# A Sensitivity Analysis of the Damage Behavior of a Leading-Edge Subject to Bird Strike
## 4 Sensitivity Analysis  
Once the numerical model was validated, a sensitivity analysis was performed in order to assess the influence of the design parameters on the deformation and on the total mass of the structure. A python script was developed to generate, automatically, all geometrical and FE models need for the analysis. Further, in order to efficiently manage all input and output data, the entire process was implemented in the ModeFrontier code. Using the python script allows to rebuild a new model each time and therefore to modify the frame geometry in order to avoid gap or overclosure in the contact zone between the skin and frames that are generated by the skin thickness variations (the outer and inner faces extend themselves into fastened zone too). The workflow of the sensitivity analysis is shown in Figure 7. From the workflow, it is possible to note that no constraint and objective functions were defined since no optimization analysis is required. The high computational cost of such simulations makes it difficult to run a full optimization process, but fruitful considerations can be derived by a cheaper sensitivity analysis that aims to define the trendline and allows to estimate the performance improvement in the function of the same geometrical parameters. It is clear that the boundary conditions applied, derived from the experimental test used as a reference, are quite different with respect to the real ones (e.g., the neighboring parts are missing). Nevertheless, the results reported hereafter can be generalized, applied and scaled to similar structures. Figure 6: Numerical results. (**A**) Time-history of the displacement along impact direction of the skin central point; (**B**) tip web distance time-history. The design parameters of the parametric procedure are the thicknesses of the inner face, of the outer face and of the core of the leading edge, as reported in Table 3. The starting values of the design parameters are shown in bold style. In order to evaluate the influence of each parameter, the last ones were changed one by one, keeping the others constant. Therefore, no full factorial design space was evaluated, but a representative subset that includes the more interesting configurations. The recorded output data were the inner, the outer and the core mass (and thus, the total skin mass), the plastic and the damage energy (for the entire model) and the displacement of the central point of the skin. A configuration is considered acceptable if the crashworthy requirements, defined for the test article, are satisfied, i.e., the maximum displacement (along the impact direction) of the central point of the skin is lower than 370 mm (which is the distance between the inner skin and the front spar) and, obviously, no penetration must occur. The plastic and the damage energies provide global information regarding the capability of the structure to dissipate impact energy both in a no catastrophic and in a catastrophic mode. The analyses have demonstrated that an increase of the outer and inner sandwich face thicknesses results in a decrease in the maximum displacement while increasing the total mass. Moreover, it was observed that similar effects are obtained also increasing the honeycomb core thickness; however, the effects in terms of the total mass increase are less relevant with respect to the outer and inner face variation, as shown in Figure 8. \begin{table}
\begin{tabular}{l l l l} \hline  & **Inner Face:** & **Outer Face:** & **Core:** \\  & _AL2024-T3_ & _AL2024-T3_ & _Hexcel—Hexweb Aluminum Flexcore_ \\ \hline Analyzed Values [mm] & **0.4**; 1; 1.4; 2 & 0.4; 1; **1.4**; 2 & 3.125; **6.35**; 9.475; 12.7 \\ \hline \end{tabular}
\end{table} 
Table 3: Design parameters. Figure 7: Sensibility analysis workflow and detail of design variables. For the sake of clarity, Figure 8 does not report all the obtained results: in particular, the central point displacement as a function of the component thickness and the total mass is reported.