# Design and Optimization of a Compliant Morphing Trailing Edge for High-Lift Generation
## 4 Design Approach and Optimization  
The development of the above-mentioned C\({}_{3}\) concept was addressed by means of the FE approach. As shown in Figure 6, the process was split in two main steps: a first step devoted to the identification of the main design parameters of the architecture and its optimization and a second step focusing on the advanced design and on the validation of the results previously obtained. The FE simulations were addressed by means of the MSC NASTRAN 2024.1 solver; the FEMAP v11.3.2 pre- and post-process software were also used to realize, analyze, and present the results for both the simplified and advanced models. To assure an adequate level of detail, the DMU of the advanced design was realized by means of the CATIA v5 CAD software. Finally, the optimization was addressed by means of an in-house genetic algorithm in the MATLAB R2020b environment. The design and optimization of the system was carried out through a genetic algorithm. The core of the algorithm was defined to estimate the functionality and the load absorption capability of a generic layout of the morphing device. For each configuration processed by the algorithm, the flowchart shown in Figure 7 was implemented. It describes the following:  
* A static analysis to estimate the stress level, the force needed by the actuation, the deflection that can be achieved through a certain layout, and the impact of the external loads on the initial and final configurations;
* A buckling analysis to exclude any instability determined by the external loads;
* A normal mode analysis: Even if the proposed system cannot be classified as a dynamic device like an aileron, to assure an adequate rigidity and exclude any undesired coupling phenomenon, a normal mode analysis is also required to verify that the lowest modal frequency is higher than a threshold. An important role in the computation of the fitness is played by the deviation, \(D\), along the curvilinear abscissa, \(s\). Then, the stress level, the 1 st buckling eigenvalue, and 1 st normal mode are also considered, enforcing the algorithm to privilege configurations with values over the thresholds. The fitness, in line with the considerations above, is computed as product of four terms:  
Figure 6: Design process. Figure 7: Flow chart of the core of the genetic algorithm. * The factor \(f_{D}\), which is the inverse of the summation of the deviation, \(D\), along the curvilinear abscissa, over the maximum of the abscissa;;
* The factor \(f_{s}\) equal to 1 or 0.1 depending on whether the maximum von Mises stress is less than or greater than 200 MPa;
* The factor \(f_{\lambda}\) equal to 1 or 0.1 depending on whether the 1 st buckling eigenvalue, \(\lambda\), is greater than or lower than 1.1;
* The factor \(f_{\omega}\) equal to 1 or 0.1 depending on whether the 1 st normal frequency, \(\omega\), is greater than or lower than 40 Hz. The values assumed by the above factors were chosen to privilege the best-performing configurations and, at the same time, preserve the heritage of the other configurations. In greater detail, a single unsatisfactory condition penalizes by the order of 1 the probability of heritage transmission. This penalization progressively arises if other conditions are not satisfied. The structure and the behavior of the fitness function must meet the main requirements of the morphing device, in terms of shape fitting, robustness, and interaction with other the wing-supporting structure. A threshold of 200 MPa for the stress level was chosen for the factor fs to guarantee the fatigue tolerance capability of the compliant structure made of 7075-T6 aluminum alloy. A small margin of 10% was then selected with respect to the 1 st eigenvalue for the instability part of the fitness function, \(\ell_{\lambda}\); this assumption, supported by the outcomes of preliminary investigations leading to an instability direction opposite to the operational loads, was then confirmed by the advanced design.