Functionally graded materials are advanced composite materials consisting two or more material ingredients that are engineered to have a continuous spatial variation of properties. There are a few analytical methods available to solve the governing equations of FGM made structures, confined to some specific and limited shapes, loadings and boundary conditions. Hence the numerical methods such as FEM are used to treat these materials. In previous studies the finite element method was used to solve thin walled FG structures like shells and plates by modification of the conventional shell and plate elements. Solving the thick walled FG structures confronts some difficulties. One of the methods to overcome this problem is laminating the structure across the direction of material variation, assuming constant material properties in each layer. When the thickness is increased, the number of layers representing the FGM should be also increased to produce an accurate result. Increasing the number of elements implies great time consumption and required memory space. One of the most commonly shapes present in FG structures are hollow cylinders whose analysis is so complicated that may not be done by conventional elements. In this study a superelement approach is chosen to confront the problem. Design and application of superelements in efficient prediction of the structural behavior in a short time has been one of the research interests in the last decade. The superelements are designed for special problems so that they could substitute a huge number of conventional elements in modeling and analysis. In this study a new cylindrical superelement is incorporated to model the functionally graded cylinders, and modal analysis is performed. The advantage of this cylindrical superelement lies in the fact that no lamination is needed, anymore and only a few superelements can predict the vibration behavior of FG cylinders accurately. Several examples are solved based on the new element formulation and the natural frequencies and mode shapes are obtained. Comparison of the findings with the conventional elements reveals time saving and accuracy of the results.
Adaptive flux-based nodeless variable finite element formulation with error estimation for thermal-structural analysis