## 3 Results  
### Static Analysis  
#### 3.1.1 Results Comparison  
In this subsection, the deflections and maximum von Mises stresses obtained from ABAQUS and RFEM are compared for the previously established comparative element. Figure 5 shows the deflections obtained from a comparison of the results.  
The shape of the deformation is almost the same, and the relative difference between the maximum values of deflections is equal to 1.8%.  
Furthermore, the maximum values of von Mises stresses are presented in Figure 6.  
It can be observed that the global maximum values of the stresses occur in the corners of the element--identically for both numerical models. Nonetheless, the relative difference in these values is quite higher than that for the displacements and is equal to 10.2%.  
Figure 5: The deflections of the comparative element obtained from: (**a**) ABAQUS (the unit of displacements is m) and (**b**) RFEM.  
Figure 6: The maximum von Mises stresses of the comparative element obtained from: (**a**) ABAQUS (the unit of stresses is Pa) and (**b**) RFEM.  
The analysis of the deflections in the corrugated steel sheets exposes several critical observations. It is noted that, while the configuration of the corrugation, specifically the various dimensions of the periodic cell, does not significantly impact the stiffening of the analysed element, the presence of corrugation itself plays a crucial role in enhancing stiffness. Among the different configurations, the square periodic cell emerges as the most optimal for this purpose.  
Figure 8: _Cont_.  
Figure 7: The relationship between the corrugation amplitude and maximum deflection of the element for various thicknesses of the steel sheet and 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**) \(n_{x}=10\), \(n_{y}=10\).  
A key finding is that, as the amplitude of the corrugation increases, the maximum deflection of the entire element decreases. This indicates that a greater corrugation amplitude contributes to an improved structural rigidity, effectively reducing the deflection under applied loads. Furthermore, the relative differences in deflections for elements with a given steel sheet thickness become more pronounced at higher corrugation amplitude-to-thickness ratios. This suggests that the benefits of an increased corrugation amplitude are more evident in thinner sheets, where the impact on deflection is more substantial.  
Another important observation is the significant impact of corrugation on reducing deflections while maintaining structural performance. For instance, the maximum deflection of the entire element decreases, the maximum deflection of the entire element decreases, the maximum deflection of the entire element decreases, the maximum deflection of the entire element decreases. This indicates that a greater corrugation amplitude contributes to an improved structural rigidity, effectively reducing the deflection under applied loads. Furthermore, the relative differences in deflections for elements with a given steel sheet thickness become more pronounced at higher corrugation amplitude-to-thickness ratios. This suggests that the benefits of an increased corrugation amplitude are more evident in thinner sheets, where the impact on deflection is more substantial.  
Another important observation is the significant impact of corrugation on reducing deflections while maintaining structural performance. For instance, the maximum deflection tion of a flat plate with a thickness of 6 mm is nearly equal to the deflection of a corrugated element with a thickness of 3 mm and a corrugation amplitude of 14 mm. This comparison highlights that the process of folding can lead to a twofold reduction in mass without compromising the bending stiffness of the analysed element.