## 5 Results and Discussion
### Fatigue Behavior  
The fatigue safety factor (FSF) is represented as a contour plot showing the safety factor relative to fatigue failure over a specified design life (typically \(1\times 10^{9}\) cycles) [38; 39]. Figure 17 shows the minimum FSF for different combinations between models and cutout geometries.  
According to obtained results, it is observed that a configuration of two longitudinal stiffeners in the bottom and inner bottom with three longitudinal stiffeners on the side girder presents the most high minimum fatigue safety factor, which results in less influence of the side girder cutouts compared to the bottom and inner bottom cutouts. A comparison between the different models indicates that cutout no. 1 presents the most beneficial results in 50% of the analyses situations. Particularly in the first of the arrangements with two longitudinals in bottom, double bottom, and side, the greatest increase in the fatigue safety factor is 17.6%, which occurs between the use of cutout no. 1 and no. 3. To account for potential scenarios that create load scenarios different from the original, fatigue-sensitivity curves are calculated to aid in structural design. These curves are represented as graphs formed by connecting points that show the remaining life for various stress range values, expressed through a loading history scale factor. The effect of the scale factor on the increase or decrease of the stress range, relative to the initial load, is examined in relation to fatigue life. For each combination of model and cutout geometry, 25 evenly spaced stress range  
Figure 16: Von [PERSON] maximum stress of different models at equal thickness (14.5 mm) and an axial loading scenario.  
Figure 17: Minimum fatigue safety factor (FSF).  
variations are considered, starting from the initial value (with a scale factor of one) and extending to \(\pm\) 50% of this value, resulting in a total of 150 numerical tests (Figure 18).  
The collective points of the fatigue-sensitivity curves suggest a potential extrapolation of the results by fitting the point cloud from each tested sub-model to a shared hyperbolic curve. Sensitivity, in terms of changes in fatigue life, generally shows an inverse relationship with the applied scale factor, regardless of the cutout geometry and model of double-bottom floor selected. Fatigue life experiences a significant decline as the scale factor increases.  
Biaxiality indication (BI) is defined as the ratio of the smaller principal stress to the larger principal stress, excluding the principal stress closest to zero from consideration [40]. A BI value of 0 indicates uniaxial stress, \(-1\) represents pure shear, and \(1\) corresponds to a purely biaxial stress state. Figure 19 shows the distribution of BI for different cases.  
Figure 19: Biaxiality indication. (**a**) Model no. 1 with cutout no. 1, (**b**) model no. 2 with cutout no. 2, (**c**) model no. 3 with cutout no. 3, (**d**) model no. 4 with cutout no. 4, (**e**) model no. 5 with cutout no. 1, (**f**) model no. 6 with cutout no. 2.  
Figure 18: Fatigue-sensitivity curves. Blue line—Model no. 1 with cutout no. 1, orange line—model no. 2 with cutout no. 2, grey line—model no. 3 with cutout no. 3, yellow line—model no. 4 with cutout no. 4, and green line—model no. 6 with cutout no. 2.  
It is observed that regardless of the model and cutout selected, the predominant state in the double-bottom floor is the uniaxial state, followed by a pure shear state located in the upper part of the central opening and in the cutouts near the side girder, which also present a pure shear state. The pure biaxial state presents a stable behavior in the different models with a marked tendency to remain in the lower part of the central opening, which is located in the vicinity of the high zone of the central cutout in models no. 2, no. 4, and no. 6.