## 1 Introduction
[20] investigated the geometrically nonlinear harmonically excited vibration of FG-GRC rectangular plates under different edge conditions using TSDPT. [PERSON] et al. [21] studied the bending, buckling and free vibration of FG-GRC plates using isogeometric analysis based on FSDPT and TSDPT. In addition to FSDPT and TSDPT, there are some articles that use other plate theories. [PERSON] et al. [22] investigated the bending, buckling and free vibration behaviors of FG-GRC plates based on refined shear deformation plate theory. [PERSON] and [PERSON] [23] performed a large-deflection geometric nonlinear analysis of FG-GRC plates based on sinusoidal shear deformation plate theory. Based on sinusoidal shear deformation plate theory, [PERSON] et al. [24] reported the effect of small-scale effects on the natural frequencies of FG-GRC nanoplates on elastic foundations. All the plate theories mentioned in the above review do not take into account the effect of thickness stretching, which can lead to large errors when we calculate moderately thick and thick plates. To compensate for the disadvantages of those theories, many researchers have proposed plate theories that take into account the effect of thickness stretching. For example, [PERSON] [25] proposed a quasi-3D higher-order shear deformation plate theory based on sinusoidal functions of in-plane and transverse displacements, while the quasi-3D theory [26] is based on the parabolic function of transverse displacement and the cubic function of in-plane displacement. Both of the above two plate theories contain six unknown quantities in the displacement field. There are also three high-order shear deformation plate theories with nine unknowns proposed by [PERSON] [27; 28; 29]. [PERSON] et al. [30] simplified the TSDPT by dividing the transverse displacement into bending and shear components so that the number of unknowns was reduced by one compared to the TSDPT. They applied this assumption to the analysis of the isotropic plates and proposed a refined plate theory (RPT). This hypothesis of dividing the displacement into a bending part and a shear part was first proposed by [PERSON] [31]. [PERSON] [32] published a detailed analysis of homogeneous plates based on RPT in 2002 and proposedtwo extended theories based on RPT. [PERSON] [33] first extended RPT to the analysis of functionally graded materials. Since then, a large number of documents [34; 35; 36; 37; 38; 39; 40] have analyzed and studied the mechanical behaviors of functionally graded materials based on RPT, which showed the good applicability of RPT in the mechanical analysis of functionally graded materials. The calculation result of RPT is very close to TSDPT [30], and because it reduces one degree of freedom, the calculation process is greatly simplified. However, RPT does not consider the effect of thickness stretching, so its shortcomings are the same as TSDPT. In order to make up for the shortcomings of RPT, [PERSON] [41] proposes an improved refined plate theory (IRPT) that takes into account the effect of thickness stretching. IRPT corrects the disadvantage of RPT in the calculation of moderately thick and thick plates by adding a thickness stretching effect term in the displacement field. The calculation results [41] in functionally graded materials show that the IRPT that takes into account the effect of thickness stretching is more accurate than the RPT that does not consider the effect of thickness stretching. Compared with the previously mentioned plate theories that consider the effect of thickness stretching, IRPT contains the least number of unknowns [41]. The importance of the effect of thickness stretching for the analysis of the mechanical behaviors of metal-ceramic functionally graded plates was emphasized by [PERSON] et al. [42].