## 3 Structure Design and Optimization
### Modal Analysis  
Modal analyses were performed on both modules in order to verify that their optimized design meets the stiffness requirements. The models were prepared through the  
Figure 12: Lattice structures optimization design framework. Figure 13: Example of local thickening (**a**) and multiple pass thickening (**b**). The original design (ID 0) considers an aluminum alloy characterized by a 74 GPa Young modulus. Nevertheless, the first natural frequency is 23 Hz, much less than the requested one. The weight of a 100 \(\times\) 100 mm\({}^{2}\) panel of this configuration weighs 58.3 g. This value is taken as a reference for comparison with the proposed designs. The first structure was selected to maintain the original total wall thickness: a 5 \(\times\) 5 \(\times\) 8 mm\({}^{3}\) cell characterized by a 0.4 mm beam was simulated considering 67 GPa and 74 GPa (ID 1 and 2, respectively). The first frequency was borderline although the weight saving was impressive. A 10 \(\times\) 10 \(\times\) 17 mm\({}^{3}\) was chosen for ID 3: in this case, two cells form the total wall thickness which was increased to 21 mm. The first frequency was not satisfying the specification, but the weight was bigger than the original. Thus, the wall thickness was reduced to 11 mm and a 20 \(\times\) 10 \(\times\) 25 mm\({}^{3}\) was selected. In this configuration, the EOS M400 building limitation is considered and the module was subdivided into four parts. As a consequence, the walls were simulated considering the bonding of the walls on joining surfaces. These modifications added weight and reduced stiffness. This solution is good for weight saving but the first frequency returned below the admissible limit for 67 GPa modulus (ID 4). The simulation employing 74 GPa modulus (ID 5) evidenced that the effect on the natural frequency is limited, and this cell cannot be effectively used. A better result was given by using an 11 \(\times\) 11 \(\times\) 17 mm\({}^{3}\) cell structure at 67 GPa modulus (ID 6). The weight saving, in this case, is about 20%. Since the results obtained by this material were in terms of rigidity, a lower modulus value was simulated in ID 7 evidencing a result just 2 Hz below the frequency request. Till now the wall skin thickness was maintained at 0.5 mm for weight saving. More stiffness is expected for increased thickness. The simulation ID 8 considers 1 mm skin thickness and the same lattice cell. The first natural frequency is now 67 but the weight is 26% more than the original. At this point, the previous configuration was subjected to the optimized design framework. The weight was marginally affected, allowing for more than 18% saving with respect to the original design. The first natural frequency was 48 Hz (ID 9) and 46 Hz (ID 10) at 67 GPa and 60 GPa, respectively. The previous analysis can be summarized by the graph in Figure 14. The green area represents the desired zone where the weight of the module does not exceed the original one and its first natural frequency is higher than the minimum admissible value. It is evident how it is easy to comply with the dynamic requirements by providing a big wall thickness (ST1) or a large structure (WT21) to the detriment of the total weight. A very small structure (WT5) is very light but too close to the frequency limit. A wall thickness of