## 3 Mixed FE-GDQ Numerical Formulation
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Aspect Ratio**} & \multirow{2}{*}{**Buckling Load (10 GPa)**} & \multicolumn{3}{c}{**PNND**} & \multicolumn{3}{c}{**PNSD**} & \multicolumn{3}{c}{**PUD**} \\ \cline{3-11}  & & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) \\ \hline \multirow{4}{*}{\(a/b=1\)} & \(\lambda_{1}\) & 1.839 & 1.935 & 1.941 & 1.954 & 1.961 & 1.982 & 1.196 & 1.212 & 1.303 \\  & \(\lambda_{2}\) & 1.913 & 1.944 & 1.951 & 1.957 & 1.961 & 1.986 & 1.196 & 1.121 & 1.303 \\  & \(\lambda_{3}\) & 2.216 & 2.255 & 2.264 & 2.236 & 2.265 & 2.274 & 1.478 & 1.480 & 1.486 \\  & \(\lambda_{4}\) & 2.240 & 2.261 & 2.273 & 2.250 & 2.266 & 2.275 & 1.478 & 1.483 & 1.486 \\  & \(\lambda_{1}\) & 1.689 & 1.863 & 1.963 & 1.942 & 2.005 & 2.012 & 1.190 & 1.281 & 1.326 \\  & \(\lambda_{2}\) & 1.738 & 1.865 & 1.964 & 1.953 & 2.029 & 2.043 & 1.203 & 1.283 & 1.326 \\  & \(\lambda_{3}\) & 1.913 & 1.968 & 2.018 & 2.050 & 2.068 & 2.094 & 1.284 & 1.334 & 1.341 \\  & \(\lambda_{4}\) & 2.038 & 2.044 & 2.048 & 2.130 & 2.139 & 2.147 & 1.343 & 1.356 & 1.386 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: First four shear buckling loads for a SSSS FG-saturated porous plate with different aspect ratios, \(a/b\), porosity distributions and Skempton coefficients, \(\beta\), while keeping \(e_{0}=0.6\) fixed. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Aspect Ratio**} & \multirow{2}{*}{**Buckling Load (10 GPa)**} & \multicolumn{3}{c}{**PNND**} & \multicolumn{3}{c}{**PNSD**} & \multicolumn{3}{c}{**PUD**} \\ \cline{3-11}  & & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) & \(e_{0}=0.3\) & \(e_{0}=0.6\) & \(e_{0}=0.9\) \\ \hline \multirow{4}{*}{\(a/b=1\)} & \(\lambda_{1}\) & 0.392 & 0.303 & 0.166 & 0.406 & 0.362 & 0.309 & 0.346 & 0.216 & 0.069 \\  & \(\lambda_{2}\) & 0.929 & 0.723 & 0.408 & 0.949 & 0.830 & 0.658  
Results denote that in drained conditions (i.e., \(\beta=0\)), the plate always features the smallest buckling load, under a fixed aspect ratio, porosity coefficient and distribution. An increasing value of the Skempton coefficient, instead, enables an increased buckling load, because of a decreased compressibility of the fluid within pores. In other words, if the compressibility of the pore fluid becomes high (\(\beta\to 0\)), the mechanical response of the plate resembles that of a porous plate in drained conditions (i.e., in the absence of fluid). In this condition, the structural stiffness reaches its minimum value along with the lowest buckling load. Differently, when the compressibility of a pore fluid becomes small (\(\beta\to 1\)), the plate behaves as a rigid solid, thus reaching its highest load magnitude. Furthermore, the effect of the Skempton coefficient on the buckling load, for a uniform distribution, seems to be more pronounced than other porosity distributions. By comparing Tables 2-6 with Tables 7-11, it is worth observing the higher sensitivity of the buckling response to the porosity coefficient than the Skempton coefficient. The first four buckling mode shapes are finally plotted in Figures 4-8, for a rectangular plate with \(a=2\,\text{m}\), \(b=1\,\text{m}\), under different loading and boundary conditions, and a fixed value of \(e_{0}=\beta=0.6\). More specifically, in Figures 4-6, the rectangular plate is subjected to a shear loading condition, with a clear compatibility among the displacement field and the selected BCs (i.e., CFCF, FCFC and