## 4 Summary  
Bidirectionally sinusoidal corrugated steel shell structures represent a versatile and compelling choice in modern engineering and architectural applications. These structures, characterised by their folded configurations, offer unique advantages such as an enhanced stiffness, efficient material usage, and aesthetic flexibility. The research presented in this paper aimed to deepen our understanding of the behaviour of such elements, focusing on both numerical modelling validation and detailed performance analyses. The initial focus of this study was to validate the methodology used for generating folds in numerical models, implemented in RFEM and ABAQUS. This validation process was crucial in establishing reliable and accurate simulations that could replicate real-world behaviour. The results showed that the method of creating waves in RFEM caused slightly greater values of the stresses due to the lack of a smooth transition between the components of the whole element. The feature of creating a regular wave, which is available in ABAQUS, allows for omitting this issue. Nonetheless, both models were sufficient to represent an enhanced stiffness of the subjected element, which could be observed in deflections and natural vibrations. One of the primary findings concerned the sensitivity of corrugated steel structures to steel sheet thickness. The research demonstrated that thinner sheets exhibited a more significant influence of the corrugation amplitude on the deflections and stresses. A critical parameter highlighted in this paper was the height-to-thickness ratio of corrugated steel sheets, where the height represents the corrugation amplitude. This parameter not only affects stiffness and load-bearing capacity, but also influences the overall efficiency of material usage in structural applications. Although the research showed that the higher the mentioned ratio was, the more efficient solution it provided, it has to be highlighted that the analysed element might lose its properties if the ratio of the corrugation amplitude to  
Figure 18: The relationship between the corrugation amplitude and the maximum von-Mises stress of the element over a given period of time for the chosen thickness of a steel sheet: (**a**) \(t=3.0\) mm; (**b**) \(t=4.0\) mm; (**c**) \(t=5.0\) mm; and (**d**) \(t=6.0\) mm. the smallest dimension of the corrugation cell is excessive. In this study, the highest value of this ratio was equal to 0.1475. The analysis concerning this issue was not the subject of this paper, and might be a relevant aspect to be consider in future research. Furthermore, the study delved into the impact of folding methods, particularly the configurations of corrugations (number of waves in each direction), on the static and dynamic characteristics of the considered structures. It was observed that these configurations influenced displacements, stresses, and natural vibration frequencies, however, the impact was not substantial. It could be stated that, in terms of design optimisation, the research identified nearly square corrugation cells as being optimal for stiffening steel sheets by bidirectionally sinusoidal corrugation. This finding provides practical guidance for future research by strongly suggesting a minor impact of these parameters. The dynamic analyses conducted in this study revealed that thinner sheets showed greater performance gains with an increasing corrugation amplitude, reducing deflections, velocities, and stresses. The superposition of forcing and natural frequency waves indicated complex dynamic interactions. Higher natural frequencies led to denser oscillations in acceleration plots, while thicker elements exhibited less variation in acceleration due to corrugation. Additionally, larger corrugation amplitudes reduced stresses up to a certain threshold, beyond which, further increases offered minimal benefit.