## 1 Introduction  
Rectangular plates at various engineering structures are subjected to thermomechanical loads, which may involve unwanted deformations and stresses. In addition, functionally graded (FG) materials are novel composite materials in which all features regularly differ in one, two, or three directions and can be fitted to decrease deformations and stresses in structures built from FGMs. Numerous studies have been performed on the behavior of FGM structures over the last years. Based on higher shear deformation theory (HSDT), [PERSON] et al. [1] studied the nonlinear bending behavior of FG plates with random properties in a thermal medium. [PERSON] and [PERSON] [2] investigated the static and free vibration behaviors of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) plates using the differential quadrature method (DQM). Based on the theory of elasticity, thermoelastic analysis of cylindrical panels reinforced with graphene platelets was presented by [PERSON] [3] utilizing the state-space Fourier series method (SS-FSM). [PERSON] et al. [4] studied the optimal design of FG sandwich nanoplates within the framework of refined plate theory with four variables using size-dependent isogeometric analysis. Based on an efficient layerwise theory, [PERSON] and [PERSON] [5] analyzed the bending and vibration of FG curved beams with temperature-dependent material properties in a thermal environment. DQM was used by [PERSON] et al. [6] to obtain the nonlinear bending response of a FG graphene-platelet-reinforced (FG-GPLR) composite plate, considering the dielectric properties within the framework of FSDT and von Karman strain relations. [PERSON] and [PERSON] [7] proposed an innovative method based on a three-dimensional (3D) deformation field to analyze the bending response of FG plates and various types of shells subjected to moisture load. It should be noted that FG materials can be classified into various types due to the function considered for defining the distribution of the material's properties. One of the main groups of FGM is composed of those for which their properties are defined based on the power law variation model [8; 9]. Additionally, double-diffusion convection in nanofluids [10; 11], the effect of magnetic loads on the thermoelastic response of nanofluid transmission systems [12; 13], and nanomaterial effects on an induced magnetic field [14; 15] are the most recent topics relating different fields of engineering to each other to investigate the effect of temperature difference on various systems and materials. Several studies are presented in the literature concerning the response of structures with embedded piezoelectric layers. In particular, [PERSON] [16] studied the bending of an FGM beam attached to sensor and actuator layers under thermomechanical load within the framework of 3D elasticity theory and using SS-FSM. [PERSON] and [PERSON] [17] studied the bending of FGM cylindrical panels bonded with the sensor and actuator using the state-space differential quadrature method (SS-DQM). [PERSON] et al. [18] investigated the buckling and instability problem of the FG piezoelectric Timoshenko beam under thermal and electric loads. Employing refined multifield two-dimensional models, [PERSON] and [PERSON] [19] studied quasi-3D thermo-electro-mechanical responses of multilayered simply supported smart shells with piezoelectric layers subjected to multifield loadings using the Navier method. [PERSON] [20] modeled the FGM plate embedded in piezoelectric layers subjected to electro-thermal load and solved the governing equations using SS-FSM. Three-dimensional thermo-piezo-elastic analysis of the FG cylindrical shell was carried out analytically by [PERSON] [21] utilizing SS-FSM. The static behavior and free vibration characteristics of cross-ply laminated composite rectangular plates surrounded by piezoelectric layers at various boundary conditions were obtained by [PERSON] et al. [22] based on 3D elasticity theory and applying DQM.