# Design and Optimization of a Compliant Morphing Trailing Edge for High-Lift Generation
## 4 Design Approach and Optimization
At this point, to avoid any premature convergences, a mutation, i.e., the random alteration of some parts of the genetic heritage of some individuals, is also performed. The new population is again processed to find the current fitness distribution. These steps (crossover, mutation, fitness evaluation, and assessment of a new population) are repeated until, after 50 iterations, no increase in the maximum fitness value is observed. More optimization processes were repeated, starting from different initial populations to further avoid the risk of premature convergences and to address a final trade-off among the best individuals. In Table 1, the parameters of the optimization model, their typology (that is to say, if they are subjected to the optimization or not), and the range are reported. The actuator location and length are determined by the position of its forward hinge, assuming that it is initially parallel to the forward sliding region of the lower skin segment. The location of the web is defined by the identification number of the nodes of the upper and lower skin to which it is connected. The thickness of the web was assumed uniform and defined through a dedicated parameter. To have a major chance of adaptation to the target shape, a stepwise thickness distribution for the upper and lower skin was considered; this was defined by a total of six parameters: with reference to Figure 8, two parameters for the thickness values of the upper and lower skin fore regions, two for the corresponding rear regions, and another two defining the identification numbers of the nodes bordering the rear and fore regions. Figure 8: Simplified FE model released for the optimization. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Parameter Id (\(\mathbf{\text{*}}\))** & **Parameter Description** & **Type** & **Range** & **Notes** \\ \hline P\({}_{1}\) & Actuator forward hinge—abscissa & \([-0.25\_\ldots-0.10]\), m & Point A in Figure 8; global reference \\ P\({}_{2}\) & Actuator forward hinge—ordinate & \([0.04\_\ldots 0.15]\), m & frame & Point B in Figure 8; progressive Id from 1 (top skin clamped node) to 101 \\ P\({}_{3}\) & Top connection node of the web & & \([12\_\ldots 83]\), node Id & 1 (top skin clamped node) to 101 \\  & Optimization & & (trailing edge) & \\  & & & Point C in Figure 8; progressive Id & from 102 (bottom skin forward edge) to 201 (node immediately upstream of the trailing edge) \\ P\({}_{4}\) & Bottom connection node of the web & & \([115\_\ldots 184]\), node Id & 201 (node immediately upstream of the trailing edge) \\ P\({}_{5}\) & Web thickness & & \([0.3\_\ldots 3.0]\), mm & \\ P\({}_{6}\) & Upper skin thickness—forward & & & \\ P\({}_{7}\) & Upper skin thickness—rearward & & \([1.0\_\ldots 3.0]\), mm & See highlighted region in Figure 8 \\ P\({}_{8}\) & Lower skin thickness—forward & & & \\ P\({}_{9}\) & Lower skin thickness—rearward & & & \\ P\({}_{10}\) & Upper skin extension—forward & & \([1\_\ldots 101]\), node Id & Rear edge of the upper skin forward region; point D in Figure 8 \\ P\({}_{11}\) & Lower skin extension—forward & & \([102\_\ldots 201]\), node Id & Rear edge of the lower skin forward region \\  & & & & region; point E in Figure 8 \\  & Skin material & & & See [48] for the mechanical properties considered \\ NA & Web material & & & considered \\  & Actuator connection to the lower skin & & Rigid & RBE2 element [49] \\  & & & & A fictitious thermal expansion \\  & & & & coefficient of \(-0.1\)\({}^{\circ}\)C\({}^{-1}\) was assumed \\  & Actuator & & Rigid & to simulate the contraction;the fictious thermal load was estimated to obtain the target trailing vertical displacement \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting for genetic optimization. Figure 9: Algorithm flowchart. For the external aerodynamic loads, the most severe condition was considered. This condition refers to the fully actuated morphing trailing edge (see green line in Figure 2) at a speed of 90 m/s at sea level with load factor 2.