A local search algorithm for natural neighbours in the natural element method

International Journal of Solids and Structures

Volumn 42, Issue 23, 2005, Pages 6059-6070

  Cai, Yongchang ^a   Zhu, Hehua ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Element free; Laplace interpolation; Meshless; Natural element; Natural neighbour

Indexed keywords

BOUNDARY CONDITIONS; ELASTICITY; FINITE ELEMENT METHOD; INTERPOLATION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING;

ELEMENT-FREE; LAPLACE INTERPOLATION; MESHLESS; NATURAL ELEMENT; NATURAL NEIGHBOUR;

ALGORITHMS;

EID: 23944509352     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2005.04.006     Document Type: Article

References (24)

1. S.N. Atluri, and T. Zhu A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Computational Mechanics 22 1998 117 127
2. S. Beissel, and T. Belytschko Nodal integration of the element-free Galerkin method Computer Methods in Applied Mechanics and Engineering 139 1996 49 74
3. T. Belytschko, Y. Krongauz, and D. Organ Meshless methods:An overview and recent developments Computer Methods in Applied Mechanics and Engineering 139 1996 3 47
4. T. Belytschko, Y.Y. Lu, and L. Gu Element-free Galerkin method International Journal for Numerical Methods in Engineering 37 1994 229 256
5. T. Belytschko, D. Organ, and C. Gerlach Element-free Galerkin methods for dynamic fracture in concrete Computer Methods in Applied Mechanics and Engineering 187 2000 385 399
6. T. Belytschko, D. Organ, and Y. Krongauz A Coupled finite element-element free Galerkin method Computational Mechanics 17 1995 186 195
7. P. Beitkopf, A. Rassineux, and T. Gibert Explicit form and efficient computation of MLS shape functions and their derivatives International Journal for Numerical Methods in Engineering 48 2000 451 466
8. J. Braun, and M. Sambridge A numerical method for solving partial differential equations on highly irregular evolving grids Nature 376 1995 655 660
9. Y.C. Cai, and H.H. Zhu Direct imposition of essential boundary condition and treatment of material discontinuity in EFG method Computational Mechanics 34 2004 330 338
10. C.A. Duarte, and J.T. Oden Hp clouds: A h-p meshless method Numerical Methods for Partial Differential Equations 12 1996 673 705
11. R.A. Gingold, and J.J. Moraghan Smoothed particle hydrodynamics: Theory and applications to non-spherical stars Monthly Notice of the Royal Astronomical Society 18 1977 375 389
12. E. Hardee, K.H. Chang, and I. Grindeanu A Structure Nonlinear Analysis Workspace based on meshless method Advances in Engineering Software 30 1999 153 175
13. S.F. Li, W.K. Liu, and A.J. Rosakis Mesh free Galerkin simulations of dynamic shear band propagation and failure mode transition International Journal of Solids and Structures 39 2002 1213 1240
14. W.K. Liu, S. Jun, and Y.F. Zhang Reproducing Kernel Particle methods International Journal for Numerical Methods in Fluids 20 1995 1081 1106
15. M.B. Liu, G.R. Liu, and Z. Zong Computer simulation of high explosive explosion using Smoothed particle hydrodynamics methodology Computers & Fluids 32 2003 305 322
16. J.M. Melenk, and I. Babuska The partition of unity finite element methods: Basic theory and application Computer Methods in Applied Mechanics and Engineering 139 1996 263 288
17. E. Onate, S. Idelsohn, and O.C. Zienkiewicz A finite point method in computational mechanics: Applications to convective transport and fluid flow International Journal for Numerical Methods in Engineering 39 1996 3839 3866
18. J.P. Ponthot, and T. Belytschko Arbitrary Lagrangian-Eluerian formulation for element-free Galerkin method Computer Methods in Applied Mechanics and Engineering 152 1998 19 46
19. N. Sukumar Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids International Journal for Numerical Methods in Engineering 57 2003 1 34
20. N. Sukumar, B. Moran, and T. Belytschko The natural element method in solid mechanics International Journal for Numerical Methods in Engineering 43 1998 839 887
21. N. Sukumar, B. Moran, and Y. Semenov Natural neighbour Galerkin method International Journal for Numerical Methods in Engineering 50 2001 1 27
22. J.G. Wang, G.R. Liu, and P. Lin Numerical analysis of Biot's consolidation process by radial point interpolation method International Journal of Solids and Structures 39 2002 1557 1573
23. J.X. Zhou, J.B. Wen, and H.Y. Zhang A nodal integration and post-processing technique based on Voronoi diagram for Galerkin meshless methods Computer Methods in Applied Mechanics and Engineering 192 2003 3831 3843
24. T. Zhu, and S.N. Atluri A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method Computational Mechanics 21 1998 211 222