# A Computational Sketch-Based Approach Towards Optimal Product Design Solutions
## 3 Results
### Optimization Process
#### 3.2.2 Topology Optimization and Mesh Refinement
In order to evaluate the performance of the introduced solution, a similar TO process was conducted using the FreeCAD v1.0 software as exhibited in Figure 13. The left part of the figure illustrates the final optimized design of the investigated use cases, where gray areas are visible representing regions with intermediate material densities, which are often undesirable due to manufacturability and performance concerns. These gray areas are  
Figure 12: Optimal configuration adjustments using AMR and the corresponding stressed regions. a common occurrence in TO and are considered undesirable because they do not clearly define whether the material should be present or absent. That specific obstacle could be resolved as in the presented TO framework via the employment of AMR techniques. In addition, the right part of Figure 13 presents the developed stress fields using the optimized geometry of the FreeCAD v1.0, where the maximum equivalent stresses are alike compared to ones computed through the introduced software as seen in the bottom part of Figure 12. Finally, a quantitative analysis of the introduced software's performance is documented in Table 1, coupled with a comparison between the developed TO module and the results of the FreeCAD v1.0 software. To sum up, the introduced TO module could be employed in engineering and design applications in order to create lightweight, high-performance structures by optimizing material distribution within a given design space without the need for deep theoretical or software knowledge. The method is based on a 2D sketch, and the designer can automatically generate a topologically optimized structure, which can be further enchanted \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Results of the Topology Optimization Procedure**} \\ \hline Weight Reduction & \(\approx\)50\% \\ Stiffness Reduction & \(\approx\)15–20\% \\ Induce Fracture & \(\times\) \\ Optimization Process Duration & \(<\)5 min \\ \hline \multicolumn{2}{c}{**Comparison with CAD/CAE Software**} \\ \hline \hline \multicolumn{2}{c}{Introduced Solution} & CAE Software \\ Process Duration & \(<\)5 min & \(\approx\)10 min \\ Technical Skills & \(\times\) & ✓ \\ Post-processing actions & \(\times\) & ✓ \\ Computational resources & \(\times\) & ✓ \\ Max. Stress on Use Case 1 & \(1.1\times 10^{5}\) Pa & \(1.2\times 10^{5}\) Pa \\ Max. Stress on Use Case 2 & \(1.2\times 10^{5}\) Pa & \(1.3\times 10^{5}\) Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative performance enhancements of the proposed approach and comparison with FreeCAD v1.0. Figure 13: Outcomes of the topology optimization process and the corresponding stress fields using FreeCAD v1.0. via sophisticated CAD software packages. In addition, the methodology is not resource-hungry; hence it can be run on personal workstations. Despite its advantages, the developed software faces limitations like manufacturability constraints where complex generated geometries may not be feasible for traditional manufacturing methods like CNC machining or casting. Furthermore, the software in its present form can handle only 2D problems and is affected by the source of the sketch data, where the sketch must be a closed geometry, and the symbols for support structures and external forces should be clearly drawn.