Open Access

ARTICLE

Large Deformation Applications with the Radial Natural Neighbours Interpolators

L.M.J.S. Dinis¹, R.M. Natal Jorge², J. Belinha³

1 FEUP, Porto, Portugal - e-mail: ldinis@fe.up.pt
2 FEUP, Porto, Portugal - e-mail: rnatal@fe.up.pt
3 IDMEC, Porto, Portugal - e-mail: jorge.belinha@fe.up.pt

Computer Modeling in Engineering & Sciences 2009, 44(1), 1-34. https://doi.org/10.3970/cmes.2009.044.001

Abstract

The Natural Neighbour Radial Point Interpolation Method (NNRPIM) is extended to the large deformation analysis of non-linear elastic structures. The nodal connectivity in the NNRPIM is enforced using the Natural Neighbour concept. After the Voronoï diagram construction of the unstructured nodal mesh, which discretize the problem domain, small cells are created, the "influence-cells". These cells are in fact influence-domains entirely nodal dependent. The Delaunay triangles 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 with the Radial Point Interpolators. In the construction of the NNRPIM interpolation functions no polynomial base is required, which is an innovation and the used Radial Basis Function (RBF) is the Multiquadric RBF. The NNRPIM interpolation functions posses the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. Once the scope of this work is to extend and validate the NNRPIM in the large-deformation analysis, the used non-linear solution algorithm is the Orthogonal Actualized Ramm's method, which permits the analysis of structures that in some point evidence instability phenomenons such as the "snap-through" and the "snap-back". Several non-linear benchmark examples are studied to demonstrate the effectiveness of the method. The numerical results indicated that NNRPIM handles large material distortion effectively and provides an accurate solution under large deformation.

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