Abstract
The meshless natural neighbour method (MNNM) is a truly meshless method, which does not need the Delaunay tessellation of the whole domain to construct the Laplace interpolation. At the same time, some difficulties in other meshless methods, such as the imposition of essential boundary conditions, the treatment of material discontinuities and the choice of weight functions are avoided. The governing equations of elasto-plastic for MNNM are obtained to apply the MNNM to the analysis of two-dimensional elasto-plastic problems. The numerical results indicate that the theory and programmes are accurate and effective.
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REFERENCES
R.A. Gingold and J.J. Moraghan (1977), Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181, 2, pp. 375–389.
W.K. Liu, S. Jun and Y.F. Zhang (1995), Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 20, pp. 1081–1106.
W.K. Liu and Y. Chen (1995), Wavelet and multiple scale reproducing kernel method. International Journal for Numerical Methods in Fluids, 21, pp. 901–931.
R.R. Ohs and N.R. Aluru (2001), Meshless analysis of piezoelectirc devices. Computational Mechanics, 27, pp. 23–36.
T. Belytschko, Y.Y. Lu and L. Gu (1994), Element-free Galerkin method. International Journal for Numerical Methods in Engineering, 37, pp. 229–256.
B. Nayroles, G. Touzot and P. Villon (1992), Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 10, pp. 307–318.
L.W. Cordes and B. Moran (1996), Treatment of material discontinuity in the Element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 139, pp. 75–89.
Y. Krongauz and T. Belytschko (1998), EFG approximation with discontinuous derivatives. International Journal for Numerical Methods in Engineering, 41, pp. 1215–1233.
E. Oñate, S.R. Idelsohn, O.C. Zienkiewicz et al. (1996), A finite point method in computational mechanics: applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering, 39, pp. 3839–3866.
C.A. Duarte and J.T. Oden (1996), Hp clouds: a h-p meshless method. Numerical Methods for Partical Differential Equations, 12, pp. 673–705.
T. Zhu, J. Zhang and S.N. Atluri (1998), A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Computational Mechanics, 21, pp. 223–235.
S.N. Atluri and T. Zhu (1998), A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 22, pp. 117–127.
J. Braun and M. Sambridge (1995), A numerical method for solving partial differential equations on highly irregular evolving grids. Nature, 376, pp. 655–660.
N. Sukumar, B. Moran and T. Belytschko (1998), The nature element method in solid mechanics. International Journal for Numerical Methods in Engineering, 43, pp. 839–887.
E. Cueto, M. Doblare and L. Gracia (2000), Imposing essential boundary conditions in the natural element method by means of density-scaled α-shapes.International Journal for Numerical Methods in Engineering, 49, pp. 519–546.
N. Sukumar, B. Moran and Y. Semenov (2001), Natural neighbour Galerkin method. International Journal for Numerical Methods in Engineering, 50, pp. 1–27.
N. Sukumar (2003), Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids. International Journal for Numerical Methods in Engineering, 57, pp. 1–34.
S.R. Idelsohn, E. Oñate, N. Calvo and F.D. Pin (2003), The meshless finite element method. International Journal for Numerical Methods in Engineering, 58, pp. 893–912.
E. Cueto, N. Sukumar, B. Calvo, M.A. Martínez, J. Cegoñino and M. Doblaré (2003), Overview and recent advances in natural neighbor Galerkin methods. Archives of Computational Methods in Engineering, 10, 4, pp. 307–384.
Y.C. Cai and H.H. Zhu (2004), A meshless local natural neighbour interpolation method for stress analysis of solids. Engineering Analysis with Boundray Elements, 28, 6, pp. 607–613.
X. Zhang, K.Z. Song, M.W. Lu et al. (2000), Meshless methods based on collocation with radial basis function. Computational Mechanics, 26, 4, pp. 333–343.
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Zhu, H., Miao, Y., Cai, Y. (2006). MESHLESS NATURAL NEIGHBOUR METHOD AND ITS APPLICATION IN ELASTO-PLASTIC PROBLEMS. In: LIU, G., TAN, V., HAN, X. (eds) Computational Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3953-9_71
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DOI: https://doi.org/10.1007/978-1-4020-3953-9_71
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