
11. Yvonnet J. Nouvelles approaches sans maillage basées sur la méthode des éléments naturels pour la simulation numérique des procédés de mise en forme. Ph.D. Thesis, Ecole Nationale Supérieure d'Arts et Métiers, 2004.
12. Gonzalez D, Cueto E, Martinez MA, Doblare M. Numerical integration in natural neighbour Galerkin methods. International Journal for Numerical Methods in Engineering 2004; 60:2077-2104.
13. Yagawa G, Matsubara H. Enriched element method and its application to solid mechanics. Computational Methods in Engineering and Science, Proceedings of EPMESC X, 21-23 August. Tsinghua University Press/ Springer: Berlin, 2006; 15-18.
14. Krongauz Y, Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Computer Methods in Applied Mechanics and Engineering 1996; 131:133-145.
15. Belytschko T, Gu L, Lu YY. Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Material Science and Engineering 1994; 2:519-534.
16. Gavette L, Benito JJ, Falcon S, Ruiz A. Penalty functions in constrained variational principles for element free Galerkin method. European Journal of Mechanics - A/Solids 2000; 19:699-720.
17. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
18. Lu YY, Belytschko T, Gu L. A new implementation of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:397-414.
19. Kaljevic I, Saigal S. An improved element-free Galerkin formulation. International Journal for Numerical Methods in Engineering 1997; 40:2953-2974.
20. Hu HC. On some variational principles in the theory of elasticity and the theory of plasticity. Scientia Sinica 1955; 4:33-54 (first published in Chinese in Acta Physica Sinica 1954; X(3):259-290).
21. Washizu K. On the variational principles of elasticity and plasticity. Technical Report 25-18, Aeroelastic and Structures Research Laboratory, MIT, Cambridge, 1955.
22. Felippa CA. On the original publication of the general canonical functional of linear elasticity. Journal of Applied Mechanics 2000; 67:217-219.
23. Eraeijs de Veubeke BM. Diffusion des inconnues hyperstatiques dans les voilures à longerons couplés. Bull. Serv. Technique de l'Aéronautique 1951; 24:56 (Imprimerie Marcel Hayez, Bruxelles).
24. Lorong PH, Yvonnet J, Coffignal G, Cohen S. Contribution of computational mechanics in numerical simulation of machining and blanking. Archives of Computational Methods in Engineering 2006; 13(1):45-90.
25. Belikov VV, lvanov VD, Kontorovich VK, Korytnik SA, Semonov AY. The non Sibsonian interpolation: a new method of interpolation of the values of a function on an arbitrary set of points. Computational Mathematics and Mathematical Physics 1997; 37(1):9-15.
26. Hiyoshi H, Sugihara K. Two generations of an interpolant based on Voronoi diagrams. International Journal of Shape Modelling 1999; 5(2):219-231.
27. Sibson R. A vector identity for the Dirichlet tessellation. Mathematical Proceedings of the Cambridge Philosophical Society 1980; 87:151-155.
28. Wilkinson JH. The Algebraic Eigenvalue Problem. Clarendon Press: Oxford, 1965.
29. Fried I. Influence of Poisson's ration on the condition of the finite element stiffness matrix. International Journal of Solids and Structures 1973; 10:323-329.
30. Westergaard HM. Bearing pressures and cracks. Journal of Applied Mechanics 1939; 6:490-531.
31. Cescotto S, Li X. A natural neighbour method for linear fracture mechanics based on Fraeijs de Veubeke variational principle. Report No AG2006-10/01, ArGEnCo Department, University of Liège, October 2006.