## 4 Numerical Results and Discussion
Moreover, the consequence of increasing the number of fictitious layers constituting the FGM part of the sandwich plate on the convergence of stresses and displacement along the thickness direction is presented in Figure 2(a)-c. Scrutinizing the diagrams shown in this figure reveals that increasing the number of fictitious layers for N \(>\) 10 has infinitesimal effect on their trend. In other words, considering N = 10 as the total number of fictitious layers guarantees the acceptable degree of stability for the applied solution. Accordingly, further computations in this research would be carried out by considering N = 10 as the minimum number of fictitious layers of FGM required for obtaining a stable rate of convergence. To carry out the validation of the present formulation, numerical results for dimensionless displacements and stresses of thick and thin FG rectangular plates subjected to a temperature gradient were computed and presented in Table 2 to compare with the published results. Comparison of the present results with the results reported by Refs. [38; 41; 42] shows that the corresponding discrepancy between the present results with those of the mentioned references is less than 1%. Accordingly, Table 2 reveals a perfect agreement between the results of the current study and the results reported in the high-quality studies published previously. To this end, it can be said that the method and solution employed in this study are of high accuracy. Finally, it is essential to notice that the discrepancy between the current results with Ref. [41] is due to the extended unified formulation used in the mentioned reference. After the convergence study and the validation analysis of the utilized methods are performed, it is time to present a parametric study regarding the effects of length-to-thickness ratio, \(a/h\); FGM layer thickness to piezoelectric layers thickness, \(h/h_{p}\); outer surface temperature, \(T_{o}\); and relaxation time constant, \(\tau\), on the thermo-visco-elastic behavior of an FGM plate surrounded by piezoelectric layers. Figure 3: _Cont._  
Figure 3: Effect of fictitious layer number of FGM layer on through-thickness distribution of dimensionless normal and shear stresses and deformation for the FG core. Figure 4a-d depicts through-thickness distribution of the axial normal stress \(\overline{\sigma}_{x}\), transverse shear stress \(\overline{\tau}_{zx}\), and deflection \(\overline{w}\) for different length-to-thickness-ratios \(a/h\). According to the figures and as expected, increasing \(a/h\) causes a decrease in the stiffness of the plate, and accordingly, the stresses decrease. Moreover, it is seen that the rate of variation decreases by increasing the value of the length-to-thickness ratio. In other words, according to Figure 4a, it can be seen that increasing the value of \(a/h\) from 10 to 20 causes the maximum value of the axial normal stress, \(\overline{\sigma}_{x}\), to change from 1692 to 544. Meanwhile, increasing the value of \(a/h\) from 20 to 40 causes the maximum value of the axial normal stress, \(\overline{\sigma}_{x}\), to be changed from 544 to 427. Additionally, according to Figure 4b, it can be stated that increasing the value of \(a/h\) from 10 to 20 causes the maximum value of the transverse shear stress, \(\overline{\tau}_{zx}\), to change from 48.129 to 8.352. Meanwhile, increasing the value of \(a/h\) from 20 to 40 causes the maximum value of the transverse shear stress, \(\overline{\tau}_{zx}\), to change from 8.352 to 2.967. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\frac{a}{b}\)=4} & \multicolumn{4}{c}{\(\frac{a}{b}\)=50} \\ \hline  & [41] & [42] & [38] & **Present** & [41] & [42] & [38] & **Present** \\ \hline \(\overline{w}(h)\) & 3.043 & 3.043 & 3.0431 & 3.043 & 28.54 &  
Figure 4: _Cont._  
Figure 5: _Cont_.