# Two-Dimensional Topology Optimization of Headtube in Electric Scooter Considering Multiple Loads
## 5 Discussion  
This study successfully demonstrates how single-load topology optimization can be extended to multiple-load conditions to achieve an optimal structural configuration. The results indicate that the optimized structure integrates key features from different load cases, resulting in a more robust and efficient design. The final optimized structure closely resembles the configurations of Groups A and B, confirming that topology optimization effectively generates optimal designs for complex structures subjected to multiple loads. Unlike designs strictly derived from a single-load condition, the optimized configuration integrates structural features from multiple groups, particularly Groups A and B, to accommodate multidirectional and multi-axial loads. This adaptability highlights the robustness of topology optimization in addressing varying load conditions, offering valuable insights for future structural developments and providing a deeper understanding of topology optimization under diverse loading scenarios. Additionally, the optimized design improves the load distribution, reducing the strain energy concentration and enhancing the overall performance. Specifically, the topology \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Loading** & **Model** & **Compliance** & \multicolumn{3}{c}{**Strain Energy [N\(\cdot\)mm]**} \\ \cline{3-6}
**Condition (LC)** & **(Case)** & **[N\(\cdot\)mm]** & **Max.** & **Avg.** & **Std.** \\ \hline \multirow{4}{*}{LC 4} & A & 138.1978 & 1.9685 & 0.0112 & 0.0367 \\ \cline{2-6}  & B & 225.3350 & 1.7904 & 0.0182 & 0.0752 \\ \cline{2-6}  & C & 414.5432 & 7.4465 & 0.0335 & 0.1596 \\ \cline{2-6}  & A & 105.0518 & 2.3131 & 0.0085 & 0.0290 \\ \cline{2-6}  & B & 298.7380 & 2.2340 & 0.0241 & 0.1022 \\ \cline{2-6}  & C & 549.4200 & 9.1967 & 0.0444 & 0.2050 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 10: Comparison of the average values of strain energy for each model (Cases A, B, and C) under different loading conditions. optimization result (Case A) exhibits a more uniform strain energy distribution than the comparison commercial models. This aligns with established structural optimization theories, which suggest that an ideal optimized structure evenly distributes stress and utilizes all parts of the structure efficiently. Moreover, the optimized headtube was also analyzed in terms of its behavior under each of the four load conditions. Figure 9 shows that the individual load could not achieve a uniform strain energy distribution in the Case A structure. However, the results of Case A, considering all three loads, indicate a more uniform strain energy distribution. This means that the topology optimization structure is designed to cope with complex multidirectional and multiaxial loads when driving an electric scooter, not a design optimized for a single load. This result is consistent with the findings of [PERSON] et al. [14], who determined that the strain energy distribution of trabecular architecture becomes more uniform during optimization to support various daily activities. Existing electric scooters are simple in structure and easy to manufacture but are not designed to consider the various load conditions that can occur while driving. Therefore, it should be emphasized that topology optimization results considering multiple loads are safer than those of existing commercial models. Table 2 clearly shows that the collision performance of the optimized design increased by at least 51% compared with that of the existing commercial models. Overall, topology optimization appears to be promising for improving the driving safety of electric scooters. Although the optimized headtube design demonstrates a more uniform strain energy distribution, localized stress concentrations may still occur owing to two main factors.