# Topology and Parametric Optimization-Based Design Processes for Lightweight Structures
## 4 Results
### Comparison of the Three Applied Design Workflows
On the other hand, any interesting correlation among the stress results cannot be identified. It appears that they are dependent on the specific model in each design process. However, they are always stuck to the given stress rule (\(\sigma_{\max}\leq 125\) MPa). Of course, one could claim that since the TO has been performed for stiffness, the stress comparison is not legitimate. However, compliance minimization is expected to result in an iso-stressed optimized boundary; thus, in general, reducing stress concentrations. Since stress-based optimization is far more complicated than compliance minimization, the authors preferred to use the latter in this work. Finally, the optimization time is increasing dramatically from the first to the last design workflow. Hence, a regression analysis was conducted in order to identify a correlation between mass reduction and time. The interval plot, depicted in Figure 18d, shows the means and the confidence intervals (CI) of the mass reduction in each design workflow for all case studies together. As it has already been mentioned, the TO workflow resulted in the smallest mass reduction while the simultaneous PO and  
\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}{*}{ \begin{tabular}{c} **Mass** \\ **Process** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Mass** \\ **Reduction** \\ **(g)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Mass** \\ **Reduction** \\ **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Mass** \\ **Reduction** \\ **Rate (g/min)** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Max** \\ **Stress** \\ **(MPa)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Time** \\ **(min)** \\ \end{tabular}  } \\ \hline \multicolumn{8}{c}{L-Bracket} \\ \hline \multicolumn{8}{c}{Initial} & 849.1 \\ \hline \multirow{4}{*}{TO} & 1 & 344.6 & 504.5 & 59.4\% & 68.2 & 101 & 7.4 \\ \cline{2-8}  & 2 & 343.4 & 505.7 & 59.6\% & 29.6 & 115.4 & 17.1 \\ \cline{2-8}  & 3 & 318.5 & 530.6 & 62.5\% & 8.4 & 106.4 & 63.3 \\ \hline \multirow{4}{*}{PO} & 4 & 71.1 & 778 & 91.6\% & 11.5 & 95.9 & 67.4 \\ \cline{2-8}  & 5 & 65.1 & 784 & 92.3\% & 11.5 & 121 & 68 \\ \cline{2-8}  & 6 & 63.9 & 785.2 & 92.5\% & 10.8 & 96.3 & 73 \\ \cline{2-8}  & 7 & 55.9 & 793.2 & 93.4\% & 7.4 & 114 & 106.7 \\ \hline \multirow{4}{*}{PO + TO} & 8 & 28.8 & 820.3 & 96.6\% & 2.2 & 84.3 & 374.6 \\ \cline{2-8}  & 9 & 27.1 & 822 & 96.8\% & 2.2 & 81.8 & 379.6 \\ \cline{2-8}  & 10 & 23.2 & 825.9 & 97.3\% & 2.0 & 105.6 & 413.2 \\ \hline \multicolumn{8}{c}{MBB-Beam} \\ \hline \multicolumn{8}{c}{Initial} & 471 \\ \hline \multirow{4}{*}{TO} & 1 & 113.9 & 357.1 & 75.8\% & 115.2 & 65.3 & 3.1 \\ \cline{2-8}  & 2 & 113.6 & 357.4 & 75.9\% & 15.6 & 26.2 & 22.9 \\ \cline{2-8}  & 3 & 52.8 & 418.2 & 88.8\% & 6.4 & 27.6 & 64.9 \\ \hline \multirow{4}{*}{PO} & 4 & 39.3 & 431.7 & 91.7\% & 6.6 & 85.6 & 65.6 \\ \cline{2-8}  & 5 & 14.9 & 456.1 & 96.8 TO led to the most lightweight structures. The PO design workflow was placed second with little difference compared to the simultaneous one. In addition, Table 9 contains all the essential statistics in each workflow. The regression equations in each of the three workflows are the following:  
TO: Mass Reduction = 447.7 + 1.82 \(\times\) time, (27)  
PO: Mass Reduction = 603.1 + 1.82 \(\times\) time, (28)  
and PO + TO: Mass Reduction = 254.0 + 1.82 \(\times\) time  
Furthermore, the mass reduction rate in the three workflows is shown in Figure 19. The total mass reduction in the simultaneous PO and TO was the highest; however, concerning the time effectiveness was the worst. The TO design workflow could result in rapid material savings for the structures. Thus, the designers looking for a quick mass reduction should go with the TO. In the case that there is a need for a further mass reduction, they can continue with the PO.