## 3 Conceptual Design
### Finite Element Analyses and Optimization Results  
#### 3.5.1 C1 FEA and Results  
Two loops of FEA were considered, which were different from each other in terms of used materials and thickness of the skin. In detail:  
Loop 1: aluminum skin with a constant thickness of 1.5 mm. Loop 2: carbon fiber skin, with a proper lay-up and a constant thickness of 2.4 mm. Each loop was investigated under three load conditions:  
* High-lift flapped condition is used to perform static analyses in order to obtain stress/strain and displacement distribution along the MF. * High-lift flapped conditions combined with actuation loads are used to perform an actuation sensitivity analysis. * Actuation loads in the absence of aerodynamic loads are used to obtain the morphing aeroshape of the MF. A scheme of the FEA approach followed for the C1 configuration is depicted in Figure 14.  
In terms of boundary conditions, for the upper skin, a fixed constraint was introduced to simulate the attachment area between the morphing flap and the wing box; for the lower skin, an axial carriage was used to model the sliding motion of that structural part in the chordwise direction. The results gained for the loop 1 have been reported in Figures 15-17; the ones relative to the loop 2 have been summarized in Figures 18-20. More in detail, Figure 15 presents static analysis results depicting displacement (left) and Von Mises stress (right) contours obtained during Loop 1 under high lift loading conditions (aerodynamic loads at the VF speed) by accounting for a skin in aluminum with a constant thickness of 1.5 mm. The displacement color map indicates a vertical deflection of 3.29 \(\times\) 10\({}^{-5}\) m at the MF tip, which remains significantly below the Tz target value due to high structural stiffness. Additionally, without actuation forces, the upper skin interface strip adjacent to the wing box (highlighted in orange in Figure 15) exhibits the highest stress concentration. This is attributed to the localized fixed constraints in this region. Figure 14: C1 FEA approach. Figure 16: C1 Loop 1 FEA results, High Lift + Actuation Loads. Figure 15: C1 Loop 1 FEA results, hgh lift loads condition. Figure 17: C1 Loop 1 FEA results, actuation loads only. Figure 18: C1 Loop 2 FEA results, high-hift load condition. Figure 19: C1 Loop 2 FEA results, high lift + actuation loads. Figure 20: C1 Loop 2 FEA results, actuation loads only. The actuation system's trade-off analysis involved simulating its performance using Single Point Constraint Displacement (SPCM). Displacements were applied either to:  
* The middle node of the lower skin. * Both lower rib attachment points. By systematically varying the SPCM magnitude within a practical operational range, researchers recorded the actuation locking force (Fx) and the vertical deflection at the morphing flap tip (Tz). A displacement of about 0.06 m (SPCM) produced a \(-0.15\) m vertical deflection (Tz) at the MF tip. This configuration fully achieved the target deflection with an actuation locking force of \(1.5\times 10^{5}\) N, as illustrated in Figure 16.  
In the final phase of Loop 1 FEA, aerodynamic loads were excluded to isolate the MF morphing mechanism's performance under actuation loads alone. These actuation loads corresponded to the previously determined SPCM value of \(\sim\)0.06 m (refer to Figure 16). Displacements and Von Mises stress distributions were calculated to assess the actuation system's impact on morphing capabilities. Figure 17 shows an achieved downward tip displacement (Tz) of \(-0.016\) m. Instead, in terms of stress distribution, localized stress peaks (\(\sim\)1.47 GPa) occurred at rigid interfaces between compliant ribs and the upper skin. The safety margin is calculated as the ratio of the aluminum's allowable tensile strength (71 GPa) to the observed maximum Von Mises maximum stress (1.47 GPa), yielding a value significantly greater than 1.