Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading Mohammad Zamani Nejad a,⇑ , Mehdi Jabbari a , Mehdi Ghannad b a Mechanical Engineering Department, Yasouj University, P. O. Box: 75914-353, Yasouj, Iran b Mechanical Engineering Faculty, University of Shahrood, Shahrood, Iran article info Article history: Received 31 October 2014 Received in revised form 11 December 2014 Accepted 18 December 2014 Available online xxxx Keywords: Thick cylindrical shell Variable thickness Rotating Axially functionally graded material Non-uniform pressure Multi-layers method (MLM) abstract A functionally graded rotating thick hollow cylinder with variable thickness and clamped ends is studied semi-analytically under arbitrarily non-uniform pressure on the inner sur- face. The material properties, except the Poisson’s ratio, are assumed to vary with the power law function in the axial direction of the cylinder. By using the first-order shear deformation theory (FSDT) the governing equations are derived. The governing equations are in the form of a set of general differential equations. Given that the FG cylinder with variable thickness is divided into n homogenous disks, n sets of differential equations are obtained. The solution of this set of equations is obtained, applying the boundary con- ditions and continuity conditions between the layers, radial displacement and stresses. The problem is also solved, using the finite element method (FEM). The obtained results of the disk form multi-layers method (MLM) are compared with those of FEM. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Functionally graded materials (FGMs) are composite materials which are preferred in many applications such as aero- space and nuclear industries (Keles & Conker, 2011). Unlike layered composites, material properties vary continuously and smoothly throughout a certain dimension in FGMs (Akgoz & Civalek, 2014). A number of papers addressing various aspects of FGM have been published in recent years (Nejad & Fatehi, 2015; Nejad, Rastgoo, & Hadi, 2014; Nejad & Kashkoli, 2014; Simsek & Reddy, 2013; Xue & Pan, 2013). Given the limitations of the classic theories of thick-walled shells, very little attention has been paid to the analytical and semi-analytical solutions for of these shells. Most of the existing literature deals with the stress or vibration analysis of thin cylindrical shells with variable thickness and is based upon a thin shell or membrane shell theory. However, very little atten- tion has been paid to the analytical solution of thick cylindrical shells with variable thickness, which is due to the limitations of the classic theories of thick-walled shells. Shear deformation theory is a very suitable method for the purpose of calculat- ing stresses and displacements in plates and axisymmetric thick shells (Ghannad, Rahimi, & Nejad, 2013). Assuming the transverse shear effect, Naghdi and Cooper (1956), formulated the theory of shear deformation. The solution of thick cylindrical shells of homogenous and isotropic materials, using the first-order shear deformation theory (FSDT) was derived http://dx.doi.org/10.1016/j.ijengsci.2014.12.004 0020-7225/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +98 7433221711. E-mail addresses: m.zamani.n@gmail.com, m_zamani@yu.ac.ir (M.Z. Nejad). International Journal of Engineering Science 89 (2015) 86–99 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci