Acta Mech 220, 299–314 (2011) DOI 10.1007/s00707-011-0478-y Ali Safari · Masoud Tahani · Seyed Mahmoud Hosseini Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method Received: 13 June 2010 / Published online: 2 April 2011 © Springer-Verlag 2011 Abstract This work is aiming to present an analytical method to study the dynamic behavior of thermoelastic stresses in a finite-length functionally graded (FG) thick hollow cylinder under thermal shock loading. The thermo-mechanical properties are assumed to vary continuously through the radial direction as a nonlinear power function. Using Laplace transform and series solution, the thermoelastic Navier equations in displace- ment form are solved analytically. The solution of the displacement field in the FG cylinder is obtained in the Laplace domain. Also, the fast Laplace inverse transform method (FLIT) is employed to transfer the results from Laplace domain to time domain. The effects of thermal shock loading on the dynamic characteristics of the FG thick hollow cylinder are studied in various points across the thickness of cylinder for various grading patterns of FGMs. A good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data. 1 Introduction The applications of functionally graded materials (FGMs) are increasing because of their capability to control the thermo-mechanical stresses in structures under thermal and mechanical loadings. FGMs are a new kind of composite materials whose thermo-mechanical properties vary continuously along certain directions. In recent years, a number of analytical solutions have been obtained by some researchers to determine the stress distribution in structures, especially in cylindrical structures. To assess the dynamic behavior of thermoelastic stresses, an analytical method was presented for a long homogeneous thick hollow cylinder subjected to thermal shock loadings by Wang [1]. Using linear theory of elasticity, a steady-state solution for the stress field in an orthotropic hollow circular cylinder subjected to asymmetric temperature distribution was obtained by Zibdeh and Farran [2]. Ootao and Tanigawa [3] dealt with three-dimensional transient piezo-thermoelasticity problem of an FGM rectangular plate. The authors devel- oped a theoretical solution based on the theory of laminated composites for studying steady-state response of a three-dimensional simply supported FGM plate. Xia and Dinga [4] obtained three-dimensional solutions for a laminated cantilever cylindrical shell with arbitrary thickness under thermal and mechanical loadings. They presented a weak formulation of mixed state equation in the cantilever cylindrical shell as a numerical method. Yee and Moon [5] derived a closed-form analytical solution for the transient, plane thermal stress analysis of a A. Safari · M. Tahani Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran S. M. Hosseini (B ) Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran E-mail: sm_hosseini@ferdowsi.um.ac.ir; sm_hoseini@yahoo.com Tel.: +98 511 8815100 (551) Fax: +98 511 8763301