## 3 Results and Discussion
### Geometric Evaluation
#### 3.3.2 Influence of \(P_{z}\) and \(h_{s}/t_{s}\) over \(\sigma_{uN}\)
Influence of \(N_{ls}\), \(\left(N_{ls}\right)_{o}\), and \(\left(h_{s}/t_{s}\right)_{oo}\) over \(\left(\sigma_{uN}\right)_{mm}\)  
From the results of \(N_{ls}\), \(\left(h_{s}/t_{s}\right)_{o}\), and \(\left(\sigma_{uN}\right)_{m}\), the once optimized \(\left(N_{ls}\right)_{o}\), the twice maximized normalized ultimate strength \(\left(\sigma_{uN}\right)_{mm}\), and their respective twice optimized height-to-thickness ratio \(\left(h_{s}/t_{s}\right)_{oo}\) were obtained, as can be viewed in Figure 16:4  
The highest value of \(\left(\sigma_{uN}\right)_{mm}\) was 3.84, achieved by P(5;4) with \(\left(h_{s}/t_{s}\right)_{oo}=8.70\), and the lowest value of \(\left(\sigma_{uN}\right)_{mm}\) was 3.52, reached from the P(2;5) with \(\left(h_{s}/t_{s}\right)_{oo}=13.48\). These highest and lowest values represent an increase on \(\sigma_{uR}\) of 284% and 252%, respectively. The displacements and stress distribution are illustrated in Figure 16:5  
As previously discussed, the highest value was obtained from P(5;4), which exhibited a geometric configuration that enabled the best distribution of displacements (Figure 27a) and stresses (Figure 27b) between the plate and stiffeners. In contrast, for P(2;5), the lowest value of \(\left(\sigma_{uN}\right)_{mm}\) resulted from poor displacement (Figure 27c) and stress distribution (Figure 27d), caused by the very high value of \(\left(h_{s}/t_{s}\right)_{oo}\). This behavior led to the highest moment of inertia, which restricted \(U_{z}\) displacements of stiffeners and acted close to dividing the plate into smaller sections. Additionally, the low number of \(N_{ls}\) increased the spacing \(S_{ls}\) between them. As a result, displacements and stresses became concentrated in areas with less contact with the stiffeners, specifically the upper and lower corners of the plate, with no significant stresses in the stiffeners, leading to a local collapse. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Plate** & \(\mathbf{N_{ls}}\) & \(\mathbf{(N_{ls})_{o}}\) & \(\mathbf{(h_{s}/t_{s})_{oo}}\) & \(\mathbf{(\sigma_{uN})_{mm}}\) \\ \hline P(2;5) & 2 & 5 & 13.48 & 3.52 \\ P(3;5) & 3 & 5 & 11.06 & 3.68 \\ P(4;5) & 4 & 5 & 9.38 & 3.78 \\ P(5;4) & 5 & 4 & 8.70 & 3.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Results of \(\left(N_{ls}\right)_{o}\), \(\left(h_{s}/t_{s}\right)_{oo}\), and \(\left(\sigma_{uN}\right)_{mm}\) for \(N_{ls}\). The influence of \(N_{ls}\), \(\left(N_{ls}\right)_{o}\), and \(\left(h_{s}/t_{s}\right)_{oo}\), over \(\left(\sigma_{uN}\right)_{mm}\) are graphically shown in Figure 28.  
From Figure 28, the plate configurations that had \(\left(\sigma_{uN}\right)_{mm}\) presented in majority, the highest value of \(\left(N_{ls}\right)_{o}\) for each \(N_{ls}\). Only the plate P(5;4) presented less value of \(\left(N_{ls}\right)_{o}\), but as discussed previously, both P(5;5) and P(5;4) presented the same value of \(\left(\sigma_{uN}\right)_{m}\), however P(54) presented less value of \(U_{z}\), being maximized. Finally, as the increase of \(N_{ls}\), the values of \(\left(h_{s}/t_{s}\right)_{oo}\) that resulted in \(\left(\sigma_{uN}\right)_{mm}\) were the highest from each plate configuration.