## 4 PBF-LB/M Process
### Design
#### 4.1.2 Structural Optimization  
The growing focus on sustainable transportation and the quest for higher efficiency, specifically through reduced energy consumption, has spurred research efforts to develop lightweight and strong designs. Reducing vehicle weight is a pivotal strategy for decreasing petroleum consumption and greenhouse gas emissions. Studies indicate that a 100 kg reduction in vehicle weight can lower fuel consumption by approximately 0.69 1/100 km [72] and lead to a decrease of 6 g/km in CO\({}_{2}\) emissions. Each kilogram of weight reduction contributes to a total reduction of approximately 20 kg of CO\({}_{2}\) emissions over a vehicle operational lifespan [105]. Two main strategies for achieving lighter structures have emerged: topology optimization (TO) and lattice. TO is a method of optimizing shapes by algorithmically adjusting material distribution within a specified space to meet prescribed loads, conditions, and constraints. The most prominent TO approaches can be summarized as follows: density-based; level set; evolutionary; topological derivatives; and phase field and homogenization [106; 107; 108]. Density-based TO is widely used in academia and generally follows a standard procedure. This approach is structured using the finite element method [109] where each element density is a design variable, allowing for an optimal layout of element distribution within the designated design area. In density-based TO, elements are assigned density values ranging from 0 to 1, where 0 signifies a void, 1 signifies a solid, and values between 0 and 1 indicate intermediate densities. To enforce a discrete combination of solid and \begin{table}
\begin{tabular}{c c c} \hline  & **Name** & **References** \\ \hline \multirow{4}{*}{**Traditional alloys**} & AlSi10 Mg & [94] \\ \cline{2-3}  & AlSi7 Mg & [95] \\ \cline{2-3}  & AlSi12 & [96] \\ \cline{2-3}  & Al6061 & [97] \\ \hline \multirow{4}{*}{**Modified alloys**} & A1000-RAM10 & [85] \\ \cline{2-3}  & A6061-RAM2 & [85] \\ \cline{2-3}  & A7050-RAM2 & [85] \\ \cline{2-3}  & Al2024 + Y element & [98] \\ \cline{2-3}  & Al7075 + Si element & [99] \\ \cline{2-3}  & Al7075 + ZrH\({}_{2}\) elements & [77] \\ \cline{2-3}  & Al6061 + ZrH\({}_{2}\) elements & [77] \\ \cline{2-3}  & AlMgty & [100] \\ \cline{2-3}  & AlZnty & [100] \\ \hline \multirow{4}{*}{**Tailored alloys**} & Al8 Ce10 Mg & [80] \\ \cline{2-3}  & Al-Fe-Zr (CP1) & [92] \\ \cline{2-3}  & Al-Mn-Ni-Cu-Zr (HT1) & [91] \\ \cline{2-3}  & Al-Mg–Li–Ag–Sc-Zr & [101] \\ \cline{2-3}  & AlZnMgScZr & [102] \\ \cline{2-3}  & Al58 Zn28 Mg6 Si8 & [103] \\ \cline{2-3}  & Al-mg-Sc (Scalmalloy) & [88] \\ \cline{2-3}  & Al-Ni-Cu & [104] \\ \cline{2-3}  & Al-Cu-Ag-Mg (A20X) & [90] \\ \hline \end{tabular}
\end{table} 
Table 2: Aluminum powders suitable for PBF-LB/M technique. void regions, density-based TO leverages the Solid Isotropic Material Penalization (SIMP) method, which penalizes intermediate-density elements. The SIMP method addresses a minimization problem typically involving the volume fraction of the design space or structural compliance (C). The goal is to maximize the stiffness of the structure, which can be evaluated over the entire domain or within the designated design space. Various constraints, such as mass, load, or displacement limits, can be applied, and customized objective functions with weighted criteria can be incorporated. Furthermore, TO can be adapted to include manufacturing constraints, ensuring that the resulting designs are feasible for fabrication [110]. The general formulation of the SIMP method for the compliance minimization problem is as Equation (1) [111; 112]:  
\[Minimize\;C=\frac{1}{2}\sum_{i=1}^{L}f_{i}u_{i}^{\mathrm{T}}=\frac{1}{2}\sum_ {i=1}^{L}f_{i}^{2}{({({\rho_{i}})^{P}{k_{0}}})^{-1}} \tag{1}\]  
In this equation, \"C\" represents compliance, \"\(f\)\" is the external load vector, \"\(u\)\" is the global displacement vector, and \"\(L\)\" is the total number of finite elements.