ABSTRACT
The nonlinear bending response of FGM plates subjected to transverse mechanical loads and thermal loadingwas the subject of recent investigations. Previous works for the linear bending of FGM rectangular, circular, and annular plates can be found in Reddy et al. (1999), Cheng and Batra (2000), Reddy and Cheng (2001), Vel and Batra (2002), Croce and Venini (2004), Kashtalyan (2004), and Chung and Chen (2007). Mizuguchi and Ohnabe (1996) employed the Poincare method to examine the large deflection of heated FGM thin plates with Young’s modulus varying symmetrically to the middle plane in thickness direction. Suresh and Mortensen (1997) presented the large deformation problem of graded multilayered composites under thermomechanical loads. When the thermomechanical load reaches a high level, nonlinear strain-displacement relations have to be employed. As a result, a set of nonlinear equations will appear no matter what kind of analysis method is used. Based on the FSDPT, Praveen and Reddy (1998) analyzed nonlinear static and dynamic response of functionally graded ceramic-metal plates subjected to transverse mechanical loads and a onedimensional (1D) steady heat conduction by using finite element method (FEM). This work was then extended to the case of FGM square plates and shallow shell panels by Woo and Meguid (2001) using Fourier series technique, and to the case of FGM circular plates by Ma and Wang (2003) and Gunes and Reddy (2008), and to the case of FGM rectangular plates by GhannadPour and Alinia (2006) and Ovesy and GhannadPour (2007) using Ritz method and finite strip method, respectively. However, in their studies the formulations were based on the classical plate=shell theory, i.e., the theory based on the Kirchhoff-Love hypothesis and therefore the transverse shear deformations were not accounted for, and the material properties were assumed to be independent of temperature. Reddy (2000) developed theoretical formulations for thick FGM plates according to the HSDPT. In his study, both Navier solutions for linear bending of simply supported rectangular FGM plates and finite element models for nonlinear static and dynamic response were presented. The paper of Cheng (2001) also contains the
Materials: of and Shells
of transversely symmetric shear deformable FGM plates. Moreover, Shen (2002) provided a nonlinear bending analysis of simply supported shear deformable FGM rectangular plates subjected to a transverse uniform or sinusoidal load and in thermal environments. In his study, the material properties were considered to be temperature dependent and the effect of temperature rise on the nonlinear bending response was reported. Subsequently, Yang and Shen (2003a,b) developed a semianalytical-numerical method to examine the large deflection of thin and shear deformable FGM rectangular plates subjected to combined mechanical and thermal loads and under various boundary conditions. This method was then extended to the case of FGM hybrid plates with surface-bonded piezoelectric layers by Yang et al. (2004). In these studies, the material properties were assumed to be temperature independent and temperature dependent, respectively. Recently, Na and Kim (2006) studied nonlinear bending of clamped FGM rectangular plates subjected to a transverse uniform pressure and thermal loads by using a 3D FEM. In their study, the thermal loads were assumed as uniform, linear, and sinusoidal temperature rises across the thickness direction, whereas the material properties were assumed to be temperature independent. On the other hand, ceramics and the metals used in FGMs do store different amounts of heat, and therefore the heat conduction usually occurs (Tanigawa et al. 1996, Kim and Noda 2002). This leads to a nonuniform distribution of temperature through the plate thickness, but it is not accounted for in the above studies. This is because when the material properties are assumed to be functions of temperature and position, and the temperature is also assumed to be a function of position, the problem becomes very complicated. More recently, Shen (2007) provided a nonlinear thermal bending analysis of simply supported shear deformable FGM rectangular plates due to heat conduction. In his study, both heat conduction and temperature-dependent material properties were taken into account.
