ABSTRACT
Buckling of circular cylindrical shells has posed baffling problems to engineering for many years. This is due to the fact that large discrepancies between theoretical prediction and experimental results had been the focus of long debate in the case of compressive buckling of cylindrical shells. As von Kármán and Tsien (1941) argued at the time, geometrical nonlinearity must play an important part in the phenomenon of thin shell buckling. Donnell and Wan (1950) reported that the initial geometric imperfection has a significant effect on the buckling and postbuckling behavior of cylindrical shells subjected to axial compression. In their analysis, however, the membrane prebuckling state was assumed, like von Kármán and Tsien (1941) did and, therefore, the boundary conditions cannot be incorporated accurately. The importance of the nonlinear prebuckling deformations and its role in the buckling analysis of cylindrical shells has been discussed by Stein (1962, 1964). On the other hand, Koiter (1945) provided a general theory of the initial postbuckling behavior of elastic bodies under static conservative load. Following the pioneer works of Kármán and Tsien (1941), Donnell and Wan (1950), Stein (1962, 1964), and Koiter (1945, 1963), numerous researches have been made on this topic. The problem may be considered to be solved completely in the domain of homogeneous, isotropic elastic materials. In the design of an FGM shell as well as a homogeneous, isotropic shell,
it is of technical importance to examine its resistance to buckling under expected loading conditions. For that purpose, the determination of the buckling load alone is not sufficient in general, but it is further required to clarify the postbuckling behavior, that is, the behavior of the shell after passing through the buckling load. One of the reasons is to estimate the effect of practically unavoidable imperfections on the buckling load and the second is to evaluate the ultimate strength to exploit the load-carrying capacity of the shell structure. Shen (2002, 2003) provided, respectively, the postbuckling solutions of
FGM cylindrical shells under axial compression and external pressure in thermal environments. In his studies, a boundary layer theory for the shell
Materials: of and Shells
and Chen (1988, 1990) adopted. However, because the shells were considered as being relatively thin and therefore the transverse shear deformation was not accounted for. These works were then extended to the case of FGM hybrid cylindrical shells under axial compression, external pressure, or their combination in thermal environments by Shen (2005), and Shen and Noda (2005, 2007) based on a higher order shear deformation shell theory. Furthermore, Shahsiah and Eslami (2003a,b) performed the thermal buckling of FGM cylindrical shells under three types of thermal loading as uniform temperature rise, linear and nonlinear temperature variation through the thickness, based on the first-order shear deformation shell theory. Similar work was then done by Wu et al. (2005) based on classical shell theory of Donnell-type. Subsequently, the effect of initial geometric imperfections and applied actuator voltage on thermal buckling of FGM cylindrical shells was discussed by Mirzavand et al. (2005) and Mirzavand and Eslami (2006, 2007). As we all know, the imperfect cylindrical shell only has limit point load, which could be obtained by solving nonlinear governing equations as initial postbuckling or full postbuckling analysis. Based on a higher order shear deformation shell theory, Woo et al. (2005) presented Fourier series solutions for the thermomechanical postbuckling of FGM plates and shallow shells, from which the results for an initially heated cylindrical shell were obtained as a limiting case. Sofiyev (2007) studied linear free vibration and buckling of FGM laminated cylindrical shells by using Galerkin method. Sheng and Wang (2008) performed the linear vibration, buckling and dynamic stability of FGM cylindrical shells embedded in an elastic medium and subjected to mechanical and thermal loads based on the first-order shear deformation shell theory. In the above studies, however, the materials properties were virtually assumed to be temperature-independent (T-ID). Moreover, Shen (2004, 2007) provided a thermal postbuckling analysis for
FGM cylindrical shells under uniform temperature field or heat conduction based on classical shell theory and higher order shear deformation shell theory, respectively. In his study, the material properties were considered to be temperature-dependent (T-D) and the effect of imperfections on the thermal postbuckling response was reported. Recently, Kadoli and Ganesan (2006) presented linear thermal buckling and free vibration analysis for FGM cylindrical shells with clamped boundary conditions. In their analysis, the material properties were assumed to be temperature-dependent, and finite element equations based on the first-order shear deformation shell theory were formulated. On the other hand, due to the temperature gradient the shell is subjected to additional moments along with the membrane forces and the problem cannot be posed as an eigenvalue problem, i.e., no buckling temperature is evident, when the edges of the shell are simply supported. Therefore, the existing solutions for simply supported FGM shells subjected to transverse temperature variation, i.e., linear and=or nonlinear gradient through the thickness, may be physically incorrect.
