# Design and Optimization of a Compliant Morphing Trailing Edge for High-Lift Generation
## 4 Design Approach and Optimization
Finally, the condition on the frequency of 40 Hz meets more needs: (1) avoiding any potential coupling with the wing-supporting structure subjected, among the others, to the aileron solicitation (up to 20 Hz); (2) mitigating any coupling with the test rig that will be used in the next part of the research for static and dynamic validation; and (3) being compliant with potential future testing in wind tunnel facilities. Other parameters were not included in the optimization loop: the structural weight and the actuation force and stroke. Since the chosen layout is already characterized by an intrinsic lightness and simplicity, the weight parameter was relaxed in favor of the robustness, thus yielding a wider range of solutions. Finally, with the intention of focusing on the compliant part of the system, the actuation features were not considered in this phase; however, a preliminary sensitivity study on the present layout confined the force and stroke of the actuator within a reasonable range compliant with the requirements. Then, it is worth noting that weight and actuation force and stroke impact were considered in the trade-off phase organized among the optimized solutions that confirmed the assumption on the ranges. Although the previously mentioned types of analyses are linear and thus relatively light, their repetition for thousands of configurations within an optimization process can significantly increase the computation times. To streamline the process, the simplified FE model shown in Figure 8 was thus specifically realized. The skin panels and the web were modeled through a total of 221 beam elements. To take into account the span dimension, a width of 0.5 m was set for the cross-section of each elements. A part of these elements, 200, were used for the upper and lower skin panels. This amount assures an adequate discretization both in terms of displacement and stress computation (element extension of about 5 mm over a skin chord of 0.5 m) and, at the same time, allows a satisfactory distribution of aerodynamic loads, matching the original trend of the pressure on 100 stations per panel. The 20 remaining beam elements were used for the web. This amount of elements provided an adequate discretization of the displacement and stress field on the component. The thickness and materials were fixed to be the same of the original architecture; the actuator and its connection to the lower skin were realized by rigid elements. The pulling action was modeled by means of RBE2 elements contracting by a fictious expansion coefficient and thermal load. According to the operational modality, the edge point of the beam-like upper panel was clamped. This constraint was chosen to take into account the continuation of the panel with its corresponding portion on the wing box further reinforced by the connection with the inner interface cap of the wing box. In addition, the seven nodes of the beam-like lower panel close to the actuator connection were constrained to slide along the skin tangent, according to the local reference frame highlighted in the figure; the actuator was then pinned on the forward edge. A static analysis of this model takes 5-8 s using a i7-8665U CPU at 1.9 GHz, with 16 Gb of RAM. The above-mentioned in-house genetic algorithm was used [47]. As shown in the flow chart of Figure 9, an initial population is randomly generated. Each individual is defined by a layout of a certain typology plus the thickness distribution of the skin and the web. Each geometric and thickness property constitutes a single chromosome of the individual. A first fitness evaluation is performed using the core scheme discussed above. On this basis, a classification is built. Then, a new population is created privileging the individuals with the higher fitness but at the same time not discharging the lowest one; a crossover operation is executed, randomly exchanging 50% of the chromosomes between individuals.