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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 9

Analysis of Laminated Plates with Third Order Plate Theory and with the Natural Neighbour Radial Point Interpolation Method

L.M.J.S. Dinis1, R.M. Natal Jorge1 and J. Belinha2

1Faculty of Engineering, University of Porto, Portugal
2Institute of Mechanical Engineering, Polo FEUP, Porto, Portugal

Full Bibliographic Reference for this paper
L.M.J.S. Dinis, R.M. Natal Jorge, J. Belinha, "Analysis of Laminated Plates with Third Order Plate Theory and with the Natural Neighbour Radial Point Interpolation Method", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 9, 2008. doi:10.4203/ccp.88.9
Keywords: natural neighbour radial point interpolator method, laminate, unconstrained third-order, dynamic analysis.

In this work an improved meshless method, the natural neighbour radial point interpolation method (NNRPIM) [1,2], is used in the numerical implementation of an unconstrained third-order plate theory applied to laminates.

The NNPRIM uses the natural neighbour [3] concept in order to enforce the nodal connectivity. Based on the Voronoï diagram [4] small cells are created from the unstructured set of nodes discretizing the problem domain, the "influence-cells". These cells are in fact influence-domains entirely nodal dependent. The Delaunay triangles [5], which are the dual of the Voronoï cells, are used to create a node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed in a similar process to the radial point interpolation method (RPIM) [6], with some differences that modify the method performance. In the construction of the NNRPIM interpolation functions no polynomial base is required and the radial basis function (RBF) used is the multiquadric RBF. The NNRPIM interpolation functions posseses the delta Kronecker property, which simplifies the imposition of the natural and essential boundary conditions.

An unconstrained third-order shear deformation theory (UTSDT) is considered and clearly described in order to define the displacement field and the strain field.

Several well-known benchmark static and dynamic laminate examples are solved in order to prove the high accuracy and convergence rate of the proposed method. The numerical results obtained with the meshless method are compared with the UTSDT exact solution, when available, and with other plate deformation theories exact solutions.

Dinis L., Jorge R.N., Belinha J., "Analysis of 3D solids using the natural neighbour radial point interpolation method", Computer Methods in Applied Mechanics and Engineering, 196, 2009-2028, 2007. doi:10.1016/j.cma.2006.11.002
Dinis L., Jorge R.N., Belinha J., "Analysis of plates and laminates using the natural neighbour radial point interpolation method", Engineering Analysis with Boundary Elements, 2007. doi:10.1016/j.enganabound.2007.08.006
Sibson R., "A vector identity for the Dirichlet tesselation", Mathematical Proceedings of the Cambridge Philosophical Society, 87, 151-155, 1980. doi:10.1017/S0305004100056589
Voronoï G.M., "Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième Mémoire: Recherches sur les parallélloèdres primitifs", J. Reine Angew. Math., 134, 198-287, 1908.
Sibson R., "A brief description of natural neighbor interpolation. Interpreting Multivariate Data", in V. Barnett (ed.), Wiley, Chichester, 21-36, 1981.
Wang J.G., Liu G.R., "A Point Interpolation Meshless Method based on Radial Basis Functions", International Journal for Numerical Methods in Engineering, 54, 1623-1648, 2002. doi:10.1002/nme.489

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