## 3 Model Description  
To study the optimal configuration for the hinge system, a simplified parametric model of the wing was developed. Both the model and the whole set of analyses were carried out in the ANSYS environment. The parametric model was created by means of a dedicated routine developed using APDL language [15] (Ansys Parametric Design Language).  
The numerical model was defined considering the main geometric dimensions and, in particular, the two points where the load was applied, i.e., the center of gravity (CoG) and the point where it is possible to concentrate the aerodynamic loads (PL).  
Figure 7 shows, schematically, the global dimensions and the location of the CoG and PtL. The estimated overall mass of the wing is 92.15 kg (including the TPS and the installed sub-systems). The rational angle in the folded configuration is 55\({}^{\circ}\).  
Figure 8 shows the simplified numerical model. The hinges were not modeled directly but by means of rigid elements, as direct modeling of the hinges is not entirely relevant for the evaluation of reaction loads. Furthermore, this choice reduces the computational costs, which is a relevant issue for the optimization analysis.  
Figure 6: Defined design variables.  
Figure 7: Global dimension and loading points.  
Hinge reaction forces are evaluated for both configurations: deployed and folded wing (55\({}^{\circ}\)). The routine is designed to analyze both configurations by properly rotating the wing (Figure 8).  
Even if a full FE model is not mandatory for such evaluations (as the rigid model was used), it was adopted to have a better understanding of the analyzed configurations and to simplify the constraints definition. Indeed, the location of the holes could be determined by geometrical/mathematical relationships and the reaction forces could be determined by solving the equation system related to a hyper-static structure. On the other hand, using an analytical formulation would introduce some approximations in order to simplify the equations and it would not provide the capability to define the exact location of the holes (the position of the stopper holes in the folded configuration depend on the other four holes and by their specific station along the chord direction. Further, C1, C2, and C3 do not lie in the same plane, nor do C4, C5, and C6).  
Furthermore, the choice to adopt an FE model, instead of analytical formulations, is also justified by the very small computational costs related to such an FE model. Indeed, a single run, which consists of a model generation and two static analyses with two post-processes, requires at most 15 s on an HP Z840 Workstation-Intel Xeon CPU E5-2620 v3 @ 2.40 GHz; RAM 128 GB.  
The outer surface of the wing has been discretized with shell elements (Shell181) that have been assigned a rigid behavior (Figure 9A). The load application points, both for the unfolded and folded configuration, are connected to the main structure by rigid elements (MPC184). The centers of the holes of the deploying system are connected to the root rib by rigid elements (MPC184) as shown in Figure 9B. The whole FE model consists of about 4000 elements (3600 shells and 400 MPCs) and about 3500 nodes. As rigid behavior has been adopted for the wing, the average element size (25 mm far from the region of the hinges and 5 mm close to them) aims to reproduce the wing shape with a discrete accuracy and to have good force distribution (both applied loads and reaction forces), but this is not a critical aspect.  
Figure 8: Simplified numerical model with axis location. (**A**) Deployed Configuration; (**B**) Folded Configuration.