## 3 Structure Design and Optimization  
### Lattice Design  
All original designs of the two types of modules consisted of an outer skin with reinforcing ribs and a coupling interface, characterized by the specifications reported in Table 3. In Figure 3 the modules are shown together with the structural load cases. The modal behavior specification is particularly critical to the extent that the original design cannot satisfy it. In fact, the first natural frequency was 23 Hz. The approach for the part re-design was to fully exploit AM advantages starting from the basic idea of a wall composed of two thin skins connected by a lattice structure, thus abandoning the traditional \"wall with ribs\" based solutions. The two different designs including the traditional one and the lattice solution are presented in Figure 4.  
Figure 2: Exploded diagram of the assembly jig (**a**), assembled jig schematic (**b**) and real part during assembly (**c**). Surfaces to be machined are indicated in red. Lattice structures are an attractive option for lightweighting applications and many cell topologies were investigated. An interesting type is the triply periodic minimal surfaces (TPMS) [57], namely a kind of periodic surface with zero mean curvature described by an implicit mathematical formulation that can be altered to tune its mechanical performance [58]. They were originally discovered by [PERSON] in 1865 who invented the well-known Gyroid (Figure 5a), Primitive (Figure 5b) and Diamond (Figure 5c). Lately, his student [PERSON] discovered the TPMS shown in Figure 5d. The Schoen I-WP exhibits viscoelastic behavior (Figure 5e). The Fischer-Koch S Surface (Figure 5f) has no mirror symmetry which leads to an anisotropic elastic behavior. The potential of AM can be empowered by considering these minimal surfaces; however, some possible issues must be considered. The PBF-LB/M technology has critical problems in the down skin, particularly  
Figure 4: From traditional wall with ribs technology (**a**) to AM technology solution (**b**). Figure 3: Sketch of module 1 (**a**,**b**) and module 2 (**c**,**d**) with the indication of the structural load for case 1 (**a**,**c**) and case 2 (**b**,**d**). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **MODULE 1** & **MODULE 2** \\ \hline Material & Aluminum & Aluminum \\ Mass & 2.78 kg & 5.26 kg \\ Dimensions—h & 200 mm & 150 mm \\ Dimensions—plant & 600 mm \(\times\) 600 mm & 600 mm \(\times\) 600 mm \\ Dimensions—wall thickness & 1 mm & 1 mm \\ Dimensions—wall thickness (overall) & 5 mm & 5 mm \\ Features & Ribs & Ribs \\ Modal behavior & \(\geq\)38 Hz & \(\geq\)38 Hz \\ Structural Loads (Case 1) & 10.5 kN compression, 6.2 kN lateral \\ Structural Loads (Case 2) & 6.2 kN traction, 4.4 kN lateral \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Original design specification and structural loads. with selected aluminum alloys and these TPMS present overhanging zones and even horizontal walls. To have an acceptable roughness it is preferable that the surface angles do not fall below 45\({}^{\circ}\). Moreover, the Gyroid, the Diamond, and the Fischer-Koch S show intricate cavities: in this application, they must be included in relatively thin components, hence the cavities must be very small. This issue is increased by the use of a 1 mm wall thickness. As the component is very large, the powder removal at the end of the fabrication is challenging for TPMS and they were excluded from the satellite design. A tailored \"star-shaped\" lattice that ensured printability without supports, as well as symmetric mechanical characteristics was introduced. Lattice type and basic dimensions were determined by taking into account both AM compatibility and structure requirements (void to full ratio equal to 5%). In particular, the chosen basic element is reasonably easy to print and offers good thermal and mechanical properties making it ideal for applications in the aerospace environment where thermal management capability is crucial [59].