The natural neighbour radial point interpolation method: dynamic applications

摘要

Purpose - The purpose of this paper is to extend the natural neighbour radial point interpolationrnmethod (NNRPIM) to the dynamic analysis (free vibrations and forced vibrations) of two-dimensional,rnthree-dimensional and bending plate problems.rnDesign/methodology/approach - The NNRPIM shape-function construction is briefly presented,rnas are the dynamic equations and the mode superposition method is used in the forced vibrationrnanalysis. Several benchmark examples of two-dimensional and plate bending problems are solvedrnand compared with the three-dimensional NNRPIM formulation. The obtained results are comparedrnwith the available exact solutions and the finite element method (FEM) solutions.rnFindings - The developed NNRPIM approach is a good alternative to the FEM for the solution ofrndynamic problems, once the obtained results with the EFGM shows a high similarity with thernobtained FEM results and for the majority of the studied examples the NNRPIM results are morernclose to the exact solution results.rnResearch limitations/implications - Comparing the FEM and the NNRPIM, the computationalrncost of the NNRPIM is higher.rnOriginality/value - The paper demonstrates extension of the NNRPIM to the dynamic analysis ofrntwo-dimensional, three-dimensional and bending plate problems. The elimination of the shear-lockingrnphenomenon in the NNRPIM plate bending formulation. The various solved examples prove a highrnconvergence rate and accuracy of the NNRPIM.