CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 6,a2015 ·1149· DOI: 10.3901/CJME.2015.0429.048, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method KHOSHGOFTAR M J 1, 2, * , MIRZAALI M J 3 , and RAHIMI G H 1 1 Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran 14115-111, Iran 2 Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-88349, Iran 3 Department of Mechanical Engineering, Politecnico di Milano, Milan 20156, Italy Received July 15, 2014; revised April 27, 2015; accepted April 29, 2015 Abstract: Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material. Keywords: non-homogenous cylinder, First order Shear Deformation Theory, matched asymptotic method, perturbation method, functionally graded material 1 Introduction  Functionally graded materials(FGMs) are composite materials made up of various material composition and micro-structures. These properties can vary spatially in FGMs. Structures made of FGMs have improved performance characteristics in terms of mechanical and thermal properties under high temperature and thermal cycling conditions. Recently, application of FGMs as heat-shielding materials have attracted a great deal of interest. Powder metallurgy methods can be used in the production of FGMs. As an example of such a manufacturing process, they can be produced by the application of a centrifugal force. Using this method, a continuously varying volume fraction of the inclusion material can be formed. The most well-known FGM is compositionally graded from a ceramic to a metal. It is able to incorporate diverse properties of ceramics, such as heat, wear and oxidation resistance, with toughness, strength, * Corresponding author. E-mail: mj.khoshgoftar@gmail.com © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2015 machinability and bending capability of metals. It will result in a material with non-homogeneous thermal and mechanical properties. In the theory of elasticity, FGM materials are mostly treated as non-homogeneous materials with material constants that vary continuously along one spatial direction. The mechanical behavior of homogeneous and non-homogeneous cylinders has been investigated in several scientific papers. NZENGWA and SIMO [1] derived a 2-Dimensional model of a thick elastic shell from the 3-Dimensional theory by considering of different ratios for h/R in horizontal and vertical components. TUTUNCU and OZTURK [2] presented the exact stress solution for spherical and cylindrical pressure vessels of a functionally graded composite. They used infinitesimal theory of elasticity and obtained a close form solution for the stresses. They have considered simple power law for stiffness and constant value for Poisson ratio. TUTUNCU [3] published another paper about finding the stress solution in thick-walled cylinders using power series. Elastic and thermoelastic analysis of functionally graded piezoelectric cylinder have been considered in the literatures [4–8] . Set of field equations for thick shell of revolution made of FGMs derived by ZAMANI NEJAD, et al [9] . They derived formulation for a