## 1 Introduction  
Functionally graded materials (FCMs) offer several advantages owing to their unique composition, wherein the volume fractions of the constituents gradually vary in specific profiles. FCMs offer effective resistance against high temperatures and substantial reduction in thermal stresses [1]. The literature concerning FGM plates under thermal loads has witnessed a rapid increase in recent times. [PERSON] and [PERSON] [2] derived series solutions for FGM plates with a continuously varying coefficient of thermal expansion along the thickness direction. These solutions were derived for FGM plates experiencing linear temperature variations in the z-direction. [PERSON] [3] extended the analysis to obtain closed-form solutions for FGM plates with temperature changes in both the \(x\)- and \(z\)-directions. The study demonstrated that by appropriately selecting material gradation from the derived closed-form solution, the deflection of the FGM plate in the thickness direction can be effectively minimized under thermal loading. In the study conducted by [PERSON] [4], a comprehensive analysis was presented for shear deformable FGM plates under thermo-mechanical loads. The analysis considered different boundary conditions and employed a first-order shear deformation plate theory and the von Karman equationsto accurately capture large deflections. [PERSON] et al. [5] investigated the thermoelastic solution of a clamped-circular thin FGM plate by utilizing the classical plates theory. Their findings highlighted the significant impact of factors on the thermoelastic behavior of the FGM circular plate during transient conditions. [PERSON] and [PERSON] [6] explored the large amplitude vibration behavior of functionally graded plates under the influence of thermal load and random pressure. [PERSON] [7] conducted a bending solution of a sandwich circular plate undercoated with a functionally graded layer under the combined thermal and mechanical loadings. The study employed the generalized differential quadrature method for the analysis. [PERSON] and [PERSON] [8] developed a hybrid optimization approach, combining a genetic algorithm with a complex method. The objective was to optimize the material constitution of a multi-layered FGM plate. [PERSON] et al. [9] examined the dynamic thermal buckling and post-buckling behavior of annular plates made of imperfect FGMs, using principles from the nonlinear plate theory. [PERSON] et al. [10] utilized a straightforward quasi-3D shear deformation theory to analyze the thermo-mechanical bending characteristics of sandwich plates composed of functionally graded materials. The researchers investigated the influence of the thermal load, geometric parameters, and gradient index on the bending response of the FGM sandwich plates. A detailed investigation was carried out by [PERSON] [11] to analyze the thermo-elastoplastic bending response of sandwich plates characterized by functionally graded (FG) face sheets and a combination of FG and homogeneous core materials. The research conducted by [PERSON] et al. [12] focused on the multi-objective design optimization of FGM plates, consisting of a primary layer made of FGM, with the possibility of including metal and/or ceramic faces. Considering the temperature dependence of material properties is crucial in the thermal analysis of FGMs, particularly in the context of thermal buckling [13; 14; 15]. Furthermore, researchers such as [PERSON] and [PERSON] [16] have examined the thermal vibration behavior of temperature-dependent FGM microbeams, while [PERSON] et al. [17] have investigated annular FGM plates. Among numerous studies on FGMs, an interesting issue is the FGM used as the coated or undercoated layers; this is attributed to the fact that incorporating FGMs as coated or undercoated layers in a sandwich or multi-layer plates results in remarkably uniform stress distributions between adjacent layers [18].