The natural neighbour radial point interpolation method: dynamic applications

Abstract

Purpose

The purpose of this paper is to extend the natural neighbour radial point interpolation method (NNRPIM) to the dynamic analysis (free vibrations and forced vibrations) of two‐dimensional, three‐dimensional and bending plate problems.

Design/methodology/approach

The NNRPIM shape‐function construction is briefly presented, as are the dynamic equations and the mode superposition method is used in the forced vibration analysis. Several benchmark examples of two‐dimensional and plate bending problems are solved and compared with the three‐dimensional NNRPIM formulation. The obtained results are compared with the available exact solutions and the finite element method (FEM) solutions.

Findings

The developed NNRPIM approach is a good alternative to the FEM for the solution of dynamic problems, once the obtained results with the EFGM shows a high similarity with the obtained FEM results and for the majority of the studied examples the NNRPIM results are more close to the exact solution results.

Research limitations/implications

Comparing the FEM and the NNRPIM, the computational cost of the NNRPIM is higher.

Originality/value

The paper demonstrates extension of the NNRPIM to the dynamic analysis of two‐dimensional, three‐dimensional and bending plate problems. The elimination of the shear‐locking phenomenon in the NNRPIM plate bending formulation. The various solved examples prove a high convergence rate and accuracy of the NNRPIM.

Citation

Dinis, L.M.J.S., Natal Jorge, R.M. and Belinha, J. (2009), "The natural neighbour radial point interpolation method: dynamic applications", Engineering Computations, Vol. 26 No. 8, pp. 911-949. https://doi.org/10.1108/02644400910996835