## 1 Introduction  
The concept of functionally graded materials has been proposed by Japanese materials scientists since 1984 [1], among which traditional metal-ceramic functionally graded materials have been widely used in aerospace engineering. Owing to their excellent thermal insulation and high strength, functionally graded materials can be used to make high-performance parts in spacecraft [2, 3]. This paper deals with a new class of functionally gradient materials, which enhance the mechanical properties by adding reinforcement to the matrix materials. Graphene nanoplatelets (GPLs) have attracted a significant amount of attention from researchers since their discovery by [PERSON] et al. in 2004 [4]. Owing to the high Young's modulus and high strength of GPLs, we can obtain composites with excellent mechanical properties by incorporating GPLs into the matrix materials. Since GPLs have a larger specific surface area than carbon nanotubes (about three times greater than carbon nanotubes), the mechanical properties of GPLs-reinforced composites are considerably improved over the previously studied carbon nanotubes reinforced composites [5]. The excellent performance of GPLs-reinforced composites gives them a very broad range of application scenarios in aerospace, civil engineering, biomedical, etc. Therefore, it is important to study the mechanical behaviors of functionally graded graphene reinforced composites (FG-GRC). Some researchers have chosen classical plate theory [6] (Kirchhoff theory) for the analysis of FG-GRC. [PERSON] et al. [7] investigated the critical buckling load of spinning FG-GRC cylindrical shells by using classical plate theory. [PERSON] et al. [8] studied the FG-GRCporous plates using classical plate theory and solved the nonlinear free vibration of the plates using the differential quadrature method. [PERSON] et al. [9] investigated the nonlinear vibration of FG-GRC sandwich porous plates based on classical plate theory. Classical plate theory neglects the effects of shear and normal deformation and is only applicable to thin FG-GRC sheet/shell, so more researchers have adopted first-order shear deformation plate theory (FSDPT) [10] and third-order shear deformation plate theory (TSDPT) [11]. [PERSON] et al. [12] analyzed the free and forced vibrations of FG-GRC plates employing FSDPT. [PERSON] et al. [13] calculated the bending and free vibration of FG-GRC plates based on FSDPT using the finite element method, and also calculated the mechanical behaviors of carbon nanotube reinforced plates for comparison purposes. [PERSON] et al. [14] performed a free vibration analysis of FG-GRC curved nanobeams on Pasternak foundation based on the displacement field described by FSDPT. [PERSON] et al. calculated nonlinear bending [15] and free vibration [16] of an FG-GRC quadrilateral plate based on FSDPT, using the element-free IMLS-Ritz method. [PERSON] et al. [17] used FSDPT and finite element method to analyze the free vibration characteristics of FG-GRC plates under various boundary conditions. Due to the assumption of a constant transverse shear strain in the transverse section, the FSDPT must be shear-corrected, and this correction factor is not only related to the materials and geometric parameters, but also to the loads as well as to the boundary conditions. Since the shear correction factor is difficult to determine, TSDPT becomes the favored choice of many researchers. The advantage of TSDPT is that it does not need to consider the shear correction factor, and the calculation result of TSDPT is also closer to the 3D solution than FSDPT. [PERSON] et al. [18] established geometric nonlinear equations of motion with von Karman strain form based on higher-order shear deformation plate theory to study the significant amplitude vibration in FG-GRC plates under an elastic foundation and thermal environment. [PERSON] [19] used Reddy-based TSDPT to obtain the total strain energy and performed thermal post-buckling analysis on FG-GRC plates. [PERSON] et al.