## 5 Results
### Third Level  
Starting from the topology solutions that arise from the second level of optimization, a higher fidelity model than the previous two-dimensional model is generated and used inside the constrained nonlinear optimization of the third level. A local optimization, based on Sequential Quadratic Programming (SQP), is used to refine the structural solution selected on the Pareto front. The second objective function of Section 5.2 becomes the single objective function, while the other two become two nonlinear constraints in such a way that their value does not get worse than the same values accepted on the Pareto front. The optimization variables are the same variables used by the GA, except for the topology (binary) variables: the number of load paths can not change at this stage. The finite element model is automatically generated and initialized considering the values that the optimization variables assume when the design point is extracted from the Pareto front. It is a constant-section model that reproduces the behavior of the portion between the two ribs, as depicted in Figure 15. The actuation stroke is introduced by a kinematic chain that can reproduce the actual displacements. The actual materials are also assigned to both the skin and compliant ribs. The Skin Structural Layer (SSL) is made of Glass Fiber-Reinforced Polymer (GFRP), the mechanical properties of which are reported in Table 1. The aim of this layer is to provide a suitable stiffness in both the chord and span direction. As in the second level of optimization, the chordwise thickness distribution is determined by the optimization, but it now considers a more accurate material model. The skin structural configuration embeds 4 T shaped stiffeners, which are not considered in the first two levels;  
Figure 14: Representation of the optimal compliant structure configuration. Figure 15: Finite element model used by the third level of optimization. these are used to reinforce the skin in the spanwise direction and to correctly model the connections between the compliant rib and skin. The stiffener lamination sequence is symmetrical with the thickness and is equal to the local SSL thickness. Two different stiffener geometries, for low and high curvature airfoil areas, are used. Two optimizations are performed by first assigning the aluminum alloy and then NiTiNOL to the compliant ribs. NITiNOL is used to exploit its superelastic capabilities, which allow it to recover from very large strains upon unloading, without permanent deformations. The existence of a transformation stress plateau guarantees near constant stress over large strain intervals. To define the superelastic material model, 15 constants must be supplied if plastic deformations are not permitted, as in the aeronautical case. A simple numerical material design is conducted while accounting for a wide range of aeronautical operative temperatures, and it is described in [37]. Some material properties are borrowed from [PERSON] and Lagoudas [40], and they are reported in Table 2. The transformation strain is 5%, while the elastic strain is 2%. The stress values that characterize the plateau, in terms of the start and end of the transformation loading, are \(\sigma_{L}^{S}\) = 441.1 MPa and \(\sigma_{L}^{E}\) = 511 MPa, respectively. The Young's modulus and the Poisson's coefficient for the aluminum alloy are equal to the same values considered for the NiTiNOL in the elastic part of its constitutive curve. The admissible stress value considered during the optimization for the aluminum alloy is 550 MPa, according to the same unfeasible value accepted during the selection in the Pareto front. The admissible stress value for the NiTiNOL is 500 MPa, which is just below the stress level at the end of the loading plateau. During the optimization, the load path thickness is free to vary between 1 mm and 7 mm, while the skin thickness distribution is free to vary between 0.5 mm and 7 mm.