## 3 Results and Discussion
### Verification and Validation of Computational Modeling of Buckling
#### 3.1.2 Verification of Elastoplastic Buckling Model Under Combined Loading on Stiffened Plates  
The first verification was developed considering [PERSON] and [PERSON] [24] study, and its results from ANSYS (version 10.0), ALPS/ULSAP (version 2006.3), and DNV PULS (version 2.05) software's, through the application of longitudinal compressive loading \(\sigma_{X}\) and transverse compressive \(\sigma_{Y}\) loading in different ratios, and a constant lateral pressure \(P_{z}=0.16\) MPa to a simply supported stiffened plate with \(E=208.5\) GPa, \(\sigma_{y}~{}=\)315 MPa, \(\
u~{}=0.3\), \(a=16300\) mm, \(b=4300\) mm, and \(t_{p}=19\) mm. The stiffeners present a T-shape, with \(t_{s}=10\) mm, \(h_{s}=100\) mm, and flange with thickness \(t_{f}=17\) mm and height \(h_{f}=172\) mm. The initial imperfections were considered as \(w_{0}=4.07\) mm from plate, \(w_{w}=0.5\) mm for stiffeners web, and \(w_{f}=4.2\) mm for fabrication-related initial distortions. The proposed model considered \(w_{0}=b/2000=2.15\) mm (Equation (8)) from the first buckling mode. The geometry of the stiffened plate with boundary conditions of the proposed model is shown in Figure 10.  
The finite element size used in the proposed model was defined according to the mesh convergence test considering the loading condition \(\sigma_{X}\sigma_{Y}=0.79\):0.21, presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element Length** & **Number of** & \(\sigma_{u}\) \\
**(mm)** & **Elements** & **(MPa)** \\ \hline
100 & 174 & 28.75 \\
75 & 345 & 28.40 \\
50 & 704 & 28.40 \\
30 & 1974 & 28.40 \\
25 & 2747 & 28.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesh convergence test for verification of elastoplastic buckling model under combined loading on unstiffened plate with rectangular perforation. Figure 9: Unstiffened plate geometry with rectangular hole and boundary conditions of the proposed model, with the blue symbols representing the displacement constraints according to the axis direction, the red arrows representing the biaxial compressive loading, and the red lines on the plate representing the applied lateral pressure. For \(\sigma_{uX}\sigma_{uY}=0.79\):0.21, the present study achieved \(\sigma_{uX}\) = 236.25 MPa and \(\sigma_{uY}=62.80\) MPa, showing differences of 5.63% and 4.93% compared to the ANSYS results, 18.52% and 17.27% compared to the ALPS/ULSAP results, and \(-3.85\%\) and \(-5.06\%\) compared to the DNV PULS results from [PERSON] and [PERSON] [24]. For the loading condition \(\sigma_{uX}\sigma_{uY}=0.40\):0.60, the present study resulted in \(\sigma_{uX}\) = 76.65 MPa and \(\sigma_{uY}=114.97\) MPa, showing, respectively, differences of 14.78% and 14.77% compared to the ANSYS results, 23.59% and 23.60% compared to the ALPS/ULSAP results, and 4.93% and 4.94% compared to the DNV PULS results from [PERSON] and [PERSON] [24]. These differences in results can be attributed to the distinct boundary conditions and the different considerations for initial imperfections between the models. However, the present study demonstrated comparable values with those of [PERSON] and [PERSON] [24]. The second verification of elastoplastic buckling model under combined loading on stiffened plates was carried out based on the study of [PERSON] et al. [25], which presents the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\sigma_{uX}\):\(\sigma_{uY}\) Ratio} & \multirow{2}{*}{**Present Study**} & \multicolumn{6}{c}{**[PERSON] and [PERSON] [24]**} \\ \cline{3-8}  & & & \multicolumn{2}{c}{**ANSYS**} & \multicolumn{2}{c}{**ALPS/ULSAP**} & \multicolumn{2}{c}{**DNV PULS**} \\ \cline{2-8}  & \(\sigma_{uX}\) & \(\sigma_{uY}\) & \(\sigma_{uX}\) & \(\sigma_{uY}\) & \(\sigma_{uX}\) & \(\sigma_{uY}\) & \(\sigma_{uX}\) & \(\sigma_{uY}\) \\ \hline
0.79:0.21 & 236.25 & 62.80 & 223.65 & 59.85 & 199.33 & 53.55 & 245.70 & 66.15 \\
0.40:0.60 & 76.65 & 114.97 & 66.78 & 100.17 & 62.02 & 93.02 & 73.05 & 109.56 \\ \hline \hline \end{tabular}
\end{table}