# Two-Dimensional Topology Optimization of Headtube in Electric Scooter Considering Multiple Loads
## 4 Results
### Topology Optimization for Multiple-Load Conditions  
Figure 8 shows the comparison of the targets and results of topology optimization considering multiple loads. Overall, the optimized result is similar to the structure of Groups A and B. However, the upper structure of the headtube appears to tilt forward due to the influence of Group B. Notably, the connection points of the board and handle support remain unchanged from Group A, indicating that this location is likely the optimal design for the headtube.  
The strain energy distributions in the comparison targets and optimized results were compared under five load conditions (four single-load conditions and multiple loads). As shown in Figure 9, the comparison target models (Cases B and C) exhibit nonuniform strain energy distributions over the entire domain. Conversely, as shown in Figure 10, the topology optimization result (Case A) exhibits a more uniform strain energy distribution in the connection area than the other cases. This quantitatively confirms that the optimized design distributes strain energy more evenly compared to the comparison models (Cases B and C). Furthermore, the optimized design (Case A) demonstrated at least a 51% improvement in collision performance compared to the commercial models (Table 2). Additionally, the optimized design reduces compliance by dist  
Figure 8: Topology optimization considering multiple loads (Case A) and two commercial models for comparison (Case B and Case C).  
Figure 7: Average and standard deviation of strain energy from topology optimization results for each group.  
evenly throughout the structure (standard deviation of 0.0155-0.0673 N\(\cdot\)mm). However, the comparison commercial models exhibited strain energy concentration with standard deviations between 0.0752 and 0.3546 N\(\cdot\)mm. Positioning the headtube closer to the front wheel increases the strain, intensifying the energy concentration within the structure.  
\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 \hline \multirow{3}{*}{LC 1} & A & 167.5879 & 3.9634 & 0.0135 & 0.0485 \\ \cline{2-6}  & B & 484.8086 & 3.9177 & 0.0392 & 0.1696 \\ \cline{2-6}  & C & 891.5683 & 14.6701 & 0.0721 & 0.3375 \\ \hline \multirow{3}{*}{LC 2} & A & 241.9688 & 5.3093 & 0.0196 & 0.0673 \\ \cline{2-6}  & B & 427.5641 & 3.6456 & 0.0346 & 0.1374 \\ \cline{2-6}  & C & 858.5088 & 20.5374 & 0.0694 & 0.3546 \\ \hline \multirow{3}{*}{LC 3} & A & 63.8170 & 0.6226 & 0.0052 & 0.0155 \\ \cline{2-6}  & B & 282.5795 & 2.8343 & 0.0280 & 0.1154 \\ \cline{1-1} \cline{2-6}  & C & 447.6028 & 8.5388 & 0.0362 & 0.1990 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Collision performance of the topology optimization (A) and two target models (B and C).  
Figure 9: Collision performance of topology optimization design considering multiple loads (Case A) and two models (Case B and Case C) for comparison.