## 2 Methodology
### Weight Breakdown Evaluation
The finite element mesh primarily focuses on the wing-box structure of the wings, excluding the fixed and movable parts of the leading and trailing edges, which are represented as point masses attached to the spar webs by means of surface-based constraint relationships. Only a stress-based static structural assessment has been performed, neglecting buckling and/or aeroelastic loads; specifically, the loading condition is evaluated according to Equation (4), referring to the cruise flight condition:  
\[F_{Z}=\ n_{z}\ L-n_{z}(m_{w}+m_{b}+m_{f})g. \tag{4}\]  
where \(L\) is the lift distribution, extracted by AVL (a qualitative distribution is shown in Figure 4), and \(n_{z}\) is the load factor fixed equal to 2.5. Battery and fuel weights have been introduced as distributed vertical load according to this assumed layout: for the BW, the two terms \(m_{b}\) and \(m_{f}\) are placed in the front (60%) and rear (40%) wing, whereas, for TW, the whole masses \(m_{b}\) and \(m_{f}\) have been placed in the main wing. Figure 3: Geometrical (**left**) and structural (**right**) design variables identifying the lifting system. The metamodel provides (simplified) interpolated functions that relate the main structural figures of merit (i.e., the values of \(u\), \(\sigma^{F}\), \(\sigma^{R}\), and \(m_{w}\)) to the geometrical \(x\) and structural \(z\) design variables. These specific (simple) functions allow for setting an optimization problem useful for sizing the structure of the lifting system by minimizing the wing structural mass according to the problem described in Equation (5):  
\[\left\{ \begin{array}{l}\min(m_{w}(\mathbf{x},\mathbf{z}))\\ \sigma^{F}(\mathbf{x},z)-\frac{\sigma_{\text{Y}}}{\sigma_{\text{F}}}\leq 0\\ \sigma^{R}(\mathbf{x},z)-\frac{\sigma_{\text{Y}}}{\sigma_{\text{F}}}\leq 0\\ u(\mathbf{x},\mathbf{z})-0.125\frac{\theta}{2}\leq 0\\ \mathbf{l}_{b}\leq\mathbf{x}\leq\mathbf{u}_{b}\\ \mathbf{l}_{b}\leq\mathbf{z}\leq\mathbf{u}_{b}\\ \end{array} \right. \tag{5}\]  
where \(\sigma_{\text{Y}}\triangleq 345\) Mpa is the yielding stress of Al2024 and \(C_{\text{F}}\triangleq 1.5\) is a safety factor. Once the geometry of the lifting system is determined, the optimization procedure can act on the structural variables to minimize the structural wing mass. The optimization problem is subject to the following constraints: _(i)_ the maximum equivalent Von Mises stress of both front and rear wing (\(\sigma^{F}\) and \(\sigma^{R}\)) must be lower than yielding stress of the material scaled by the safety factor; and _(ii)_ the maximum tip displacement \(u\) must be lower than \(12.5\%\) of the half-wingspan. The optimization problem described in Equation (5) focuses on the minimization of the structural mass of the lifting system; however, non-structural mass has been considered as well in the FE model. The movable surfaces of secondary structures, namely the leading edge and trailing edge, are represented as point masses connected to the primary structures, specifically to the spar webs of the wingbox structure. The determination of these masses has been conducted following the methodology outlined in [57]. Apart from considering the weight of primary and secondary aircraft structures, the finite element (FE) model also incorporates additional masses associated with systems, equipment, and other non-structural components; these miscellaneous masses have been assessed based on the guidelines presented in [58].