## 4 Multidisciplinary Design, Analysis, and Optimization of an Adaptive Wing  
The aerodynamic characteristics of the under-actuated airfoil (wing without actuators) are determined by evaluating the aerodynamics coefficients \(C_{t}\), \(C_{d}\) and the lift-to-drag ratio, which are also the same parameters used to measure the performance of the new shapes produced by the actuators inside the wing. The airfoil shape configurations are determined through the activation of the actuators and by considering the effects of the actuators and aerodynamic forces acting on the wing's skin simultaneously. The shape of the initial airfoil is defined through a set of parameters determined in the design and manufacturing phases. The configuration and structural properties of the prototype wing's inner structure and the size of the actuators were used to generate a finite element model; in this way, the upper surface of the FE model fit with the desired initial airfoil shape.  
The values characterizing the structural properties are directly modified in the finite element FE model, thus allowing the structural and geometrical parameters to be changed simultaneously.  
The ability to improve the wing aerodynamic coefficients with internal actuators, and for that system to withstand the aerodynamic forces, is dependent on the size, weight, location, and properties of the wing structure. Additionally, it is necessary to design an underlying structure with reduced stiffness to achieve the needed deformations. This reduced stiffness, however, increases the probability of a structure being influenced by aero-elastic effects (such as flutter).  
These challenges drive the need for a multidisciplinary optimization method designed from the early phases of the project, namely preliminary analysis and concept development. The methodology presented in Figure 6 will be followed in this study.  
The optimization method consists in the coupling of XFoil with the genetic algorithm (GA). The GA routine determines the best spline curve shape passing through the beginning, the middle, and the end of the airfoil geometry. Thus, the coordinates of this spline correspond to the new airfoil shape. These coordinate files (.dat file) are introduced in XFoil to perform the aerodynamic analysis. The optimization method evaluated all of the optimized shapes possible, with a \(\pm 5\) mm vertical displacement of the actuators. The optimization method can find the optimal shape with the corresponding actuators'  
Figure 6: The methodology for the study of an adaptive wing.  
displacements; the optimal shape corresponded to the optimal \(C_{p}\) curve where the transition point was pushed toward the direction of the trailing edge. Delaying or holding back the laminar-to-turbulence flow process has an important impact in drag reduction.  
This optimization method allows the real structural deformation shape to be compared with the predicted one given by the GA. When the best shape has been defined, the new airfoil coordinates are tested in XFoil to determine whether the aerodynamic coefficients are better, equal, or worse. The optimization method gives the maximal displacement of the actuators as well as the shape coordinates of the new optimized airfoils.