Free vibration characteristics of functionally graded structures by an isogeometrical analysis approach

An improved methodology based on isogeometric analysis (IGA) approach is suggested to investigate the free vibration characteristics of functionally graded structures. The proposed method, which can be considered as an extension of the isogeometric analysis method to inhomogeneous elasticity, employs a fully isogeometric formulation for construction of the geometry, approximation of the solution as well as modelling the variations of material properties. The gradations of material properties are captured using the same NURBS basis functions employed for geometric and computational modelling by utilization of an interpolation technique. It will be seen that the proposed NURBS-based analysis method constitutes an efficient tool for studying integrated modelling and vibration analysis of functionally graded structures. Some numerical examples of 2D plane elasticity problems are presented and the effects of different types of unidirectional and bidirectional material profiles on dynamic characteristics of functionally graded structures are investigated. The obtained numerical results are verified with available exact elasticity solutions or the results of commercial finite element method software. It is shown that the difficulties encountered in free vibration analysis of functionally graded structures using the conventional finite element method are considerably circumvented by adopting the proposed procedure.