Application of isogeometric analysis to free vibration of truss structures

Abstract

The Finite Element Method (FEM) is a standard tool to find natural vibration modes and frequencies of a structure, but the main problem is related with the inaccurate higher frequencies of a sample. Recently, there has appeared a new numerical method to solve partial differential equations, called Isogeometric Analysis (IGA), which uses NURBS (Non Uniform Rational B-Splines) as weighting functions to the solution of the problem and also as approach to the object geometry. In this paper, a study on the free vibration analysis based on isogeometric approach of truss structures is presented. Three refinement schemes such as h-, p- and k- refinement are used to obtain the accuracy of solution. Numerical results are then explored to show the effectiveness and accuracy of the present method by comparing its performance with finite element method (FEM), composite element method (CEM) and generalized finite element method (GFEM) reported in the literature. Based on the results, IGA is a promising tool, giving accurate results and high convergence rates.