Functionally graded materials are a new generation of advanced inhomogeneous composite materials, which usually exhibit better performance compared to traditional homogeneous objects. Since the material properties of FGMs are spatially dependant, serious difficulties may arise when conventional computational methods, such as finite elements are employed for their analysis. In this research, we introduce a new methodology based on isogeometric analysis approach to address the free vibrations of functionally graded plane elasticity problems. The proposed method which can be considered as the generalization of the well-known isogeometric analysis method to variable elasticity, employs a fully isogeometric formulation for construction of the geometry, approximation of the solution, and modeling the variations of material properties. Due to the possibility of simultaneously modeling of the structural shape, material distribution, and structural analysis, the proposed NURBS based analysis constitutes an important tool for studying integrated modeling and analysis of FGMs. The recently developed isogeometric analysis numerical method is concisely explained and the functionally graded materials are briefly introduced. A few numerical examples are presented and compared to available exact elasticity solutions as well as the finite elements, to demonstrate the performance and efficiency of the proposed method in this type of field problems. It is shown that the difficulties encountered in the finite element analysis of FGMs are alleviated to a large degree by employing the mentioned method.

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