## 3 Results and Discussion
### Geometric Evaluation
#### 3.3.2 Influence of \(P_{z}\) and \(h_{s}/t_{s}\) over \(\sigma_{uN}\)
3.3 Highest Values of \(h_{s}\)/\(t_{s}\), \(N_{ls}\), and \(N_{ls}\) over \(\sigma_{uN}\)  
The highest value of \(\sigma_{uN}\) was 3.84, reached from the P(5;4) with \(h_{s}\)/\(t_{s}\) = 8.74 and from the P(5;5) with \(h_{s}\)/\(t_{s}\) = 8.14, and the P(5;4) selected as better due its lower displacements. The lowest value of \(\sigma_{uN}\) was 1.22 achieved by P(3;5) with \(h_{s}\)/\(t_{s}\) = 0.57. These highest and lowest values represent an increase on \(\sigma_{uR}\) of 284% and 22%, respectively. The displacement and von Mises stress distributions for both cases are depicted in Figure 22.  
The best configuration collapsed with local displacements (Figure 22a), while the worst configuration collapsed with global displacements (Figure 22c). In comparison with their von Mises stress distribution, it noted that the stiffened plate which presented the best stress distribution resulted in the highest \(\sigma_{uN}\) (Figure 22b). Conversely, the stiffened plate with the worst stress distribution (Figure 22d) displayed the lowest value of \(\sigma_{uN}\), in accordance with the constructal law. 3.4 Influence of \(N_{ls}\) and \(N_{ls}\) over Once Optimized \(\left(h_{s}\middle/t_{s}\right)_{o}\) and Once Maximized \(\left(\sigma_{uN}\right)_{m}\)  
From the results of \(\sigma_{uN}\) for each \(h_{s}\)/\(t_{s}\) value in each plate configuration, the \(\left(\sigma_{uN}\right)_{m}\) and their respective \(\left(h_{s}\middle/t_{s}\right)_{o}\) were obtained, as described in Table 10.  
Based on the results of Table 10, the highest value of \(\left(\sigma_{uN}\right)_{m}\) was 3.84, achieved by P(5;4) with \(\left(h_{s}\middle/t_{s}\right)_{o}\) = 8.70, while the lowest value of \(\left(\sigma_{uN}\right)_{m}\) was 3.28, reached from the P(2;2) with \(\left(h_{s}\middle/t_{s}\right)_{o}\) = 8.98. These highest and lowest values represent an increase on \(\sigma_{uR}\) of 284% and 228%, respectively. The displacements and stress distributions are shown in Figure 23, with both P(5;4) and P(2;2) collapsing with local displacements. In comparison with their von Mises stress distribution, it can be noted that the stiffened plate which presented the best stress distribution between plate and stiffeners resulted in the highest \(\left(\sigma_{uN}\right)_{m}\) (Figure 23b), while the stiffened plate that presented the worst stress distribution (Figure 23d) resulted in the lowest \(\left(\sigma_{uN}\right)_{m}\), also respecting the constructal law. Figure 16:0 Best and worst plate configurations displacements and von Mises stress distribution: (**a**) P(5;4) displacements, (**b**) P(5;4) stress distribution, (**c**) P(3;5) displacements, and (**d**) P(3;5) stress distribution. The influence of \(N_{ls}\), \(N_{ls}\), and \(\left(h_{s}/t_{s}\right)_{o}\) on \(\left(\sigma_{uN}\right)_{m}\) from Table 7 was plotted in Figure 16:1 The increase in \(N_{ls}\) and \(N_{ls}\) improved \(\left(\sigma_{uN}\right)_{m}\) and, in general, the \(\left(\sigma_{uN}\right)_{m}\) was obtained by higher values of \(\left(h_{s}/t_{s}\right)_{o}\) from most respective plate configurations, except for plates with P(2;2), P(2;3), and P(2;4). To understand this aspect, the plate configuration P(2;4) served as a model to investigate this behavior through comparison of the resulting displacements and von Mises stress distributions, depicted in Figures 25 and 26 (in which the red color on  
Figure 16:2 Displacements and von Mises stress distribution of best and worst plate configurations on \(\left(\sigma_{uN}\right)_{m}\): (**a**) P(5;4) displacements, (**b**) P(5;4) stress distribution, (**c**) P(2;2) displacements, and (**d**) P(2;2) stress distribution. Several key findings can be drawn from the behavior of the stiffened plate configurations P(2;2), P(2;3), and P(2;4), as seen in Figures 25 and 26. The ratio \(h_{s}/t_{s}\) significantly influenced \(\sigma_{uN}\), with the potential to either improve or reduce the ultimate strength of the stiffened plate.