Thermal stability analysis of circular functionally graded sandwich plates of variable thickness using pseudo-spectral method S.K. Jalali * , M.H. Naei, A. Poorsolhjouy School of Mechanical Engineering, University of Tehran, Tehran, Iran article info Article history: Received 9 January 2010 Accepted 5 May 2010 Available online 8 May 2010 Keywords: A. Functionally graded materials B. Variable thickness sandwich plates I. Buckling abstract In the present study, the thermal stability of laminated functionally graded (FGM) circular plates of var- iable thickness subjected to uniform temperature rise based on the first-order shear deformation plate theory is presented. Furthermore, two models for FGM plates with variable thickness, corresponding with two manufacturing methods, are proposed. The laminated FGM plate with variable thickness is consid- ered as a sandwich plate constituted of a homogeneous core of variable thickness and two constant thick- ness FGM face sheets whose material properties are assumed to be graded in the thickness direction according to a simple power law. In order to determine the distribution of the prebuckling thermal load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudo-spectral method that makes use of Chebyshev polynomials, the stability equations are solved numerically to evaluate the critical temperature rise. The results demonstrate that the thermal stability is significantly influenced by the thickness variation profile, aspect ratio, the volume fraction index, and the core-to-face sheet thickness ratio. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Stability analysis and studies on the buckling behavior of plates have always been considered as one of the important subjects in structural analysis (Timoshenko and Gere [1], Almroth and Brush [2], and Turvey and Marshall [3]). On the other hand, variable thick- ness plates have always been attractive for designers, and a lot of researches have been done on this subject. The most conspicuous usage of variable thickness plates is to lighten structures, especially when used in high-speed aircrafts. With an accurate design of the thickness distribution, one can make an increase in buckling capac- ity of the plate compared to its uniform thickness counterpart. Wang et al. [4] investigated the elastic buckling of tapered circular plates based on the shooting method and the Rayleigh–Ritz approach. Raju and Rao [5] evaluated the post-buckling behavior of linearly tapered moderately thick isotropic circular plates subjected to thermal load by employing a general finite element formulation. Özakça et al. [6] carried out the buckling analysis of tapered circular and annular plates using the finite element method. A family of variable thick- ness, Mindlin–Reissner axisymmetric finite elements is developed which include shear deformation and rotary inertia effects. Shufrin and Eisenberger [7] studied the buckling behavior of thick elastic rectangular plates with variable thickness, applying both the first- order and high order shear deformation plate theories, using the extended Kantorovich method. Functionally graded materials (FGM) are a group of composite materials whose properties vary continuously from one side to an- other. The concept of FGM was first introduced by a group of mate- rial scientists in Japan in 1984 [8]. These materials are typically constructed from a mixture of ceramic and metal and they can survive environments with high-temperature gradients such as nuclear reactors and high-speed aircrafts. The low thermal conduc- tivity of ceramic provides the high-temperature resistance. On the other hand, the ductile metal prevents fracture caused by thermal stresses. Aboudi et al. [9] used a higher-order theory for the re- sponse of a functionally graded composite plate subjected to a through-thickness thermal gradient to optimize the composite’s microstructure. Praveen and Reddy [10] investigated the static and dynamic response of functionally graded ceramic–metal plates, using a plate finite element that accounts for the transverse shear strains, rotary inertia and moderately large rotations in the von-Karman sense, and discussed the effect of the imposed tem- perature field on the response of the FGM plate. Najafizadeh and Eslami [11] analyzed the thermal buckling of FGM circular plates under uniform temperature rise, thermal gradient across the thick- ness, and thermal gradient across the radius. Ma and Wang [12] investigated axisymmetric large deflection bending and thermal post-buckling behavior of an FGM circular plate, based on the 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.05.009 * Corresponding author. Address: School of Mechanical Engineering, P.O. Box: 1439955961, University of Tehran, Tehran, Iran. Tel.: +98 21 61114021; fax: +98 21 66480290. E-mail address: skjalali@ut.ac.ir (S.K. Jalali). Materials and Design 31 (2010) 4755–4763 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes