# Design and Optimization of a Compliant Morphing Trailing Edge for High-Lift Generation
## 6 Refined Model and Result Evaluation  
Once the best compromise was identified, a refined FE model was developed to verify the outcomes of the optimization process. The scope of this model was both to validate the predictions of the optimization approach and to determine details that cannot be covered by the coarse model, as the actuation chain acts on more regions: the stress variation along the span, stress level, and distribution at some interfaces. In line with the selected layout (configuration 3), for the upper skin, thickness values of 2.84 and 2.11 mm were set for the front and rear regions, respectively, with the transition at 34% of the entire length of the panel. In the same way, for the lower skin, thickness values of 2.84 and 2.13 mm were assumed for the front and rear regions, with a transition at 40%. Finally, the thickness of the web was set at 2.74 mm. The refined digital mock-up is illustrated in Figure 14, while the relevant FE model and the main features are reported in Figure 15 and Table 4. A central flange is fixed on the lower skin at mid-span. On its upper part, there is a pin to which one edge of the actuator is connected. To assure a uniform transmission in span-wise direction of the forces and displacements produced by the actuator, two transversal bars were used to connect the central flange to the left and right sides of the lower panel. The same bars are also exploited to join the lateral flanges to the sliding tracks. All the parts are made of 7075-T6 aluminum alloy [48] except the two bars and the actuator hinge pin, which are made of UHSS [51]. Figure 13: Configuration 3: target morphed shape (green); clean configuration (blue); fully actuated with and without aerodynamic loads (cyan and red). \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Parameter Description** & **Value** \\ \hline P\({}_{7}\) & Upper skin thickness—rewarward region & 0.0021 m \\ P\({}_{8}\) & Lower skin thickness—forward region & 0.0028 m \\ P\({}_{9}\) & Lower skin thickness—rewarward region & 0.0021 m \\ P\({}_{10}\) & Upper skin extension—forward region & 33.7\% \\ P\({}_{11}\) & Lower skin extension—forward region & 39.6\% \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 14: Refined digital mock-up of the compliant trailing edge: lateral view (**a**) and isometric view (**b**). Figure 15: Refined FE model (**a**) and detail of the transmission chain (**b**). The skin is modeled using square CQUAD [52] elements with a characteristic length of 1 mm both in chord and span-wise directions, while the mechanism components (flanges, sliding tracks, actuator hinge pin, and bars) are modeled by 3D CTETRA [53] elements. RBE2 [49] elements were used to connect the flanges to the skin, the bars, and the actuator pin to the flanges and the sliding tracks. At first, a static analysis was performed actuating the morphing trailing edge with and without the aerodynamic loads. The results are presented in terms of displacement (deformed shape and maximum displacement printed in the caption) and stress level (contour map and relevant color bar) for the actuation alone (Figure 16a) and in combination with the aerodynamic loads (Figure 16b). The aerodynamic loads diminish the vertical displacement of the trailing edge, which passes from 0.139 to 0.132 m. Their impact in terms of stress is remarkable, passing from a maximum value of 162 MPa for the actuation alone to 193 MPa when the aerodynamic loads also act on the structure. This value is well below the ultimate stress limit of the aluminum alloy (572 MPa [48]). Finally, the force required by the actuator passes from 833 to 1293 N in the presence of the aerodynamic loads. Finally, the weight of the structure, including the actuation, was 8.85 kg. A modal analysis was then addressed. The 1 st modal shape, corresponding to a frequency of 45.2 Hz, is represented in Figure 17a; in the same figure, the next two modes are also illustrated (93 Hz and 96 Hz--Figure 17a,b).