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CivilComp Proceedings
ISSN 17593433 CCP: 91
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 101
The Natural Neighbour Radial Point Interpolation Method: A NonLinear Analysis Review L.M.J.S. Dinis^{1}, R.M. Natal Jorge^{1} and J. Belinha^{2}
^{1}Faculty of Engineering, University of Porto, Portugal
L.M.J.S. Dinis, R.M. Natal Jorge, J. Belinha, "The Natural Neighbour Radial Point Interpolation Method: A NonLinear Analysis Review", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 101, 2009. doi:10.4203/ccp.91.101
Keywords: natural neighbour radial point interpolator method, meshless methods, nonlinear analysis, large deformations, elastoplastic analysis.
Summary
This paper presents the large deformation analysis of nonlinear elastic and elastoplastic structures based on the natural neighbour radial point interpolation method (NNRPIM) [1,2], which is an improved meshless method.
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 "influencecells". These cells are in fact influencedomains entirely nodal dependent. The Delaunay triangles [5], which are the dual of the Voronoï cells, are used to create a nodedependent background mesh used in the numerical integration of the NNRPIM interpolation functions. Unlike the finite element method, where geometrical restrictions on elements are imposed for the convergence of the method, in the NNRPIM there are no such restrictions, which permits a random node distribution for the discretized problem. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed in a similar process to the radial point interpolation method (RPIM) [6,7], 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 posses the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. Several nonlinear elastoplasticity problems are studied to demonstrate the effectiveness of the method. The numerical results indicated that the NNRPIM handles large material distortion effectively and provides an accurate solution under large deformation. References
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