## 5 Numerical Results
The base matrix material is epoxy with the elastic properties [58] given by \(E_{m}=3.0\) GPa, \(v_{m}=0.34\), and \(\alpha_{m}=60\times 10^{-6}/\)K, while the sizes and the elastic properties of GPLs are as fol  
Figure 6: Comparison of thermal postbuckling paths of a PIMM simply-supported isotropic plate under uniform temperature rise [19,54]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{5}{c}{**Ceramic Volume Fraction Index (\(n\))**} \\ \cline{2-6}  & **0** & **0.5** & **1** & **2** & **5** \\ \hline Present & 9.092 & 6.360 & 5.325 & 5.034 & 4.711 \\ [PERSON] et al. [56] & 8.894 & 6.114 & 5.412 & 5.012 & 4.771 \\ [PERSON] et al. [57] & 8.735 & 6.035 & 5.415 & 5.047 & 4.742 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of CBTRs for simply-supported square Al/ZrO\({}_{2}\) functionally graded plate with an inclined central crack (\(a/b=1\), \(c/a=0.6\), \(\alpha=90^{\circ}\)). lows [59]: \(E_{GPL}=1.01\) TPa, \(\
u_{GPL}=0.186\), \(l_{GPL}=2.5\) um, \(w_{GPL}=t_{GPL}=1.5\) um, and \(\alpha_{GPL}=5.0\times 10^{-6}\)/K. This method appears to provide CBTR that is reasonably consistent with the method of [PERSON] et al. [19] with the maximum relative difference of 10.619% at \(a/h=45\) for PIMM simply-supported condition. Meanwhile, the CNTRs of PIMM S are higher than those of PIMM S because thermally induced deformation in PIMM S can occur in the in-plane direction of the plate more easily than in PIMM S [19]. Meanwhile, CBTR decreases uniformly as the relative thickness ratio \(a/h\) increases, regardless of the GPL distribution pattern, as represented in Figure 7a. This is because the buckling stiffness of the plate becomes lower as the plane thickness becomes smaller. Among the GPL distribution patterns, FG-X has the highest CBTR because the GPL with a high modulus of elasticity is biased toward the top and bottom of the plate, increasing the buckling rigidity of the plate. This fact can be clearly justified by the fact that FG-O shows the lowest level in CNTRs. The results show that the CBTR value of the GPLRC plate is remarkably affected by the thickness-wise GPL distribution. The effect of GPL mass fraction \(g^{*}_{GPL}\) on CBTR is shown relatively well in Figure 7b, where the variation of CBTR with respect to \(g^{*}_{GPL}\) is strongly affected by the GPL distribution pattern. This conflicting trend depends on whether the bias of the GPLs with a higher elastic modulus toward the top/bottom sides is superior to the bias of epoxy with a higher thermal expansion coefficient toward the top/bottom as the GPL mass fraction \(g^{*}_{GPL}\) increases. The former corresponds to FG-X, but FG-O and FG-\(\Lambda\) belong to the latter, while both biases are equal at FG-U. It is worth noting that this variation with respect to \(g^{*}_{GPL}\) becomes less pronounced as the value of \(g^{*}_{GPL}\) becomes sufficiently large. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Pattern**} & \multicolumn{4}{c}{**Partially Immovable**} & \multicolumn{4}{c}{**Fully Immovable**} \\ \cline{3-8}  & & _a/h = 25_ & _a/h = 35_ & _a/h = 45_ & _a/h = 25_ & _a/h = 35_ & _a/h = 45_ \\ \hline \multirow{3}{*}{Present} & FG-X & 80.661 & 41.699 & 27.339 & 39.462 & 20.401 & 13.385 \\  & FG-U & 65.308 & 33.927 & 22.365 & 33.055 & 17.171 & 11.316 \\  & FG-O & 49.603 & 24.289 & 16.998 & 24.986 & 12.238 & 8.555 \\ \hline \multirow{3}{*}{[PERSON] et al. [19]} & FG-X & 80.523 & 41.320 & 25.056 & 40.261 & 20.660 & 12.528 \\  & FG-U & 65.077 & 33.357 & 20.218 & 32.539 & 16.679 & 10.109 \\ \cline{1-1}  & FG-O & 49.635 & 25.414 & 15.396 & 24.817 & 12.707 & 7.698 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CBTR \(\Delta T_{cr}(K)\) of intact FG-GPLRC plates (\(a/b=1\), \(g^{*}_{GPL}=0.3\%\), immovable SSSS). Figure 7: CBTR \(\Delta T_{cr}(K)\) of the intact FG-GPLRC plate (SSSS): **(a)** The relative thickness ratio \(a/h\) (\(g^{*}_{GPL}=0.3\%\)); **(b)** The total GPL mass\(g^{*}_{GPL}\) (\(a/h=25\), PIMM).