## 1 Introduction  
The concept of functionally graded materials (FGMs) was first suggested by a group of Japanese scientists as thermal barrier materials for aerospace structural applications and fusion reactors. The properties of functionally graded materials vary gradually with the thickness direction within the structure, which eliminates interface problems, and thus, the stress distributions are smooth. Thin plate structures made of functionally graded materials have been found many applications in aerospace, automotive, and biomedical fields. Therefore, there are many studies on FGM plates during the past decades, for example, Refs. [1; 2; 3; 4; 5; 6; 7; 8; 9; 10], to list but only a few. Studies on FGM plates involve many interesting topics, including static and dynamic analyses, stability analysis, buckling analysis, and so on. The methods used include some innovative analytical, numerical, and experimental techniques, in which analytical methods are established based on two-dimensional plate theory or three-dimensional elasticity theory, and numerical methods are based mainly on finite element method and meshless method. [PERSON] et al. [11] presented a comprehensive review of the various methods employed to study the static, dynamic, and stability behavior of FGM plates. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) also presented a comprehensive review of various theories for the modeling and analysis of functionally graded plates and shells. This review mainly focuses on the equivalent single layer theories, including the classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, simplified theories, and mixed theories, since they were widely used in the modeling of functionally graded plates and shells. Besides, [PERSON] (2010); [PERSON] (2010); [PERSON] (2010) presented an interesting 3D exact model for FGM plates and shells, and also made the static analysis [PERSON] (2010); [PERSON] (2010) and the free vibration analysis [PERSON] (2010). More recently, [PERSON] and [PERSON] [PERSON] and [PERSON] (2010) analyzed the post-buckling behavior and nonlinear vibration of a fluid-conveying pipe composed of functionally graded materials. Given that there are many references in this field, we do not review them in detail. With the deepening of the study, the analysis of functionally graded thin plates tends more and more refined, especially on geometrically nonlinear problems from large deformations of structures, as well as on the excavation of potential advantages of functionally graded materials used. One requirement may come from large deformation analysis of flexible thin-plate-like structures, since only after the large deformation problem is made clear, one can say, under what conditions small deformation theory is reasonable. The large deformation analysis needs to resort to the classical Foppl-von Karman equations, which is a set of high-order partial differential equations and the mathematical solving is relatively difficult, particularly in the use of analytical methods. Based on a layerwise theory, [PERSON] and [PERSON] [PERSON] and [PERSON] (2010) analyzed, analytically, displacement and stress in functionally graded composites plates in cylindrical bending under thermomechanical loadings, in which the geometrical nonlinearity was considered by strain-displacement relation in the von Karman sense, and a perturbation technique was used. Recently, [PERSON] et al. [PERSON] et al. (2012) studied the large deformation problem of arbitrarily straight-sided quadrilateral FGM plates. The analysis is carried out using the IMLS-Ritz method. Based on the IMLS-Ritz approximation, the discrete nonlinear governing equation for the large deformation is derived. Due to the complexity of analysis, however, the nonlinear solution to the quadrilateral FGM plates is obtained numerically, i.e., through the hybrid arc length iterative procedure with the modified Newton-Raphson method.