## 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{4}{c}{**PNND**} & \multicolumn{4}{c}{**PNND**} & \multicolumn{4}{c}{**PUD**} \\ \cline{3-11}  & & \(\mathbf{c_{0}=0.3}\) & \(\mathbf{c_{0}=0.6}\) & \(\mathbf{c_{0}=0.9}\) & \(\mathbf{c_{0}=0.3}\) & \(\mathbf{c_{0}=0.6}\) & \(\mathbf{c_{0}=0.9}\) & \(\mathbf{c_{0}=0.3}\) & \(\mathbf{c_{0}=0.6}\) & \(\mathbf{c_{0}=0.9}\) \\ \hline \multirow{6}{*}{\(a\)/\(b\) = 1} & \(\lambda_{1}\) & 1.143 & 0.897 & 0.536 & 1.199 & 0.978 & 0.692 & 1.020 & 0.636 & 0.177 \\  & \(\lambda_{2}\) & 1.150 & 0.900 & 0.543 & 1.208 & 0.983 & 0.693 & 1.020 & 0.645 & 0.182 \\  & \(\lambda_{3}\) & 1.653 & 1.267 & 0.77  
The same parametric investigation was then repeated for a biaxial loading (Table 5) and a uniaxial loading acting in the \(x\)-direction of a SSSS structure (Table 6). Based on a comparative evaluation of results in Tables 5 and 6 with Table 2, a uniaxial or biaxial loading condition clearly reduces the buckling load of the structure under the same values of \(e_{0}\), \(a/b\) and porosity distribution. As expected, this reduction is much more pronounced for rectangular plates subjected to a biaxial loading condition, due to the overall decay of the structural stiffness. A further investigation considered the effect of the porosity distribution and Skempton coefficient on the first four buckling loads of FG-saturated plates, as listed in Tables 7-9 (for a shear loading condition), in Table 10 (for an axial loading condition) and in Table 11 (for a biaxial loading condition), while keeping the porosity coefficient fixed at \(e_{0}=0.6\). The same BCs from Table 1 are accounted here for the analyses. Based on a comparative estimation of results from these tables, it is confirmed that the maximum and minimum buckling loads are always associated with a symmetric (PNSD) and uniform (PUD) porosity distribution, respectively. \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}{*}{\(a/b=1\)} & \(\lambda_{1}\) & 0.781 & 0.603 & 0.330 & 0.808 & 0.721 & 0.614 & 0.690 & 0.430 & 0.122 \\  & \(\lambda_{2}\) & 0.981 & 0.774 & 0.446 & 0.983 & 0.875 & 0.703 & 0.879 & 0.568 & 0.168 \\  & \(\lambda_{3}\) & 1.554 & 1.225 & 0.724 & 1.526 & 1.320 & 0.981 & 1.394 & 0.895 & 0.261 \\  & \(\lambda_{4}\) & 2.147 & 1.688 & 1.017 & 2.081 & 1.856 & 1.218 & 1.925 & 1.225 & 0.350 \\  & \(\lambda_{1}\) & 1.053 & 0.816 & 0.462 & 1.073 & 0.943 & 0.771 & 0.930 & 0.574 & 0.159 \\  & \(\lambda_{2}\) & 1.101 & 0.860 & 0.495 & 1.117 & 0.982 & 0.795 & 0.977 & 0.613 & 0.173 \\  & \(\lambda_{3}\) & 2.097 & 1.553 & 0.880 & 2.082 & 1.725 & 1.314 & 1.801 & 1.020 & 0.260 \\  & \(\lambda_{4}\) & 2.331 & 1.771 & 1.042 & 2.293 & 1.907 & 1.405 & 2.035 & 1.204 & 0.319 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: First four uniaxial buckling loads (in the \(x\)-direction) for a SSSS FG-saturated porous plate with different aspect ratios, \(a/b\), porosity distributions and porosity coefficients, \(e_{0}\), keeping \(\beta=0.6\) fixed.