## 3 Results and Discussion
### Geometric Evaluation
#### 3.3.2 Influence of \(P_{z}\) and \(h_{s}/t_{s}\) over \(\sigma_{uN}\)
Figure 19: Influence of \(h_{s}/t_{s}\), negative lateral pressure, and subsequent biaxial compressive loading on displacements of plates with \(N_{ls}<4\): (**a**) \(h_{s}/t_{s}=1.02\) and lateral pressure, (**b**) \(h_{s}/t_{s}=1.02\), lateral pressure, and biaxial loading, (**c**) \(h_{s}/t_{s}=20.13\) and lateral pressure, and (**d**) \(h_{s}/t_{s}=20.13\), lateral pressure, and biaxial loading. Figure 20: Influence of \(h_{s}/t_{s}\) and lateral pressure on \(\sigma_{uN}\) in plates with \(N_{ls}\geq 4\): (**a**) P(4;2), (**b**) P(4;3), (**c**) P(4;4), and (**d**) P(4;5). It is interesting to emphasize that due to the conservation of the total volume of the stiffened plates (Equation (15)), the increasing number of stiffeners requires reducing the maximum and minimum available \(h_{s}/t_{s}\) values to respect this premise, consequently propitiating global displacements distributions. In Figure 20, for lower values of \(h_{s}/t_{s}\), the application of positive lateral pressure leads to global displacements distributions, which evolve into global collapse due to compressive biaxial loading, resulting in low values of \(\sigma_{uN}\) for these geometric configurations. While for higher values of \(h_{s}/t_{s}\), the lateral pressure induces global displacements distributions that evolve into local displacements collapse, resulting in the best \(\sigma_{uN}\) values for these plate configurations. Figure 20 also indicates that the negative lateral pressure increased or decreased \(\sigma_{uN}\) according to \(h_{s}/t_{s}\) values. This fact can be explained by the resulting displacements due to negative lateral pressure application and subsequent biaxial loading, as illustrated in Figure 21.  
In Figure 21, one can infer that lower values of \(h_{s}/t_{s}\) led to negative global displacements distributions due to the application of negative \(P_{z}\) (Figure 21a), and the subsequent application of biaxial loading contributed to these negative displacements and consequently considerably reduced \(\sigma_{uN}\), causing the structural collapse (Figure 21b). Whilst higher values of \(h_{s}/t_{s}\) resulted in negative global displacements distributions due to negative \(P_{z}\) application (Figure 21c), and the subsequent application of biaxial compressive loading resulted in positive displacements (Figure 21d), overcame negative displacements and consequently improved \(\sigma_{uN}\), collapsing with local displacements (Figure 21b) and achieving better values of \(\sigma_{uN}\). With this, for negative pressure application (Figure 20), at the \(h_{s}/t_{s}\) as \(\sigma_{uN}\) presented lower values, the stiffened plate displacements maintained global displacements distributions from negative lateral pressure to biaxial loading until collapse, and the increase of \(h_{s}/t_{s}\) resulted in higher values of \(\sigma_{uN}\), indicating that the biaxial loading overcame the global displacements into local displacements until collapse. It could be stated that lower values of \(N_{ls}\) allow for higher values of \(h_{s}/t_{s}\), but in contrast, this results in an increased spacing \(S_{ls}\) between them, leading to local displacements on the stiffened plate, which tends to improve \(\sigma_{uN}\). On the other hand, higher values of \(N_{ls}\) reduce the spacing \(S_{ls}\), but the necessary reduction in \(h_{s}/t_{s}\) to maintain the constant volume  
Figure 21: Influence of \(h_{s}/t_{s}\), negative lateral pressure, and subsequent biaxial compressive loading on displacements of plates with \(N_{ls}\geq 4\): (**a**) \(h_{s}/t_{s}=0.61\) and negative lateral pressure, (**b**) \(h_{s}/t_{s}=0.61\), negative lateral pressure, and biaxial loading, (**c**) \(h_{s}/t_{s}=12.10\) and lateral pressure, and (**d**) \(h_{s}/t_{s}=12.10\), negative lateral pressure, and biaxial loading. constraint makes the stiffened plate more susceptible to global displacement distribution, tending to reduce \(\sigma_{uN}\).