## 4 Use Case
### Strain, Stresses and Buckling Analysis
#### 4.1.5 Obtained Results  
The prepared model was used to perform the computation procedure. In the first step, natural frequencies were calculated for both no constraints and with constraints. An example of the commutated natural frequency is shown in Figure 16. In the process, the first 50 frequencies were calculated for further aeroelastic analysis.  
In the second step, standard structural analysis was performed. In this case, two analyses were conducted, the first one for the positive loads' envelope, and the second for the negative loads' envelope. As a result of this stage of the study, we obtained colored stress and displacement maps. Examples of the obtained results are presented in Figures 17 and 18.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & \multicolumn{3}{c}{**Carbon Fiber Composite**} & **Honeycomb Expanded Core** \\ \hline Elastic modulus, MPa & \(\mathrm{E_{cv}}\) & 110,000 & 1700 \\  & \(\mathrm{E_{cy}}\) & 8500 & 1700 \\  & \(\mathrm{E_{cz}}\) & - & 576 \\ \hline Shear modulus, MPa & \(\mathrm{G_{cyz}}\) & 4000 & 110 \\  & \(\mathrm{G_{cyz}}\) & - & 646 \\  & \(\mathrm{G_{czz}}\) & - & 2500 \\ \hline Allowable compressive stress, MPa & \(\mathrm{X_{c}}\) & 900 & - \\  & \(\mathrm{Y_{c}}\) & 170 & - \\ \hline Allowable tensile stress, MPa & \(\mathrm{X_{t}}\) & 1500 & - \\  & \(\mathrm{Y_{t}}\) & 58 & - \\ \hline Allowable shear stress, MPa & S & 80 & - \\ \hline Density kg/m\({}^{3}\) & & 1700 & 915 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Anisotropic material properties used in the study definition.  
Figure 16: The first calculated natural frequency.  
Figure 17: Global stress plot.  
Figure 15: An example of applied restraints.  
The last part of the computation process is buckling analysis used for stiffens and stability evaluation. An example of the result of this analysis is presented in Figure 19.  
Based on the performed computations, it was possible to avoid some potential issues in the design. For example, the buckling analysis showed the area that needed to be revamped, because it is possible that in this area the UAV may lose stability and cause a crash. To address this issue, the authors, using generative modelling for honeycomb structures, changed the thickness to find out the proper value to fulfil the project's assumptions. In this case, the authors used the generative model as a tool to making models of the structure with different thickness. In the tests, the thickness of the filling layer of the sandwich structure was increased without changing the form of the filling. The study was intended to increase the viewer on the loss of stability in compressed structures. Finally, it finds out that in particularly endangered places 10 mm structure is an optimal value. The summary of the most important obtained results is presented in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Max von Mises stress & \(1.197\times 10^{3}\) & MPa \\ Max displacement & \(4.118\times 10^{3}\) & mm \\
1 st mode & 2.1984 & Hz \\
10 th mode & 11.817 & Hz \\
50 th mode & 47.078 & Hz \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the use case results.  
Figure 19: Example of stability lose in the central part of the UAV.  
Figure 18: Global displacement plot.