# Topology and Parametric Optimization-Based Design Processes for Lightweight Structures
## 4 Results
### Comparison of the Three Applied Design Workflows  
In this section, differences and similarities of the results in the three implemented design workflows will be identified. It is important to recap that when we mention here TO, PO, and simultaneous PO and TO design workflows, we are referring to the workflows as they were presented in Figure 3. All these workflows were a combination of topology and size/shape optimization. However, they differ in the execution order of their optimization levels. As it was presented in Section 1, the TO workflow began with a TO of the structure and could be either ended with a validation study, at the second level or be continued with a further PO on the third level. On the contrary, the PO workflow began with a PO and could be followed up with a TO and a second PO. Finally, the third design workflow was simultaneous parametric and topology optimization. In addition, all the applied design processes in these workflows were clustered into the processes with or without redesign at the post-processing. In this way, the CMP could be added as an alternative to AM. Thus, ten different design processes that were committed in each case study made them 30 simulations in total. The results of all the implemented simulations are summarized in Table 8. It is observed that there is a gradual mass reduction of the three structures from the first to the tenth design process, while the optimization time is increasing. Comparing the three design workflows, the simultaneous PO and TO, at design process (10), resulted in the most lightweight structures. The mass reduction here of the Hollow Plate, L-Bracket, and MBB-Beam were 96.9%, 97.3%, and 99.1%, respectively. In addition, the highest mass reduction in the PO workflow could be achieved at process (7) with 95%, 93.4%, and 97.7% mass saving in the three cases. Finally, the dominant process in the TO workflow was process (3) with 74.1%, 62.5%, and 88.8% mass reduction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Design** \\ **Workflow** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Design** \\ **Process** \\ \end{tabular} } & \multirow{2}{*}{**Mass**} & \begin{tabular}{c} **Mass** \\ **Reduction** \\ **(g)** \\ \end{tabular} & \begin{tabular}{c} **Mass** \\ **Reduction** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Mass** \\ **Reduction** \\ **Rate (g/min)** \\ \end{tabular} & \
\begin{tabular}{c} **Max** \\ **Stress** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Time** \\ **(min)** \\ \end{tabular} \\ \hline \multicolumn{8}{c}{Hollow Plate} \\ \hline \multicolumn{8}{c}{Initial} & 1103.5 \\ \hline \multirow{4}{*}{TO} & 1 & 450.7 & 652.8 & 59.2\% & 118.7 & 120.1 & 5.5 \\ \cline{2-8}  & 2 & 448.1 & 655.4 & 59.4\% & 32.6 & 60.2 & 20.1 \\ \cline{2-8}  & 3 & 285.9 & 817.6 & 74.1\% & 11.6 & 109.4 & 70.4 \\ \hline \multirow{4}{*}{PO} & 4 & 101.5 & 1002 & 90.8\% & 13.2 & 55.7 & 75.9 \\ \cline{2-8}  & 5 & 66.6 & 1036.9 & 94.0\% & 13.5 & 94.8 & 76.9 \\ \cline{2-8}  & 6 & 65.6 & 1037.9 & 94.1\% & 12.0 & 106.5 & 86.8 \\ \cline{2-8}  & 7 & 55.5 & 1048 & 95.0\% & 8.4 & 115.4 & 124.7 \\ \hline \multirow{4}{*}{PO + TO} & 8 & 45 & 1058.5 & 95.9\% & 3.8 & 75.2 & 275.5 \\ \cline{2-8}  & 9 & 39.8 & 1063.7 & 96.4\% & 3.7 & 115.4 & 285.5 \\ \cline{1-1} \cline{2-8}  & 10 & 34.7 & 1068.8 & 96.9\% & 3.3 & 114.6 & 323.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: An overview of the simulations’ results in the three case studies. The results of mass, maximum stress, and optimization time are categorized into the three design workflows and are depicted in Figure 18. It seems that the mass of the design solutions in the TO workflow is not converged from design process (1) to (3). On the other hand, the PO and the simultaneous PO and TO workflows have almost been converged. Thus, using these two design workflows, a high mass reduction can be attained even with one design process, such as processes (4) and (8).