## 3 Results
### Static Analysis
#### 3.1.3 Stresses  
Based on the obtained results, a series of graphs illustrating the relationship between the corrugation amplitude and maximum von Mises stress of the element for various thicknesses of the steel sheet and the chosen number of periodic cells in each direction was created (Figure 10).  
Furthermore, Figure 11 presents the relationship between the corrugation amplitude and maximum von Mises stress of the element for various numbers of periodic cells in each direction and the chosen thickness of the steel sheet.  
Lastly, a graph illustrating the relationship between the corrugation amplitude and maximum von Mises stress of the element for various numbers of periodic cells in each direction and for various thicknesses of the steel sheet was created and is shown in Figure 12. Each colour in the graph refers to each considered thickness of the steel sheet.  
An analysis of the stress distribution in the corrugated steel sheets reveals several important insights. It is evident that, as the thickness of certain parts of the sheet decreases, there is a corresponding increase in the maximum values of the stresses. This is consistent with the general understanding that thinner materials are less capable of distributing and withstanding applied loads, leading to higher stress concentrations.  
Figure 11: _Cont._  
Figure 10: The relationship between the corrugation amplitude and maximum von Mises stress of the element for various thicknesses of the steel sheet and the following number of periodic cells in each direction: (**a**) \(n_{x}=6\), \(n_{y}=6\); (**b**) \(n_{x}=6\), \(n_{y}=8\); (**c**) \(n_{x}=6\), \(n_{y}=10\); (**d**) \(n_{x}=8\), \(n_{y}=6\); (**e**) \(n_{x}=8\), \(n_{y}=8\); (**f**) \(n_{x}=8\), \(n_{y}=10\); (**g**) \(n_{x}=10\), \(n_{y}=6\); (**h**) \(n_{x}=10\), \(n_{y}=8\); and (**i**) \(n_{x}=10\), \(n_{y}=10\).  
This study observes that, for small corrugation amplitudes, the maximum value of the von Mises stress initially increases. This suggests that minor corrugation does not sufficiently enhance structural rigidity, thereby failing to mitigate stress effectively. However, as the amplitude of the corrugation continues to increase, a notable trend emerges. Beyond a specific corrugation amplitude threshold, the maximum von Mises stress begins to decrease. This correlation indicates that larger corrugation amplitudes significantly improve the structural integrity of the sheet, thereby reducing the maximum stresses experienced.  
Figure 11: The relationship between the corrugation amplitude and maximum von Mises stress of the element for various numbers of periodic cells in each direction and the following thicknesses of the steel sheet: (**a**) \(t\) = 3.0 mm; (**b**) \(t\) = 4.0 mm; (**c**) \(t\) = 5.0 mm; (**d**) \(t\) = 6.0 mm; and (**e**) \(t\) = 7.0 mm.  
Figure 12: The relationship between the corrugation amplitude and maximum von Mises stress of the element for various numbers of periodic cells in each direction and for various thicknesses of the steel sheet.  
A similar pattern is observed with deflections, where the relative change in maximum stresses becomes more pronounced as the thickness of the steel sheet decreases. Thinner sheets demonstrate a higher sensitivity to variations in corrugation amplitude, leading to more significant changes in stress distribution.  
Moreover, the geometric configuration of the corrugation plays a crucial role in stress distribution. The study finds that square periodic cells are the most effective in reducing maximum stress values. In contrast, more rectangular cells result in a lower reduction in stress, indicating that the shape and periodicity of the corrugation significantly influence the stress mitigation capabilities of the sheet.