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In the present work, a new axisymmetric weak form meshless method is presented for analysis of free vibration of functionally graded material (FGM) cylinders. This method is based on weak form of equilibrium equation and moving least squares (MLS) approximation. Essential boundary conditions are imposed by transformation method. In this method, shape functions that do not satisfy the Kronecker delta condition are corrected, then essential boundary conditions are imposed easily as in the finite element method (FEM). In the present work, the material is assumed to be functionally graded in the radial direction. Variations in the material properties such as Young’s modulus and Poisson’s ratio may be arbitrary functions of the radial coordinate. The FGM cylinder material varies continuously from silicon carbide (SiC) on the inner surface to stainless steel (SUS304) on the outer surface. Free vibration analysis of FGM cylinders with any arbitrary combination of boundary conditions is possible by the proposed model. Natural frequencies obtained from the presented model are in good agreement with results of finite element simulation. Effects of various types of boundary conditions, geometrical parameters, and mechanical properties on the natural frequencies are studied.

In this paper, static analysis of nanocomposite cylinders reinforced by single-walled carbon nanotubes subjected to internal and external pressure was carried out by a mesh-free method. In the mesh-free analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of equilibrium equation. Four types of distributions of the aligned carbon nanotubes are considered: uniform and three kinds of functionally graded distributions along the radial direction of cylinder. Material properties are estimated by a micro-mechanical model. In this simulation, an axisymmetric model is used. Detailed parametric studies have been carried out to investigate the influences of the kind of distribution and volume fractions of carbon nanotubes and cylinder thickness on displacement and stress fields for carbon nanotube-reinforced composite cylinders. Results obtained for this analysis were compared with analytical solutions and good agreement was seen between them.

This work reports the effect of nanotube aspect ratio on the free vibration characteristics of a functionally graded nanocomposite cylinders reinforced by wavy single-walled carbon nanotubes (CNTs) based on mesh-free method. In this simulation, an axisymmetric model is used and axisymmetric natural frequencies of CNT reinforced composite cylinders are presented. The material properties of functionally graded CNT reinforced composites are assumed to be graded in the thickness direction and are estimated by a micromechanical model. The effect of the waviness of the CNTs and its parameters are studied. In the mesh-free analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. It is observed that the waviness significantly reduces the effective reinforcement of the nanocomposites. The effective moduli and frequency response are very sensitive to the waviness but this sensitivity decreases with the increase of the waviness. The validity of the Young's modulus and the frequency response were assessed by a comparison with available literature data, providing a good agreement.

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