Journal of Mechanical Science and Technology 24 (12) (2010) 2519~2527 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-010-0918-y Thermal buckling analysis of cross-ply laminated rectangular plates under nonuniform temperature distribution: A differential quadrature approach † M. Mansour Mohieddin Ghomshei * and Amin Mahmoudi Department of Mechanical Engineering, Islamic Azad University-Karaj Branch, Karaj, Alborz, 31485-313, I.R. Iran (Manuscript Received March 29, 2010; Revised August 31, 2010; Accepted August 31, 2010) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Differential quadrature method (DQM) is implemented for analyzing the thermal buckling behavior of the symmetric cross-ply lami- nated rectangular thin plates subjected to uniform and/or non-uniform temperature fields. The approach includes two steps: (1) solving the problem of in-plane thermo-elasticity to obtain the in-plane force resultants and (2) solving the buckling problem under the force distribution obtained in the previous step. Solution procedures are numerically performed by discretizing the governing differential equa- tions and boundary conditions using DQM method. Applying the developed DQ formulation, the buckling loads are obtained for several sample plates. The numerical results compared well with those available in the literature as well as those obtained by ABAQUS. Para- metric studies are conducted to investigate the influence of some important parameters including the plate aspect ratio, cross-ply ratio, and stiffness ratio on the critical temperature and mode shape of buckling. Keywords: Thermal buckling; DQM; Cross-ply laminate; Non-uniform thermal load; Laminated plate ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Thermal buckling is a crucial failure mode in plates and shells. When geometrically perfect plates restrained from in- plane expansion are slowly heated, they generally develop compressive stresses and then buckle at a specific temperature. Attention was first given to thermal buckling problem during the onset of the jet age, when aircraft and missile structural elements, such as plates and shells became exposed to high temperatures inherent to supersonic flight. Fiber-reinforced composite laminates have important structural applications in aircraft and space vehicles and other weight-sensitive applica- tions, These materials are usually subjected to non-uniform temperature distributions due to aerodynamic and solar radia- tion heating. In this respect, the analysis of thermal buckling due to non-uniform thermal load is of special interest. Thangaratnam and Ramachandran [1] studied thermal buck- ling behavior of composite laminated plates subjected to a uniform temperature distribution on simple edge supports. Chen et al. [2-4] used the finite element method to study the problems of thermal buckling and postbuckling behavior of composite laminated plates, taking into account the effect of transverse normal strain. Chen et al. [5] also analyzed the thermal buckling behavior of composite laminated plates sub- jected to non-uniform temperature fields using the finite ele- ment method, wherein the effect of shear deformation and rotary inertia was accounted for using thermal-elastic Mindlin plate theory. Implementing the equivalent mechanical loading concept, Jones [6] developed solutions for unidirectional and symmetric cross-ply laminated fiber-reinforced composite rectangular plates and uniform heating throughout the plate volume that are uniaxially restrained in their plane on two of the four edges, but have no rotational restraint on any edge. In this research, the problem of thermal buckling behavior of thin unidirectional and symmetric cross-ply laminated fi- ber-reinforced composite rectangular plates under uniform or non-uniform temperature field is studied by implementing the differential quadrature method (DQM). Parametric studies are conducted to investigate the influence of various important parameters, including plate aspect ratio, cross-ply ratio, stiff- ness ratio, and boundary conditions on the critical thermal load and mode shape of buckling. 2. Governing equations Consider a thin rectangular composite plate with length a, width b, and thickness t, which has a symmetric cross-ply laminated structure (so-called laminate), as shown in Fig. 1. The plate is subjected to a non-uniformly distributed tempera- ture change T (x,y), which is an arbitrary function of in-plane † This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho * Corresponding author. Tel.: +98261-4418143-9, Fax.: +98261-4418156 E-mail address: ghomshei@kiau.ac.ir © KSME & Springer 2010