## 4 Case study
### Topological Optimization Result  
Given the structural application, the definition of a new geometry has been based on the TO approach. Altair Inspire 2019 was used as TO software. An optimized design \begin{table}
\begin{tabular}{c|c c c c c c c c c c c c c c} \hline \hline  & **D1** & **D2** & **D3** & **D4** & **D5** & **D6** & **D7** & **D8** & **D9** & **D10** & **D11** & **D12** & **D13** & **D14** \\ \hline
**D1** & 1.00 & 2.00 & 1.00 & 1.00 & 1.00 & 2.00 & 2.00 & 7.00 & 9.00 & 7.00 & 7.00 & 9.00 & 9.00 \\
**D2** & 0.50 & 1.00 & 0.50 & 0.50 & 0.50 & 1.00 & 0.50 & 1.00 & 5.00 & 2.00 & 2.00 & 2.00 & 1.00 & 7.00 \\
**D3** & 1.00 & 2.00 & 1.00 & 1.00 & 1.00 & 2.00 & 1.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 9.00 \\
**D4** & 1.00 & 2.00 & 1.00 & 1.00 & 0.50 & 2.00 & 1.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 9.00 \\
**D5** & 1.00 & 2.00 & 1.00 & 2.00 & 1.00 & 2.00 & 1.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 7.00 & 9.00 \\
**D6** & 0.50 & 1.00 & 0.50 & 0.50 & 0.50 & 1.00 & 0.50 & 2.00 & 5.00 & 2.00 & 2.00 & 1.00 & 7.00 \\
**D7** & 0.50 & 2.00 & 1.00 & 1.00 & 1.00 & 2.00 & 1.00 & 5.00 & 7.00 & 2.00 & 7.00 & 7.00 & 2.00 & 9.00 \\
**D8** & 0.14 & 1.00 & 0.14 & 0.14 & 0.14 & 0.50 & 0.20 & 1.00 & 2.00 & 1.00 & 1.00 & 1.00 & 1.00 & 5.00 \\
**D9** & 0.11 & 0.20 & 0.14 & 0.14 & 0.14 & 0.20 & 0.14 & 0.50 & 1.00 & 1.00 & 1.00 & 0.50 & 0.50 & 2.00 \\
**D10** & 0.14 & 0.50 & 0.14 & 0.14 & 0.14 & 0.50 & 0.50 & 1.00 & 1.00 & 1.00 & 0.50 & 0.50 & 1.00 & 5.00 \\
**D11** & 0.14 & 0.50 & 0.14 & 0.14 & 0.14 & 0.50 & 0.14 & 1.00 & 2.00 & 2.00 & 1.00 & 1.00 & 1.00 & 5.00 \\
**D12** & 0.14 & 0.50 & 0.14 & 0.14 & 0.14 & 0.50 & 0.14 & 1.00 & 2.00 & 2.00 & 1.00 & 1.00 & 1.00 & 5.00 \\
**D13** & 0.11 & 1.00 & 0.14 & 0.14 & 0.14 & 1.00 & 0.50 & 1.00 & 2.00 & 1.00 & 1.00 & 1.00 & 5.00 \\
**D14** & 0.11 & 0.14 & 0.11 & 0.11 & 0.14 & 0.11 & 0.20 & 0.50 & 0.20 & 0.20 & 0.20 & 0.20 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: AHP pairwise matrix to compute relative weights of the drivers for a generic structural application. \begin{table}
\begin{tabular}{l c} \hline \hline
**Drivers** & **Weight** & **Given Score** \\ \hline (D1) Does the use of AM lead to potential cost savings considering the entire life cycle? & 0.1573 & 9 \\ \hline (D2) Can assembly, logistic or procurement cost be reduced? & 0.0593 & 7 \\ \hline (D3) Can the product benefit from a reduced time-to-market? & 0.1431 & 7 \\ \hline (D4) Is the production batch size limited? & 0.1375 & 9 \\ \hline (D5) Is the post processing phase limited? & 0.1520 & 6 \\ \hline (D6) Can material waste be reduced? & 0.0610 & 8 \\ \hline (D7) Would the product benefit from a mass reduction? & 0.1166 & 10 \\ \hline (D8) It is beneficial to increase the complexity of the part? & 0.0294 & 7 \\ \hline (D9) It is feasible to consolidate parts? & 0.0165 & 1 \\ \hline (D10) Is customization required? & 0.0268 & 4 \\ \hline (D11) Would the product benefit from areas with differentiated material properties? & 0.0284 & 5 \\ \hline (D12) Would the product benefit from varied density along the volume? & 0.0284 & 5 \\ \hline (D13) Is a volumetric lattice or a superficial texture required? & 0.0338 & 5 \\ \hline (D14) Is it advantageous to add functionalities in the parts? & 0.0099 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Potential index calculation for the PPC case. has been developed by selecting the material and imposing the constraints and loads to which the part is subjected. After that, the geometry has been redesigned in Solidworks 2020 to achieve more regular shapes. Standard algorithms to create Non-Uniform Rational B-Spline (NURBS) patches from the tessellated models have not be employed due to the strong irregularity of the surfaces. Instead, a new geometry has been modelled by tracing the OT result. In Figure 8, the new geometry is presented. The new geometry has been verified by an additional FEM simulation, using the Solidworks 2020 dedicated module. Two solutions have been devised, using aluminium and steel as alternative materials.