Keywords: functionally graded materials, thick hollow cylinders, finite length, graded finite element, elasticity, hydrostatic internal pressure.

Functionally graded materials (FGMs) have attracted much attention as advanced structural materials because of their superior resistance to interfacial failure. In this paper a thick short length hollow cylinder made of functionally graded materials under hydrostatic internal pressure is considered. Investigations are more in-plane strain conditions, also analytical or semi-analytical solutions are available only through a number of problems with simple boundary condition or a special material properties variation. For example, Shao et al. [1,2] analytically obtained the elastic behaviour of FG hollow cylinders of finite length with simply supported end conditions under the hydrostatic pressure, in this research, in order to satisfy the boundary conditions, the sinusoidal load along the axial direction can only be used. Therefore to find the solution for any FGM cylinder which is subject to any arbitrary loading function, especially, uniform internal pressure, we used the graded finite element method. In this method, material properties are interpolated using linear shape functions. Therefore, the material composition varies continuously through the cylinder. Using this method, different types of displacements and stresses for three different functionally graded materials are investigated. Two of them are one dimensional FGMs and material distribution varies according to the power law distribution through the thickness. In the first model of one-dimensional FGMs, the cylinder is made of a combined ceramic-metal material. The inner surface of the cylinder is pure ceramic and the outer one is pure metal. In the second type, the outer surface of the cylinder is made of pure ceramic and by increasing the power law exponent, the modulus of elasticity of cylinder decreases. The third type of material distribution is for two dimensional FGMs and material properties vary through both the radial and the axial directions. In this case, the inner surface of the cylinder is made of two different ceramics and the outer surface of two different metal alloys.

The finite element approximation of the domain is in the rz plane, which is the plane of revolution and the domain is meshed using the simplex linear triangular element. Axial symmetry is assumed, therefore, the formulation is reduced to two dimensions. Results denote that the functionally graded properties can provide information about the static behavior of a cylinder, which may be used in its optimization for a particular situation. To compare the model with the existing literature, the result of an infinite FG thick hollow cylinder under the same loading were obtained and they demonstrate very good agreement.

1

Z.S. Shao, "Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length", International Journal of Pressure Vessels and Piping, 82, 155-163, 2005. doi:10.1016/j.ijpvp.2004.09.007

2

Z.S. Shao, L.F. Fan, T.J. Wang, "Analytical solutions of stresses in functionally graded circular hollow cylinder with finite length", Key Engineering Material, 261-263, 651-656, 2004. doi:10.4028/www.scientific.net/KEM.261-263.651

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