## 1 Introduction  
Functionally graded materials (FGMs) are heterogeneous materials characterized by gradually changing composition and material properties. FGMs can effectively avoid stress concentration between interfaces and are suitable for applications requiring conflicting properties. Due to their exceptional mechanical strength, high temperature resistance, and other characteristics, FGMs are widely used in various fields, such as aerospace equipment, electronic equipment, automobile engines, and medical equipment [1, 2]. Mechanical analyses of functionally graded material (FGM) plates have been extensively discussed in the past decades using various theories [2, 3, 4]. The classical plate theory (CPT) [4], known as Kirchhoff theory, is only suitable for analyzing thin FGM plates where shear effects can be ignored. The first-order shear deformation theory (FSDT) [5], developed by Mindlin and Reissner, can handle the mechanical analyses of moderately thick FGM plates. However, problem-dependent shear correction factors are usually necessary to improve the accuracy. In addition, applying FSDT to thin plates leads to troublesome shear locking problems. Many higher-order shear deformation theories (HSDTs) have been proposed to analyze thick FGM plates, such as the third-order shear deformation theory (TSDT) [6, 7], the fifth-order shear deformation theory, the nth-order shear deformation theory [8, 9], the sinusoidal shear deformation theory, the exponential shear deformation theory, and the hyperbolic shear deformation theory [10, 11, 12, 13, 14]. Traction-free boundary conditions on the top and bottom surfaces are satisfied automatically in these HSDTs; thus, using shear correction factors becomes unnecessary. Generally, HSDTs also provide more accurate displacement and stress results than CPT and FSDT. Carrera et al. [15] demonstrated the importance of the thickness stretching effect in analyzing FGM plates and shells and introduced the quasi-3D Carrera's unified formula (CUF). CUF expands all displacement components as Taylor series in the thickness direction; adjustable precision can be achieved by alternating the truncation numbers. Quasi-3D HSDTs have also been proposed. Zenkour [16] developed a quasi-3D trigonometric shear deformation theory and presented benchmark solutions for the bending of exponential FGM rectangular plates. Matsunaga [17, 18] constructed a quasi-3D theory based on power series expansion for the vibration and buckling analyses of FGM plates and shallow shells, and the effects of shear deformation and rotatory inertia were investigated. Using a new quasi-3D theory, Talha and Singh [19] developed a nine-node isoparametric element for bending and free vibration analyses of FGM plates; the influences of aspect ratio, thickness ratio, volume fraction index, and boundary conditions were studied. Mantari and Soares [20] proposed a general formulation in which various quasi-3D theories can be formulated using combined polynomial, trigonometric, or hybrid functions [21, 22]. Thai and Kim [23] constructed a quasi-3D sinusoidal shear deformation theory with five unknowns, in which the transverse displacement is divided into bending, shear, and stretching parts to reduce the number of unknowns and overcome the shear locking problem. Similarly, Thai [24], Hebali [25], Bessaim [26] and Bennoun [27] employed hyperbolic functions to construct shear-locking-free quasi-3D shear deformation theories. Belabed [28] and Mantari [29, 30] presented a quasi-3D shear deformation theory by combining the polynomial and hyperbolic, or sinusoidal and hyperbolic functions. Neves and Ferreira et al. [31, 32, 33] combined polynomials and trigonometric functions to formulate various quasi-3D shear deformation theories. Farzam-Rad et al. [34] presented a new simple and efficient quasi-3D shear deformation theory with only five unknowns. As the thickness stretching effect is well accounted for, these quasi-3D HSDTs generally show improved accuracy compared to conventional HSDTs.