# Finite Element Analysis and Optimization of Hydrogen Fuel Cell City Bus Body Frame Structure
## 3 Simulation Analysis of Static and Dynamic Characteristics of Bus Body Frame
### Performance Comparison Analysis before and after Optimization  
Based on the static simulation results of the four typical conditions conducted on the bus body frame before and after optimization, a comparison of the maximum stress and maximum displacement results is presented in Table 5.  
The comparison results of the first ten natural frequencies of the bus body frame before and after optimization are shown in Table 6. After optimization, the first natural frequency increases to 6.44 Hz, which is no longer within the range of external excitation resonance, meeting the design requirements of the body frame. Under static simulation tests, according to Table 5, it can be observed that the optimization results for the selected ultimate torsion and emergency cornering, which are the two critical operating conditions in this study, are quite satisfactory. Under the ultimate torsion condition, the maximum stress in the optimized bus body frame decreased from 348.6 MPa, which exceeded the material yield strength, to 300.6 MPa, representing a reduction of 13.77% compared to the pre-optimization value, thereby meeting the design requirements for strength. Additionally, the maximum displacement decreased by 4.743 mm, accounting for a reduction of 16.70%, resulting in an improvement in the stiffness performance of the body frame. Subsequently, under the emergency cornering condition, the maximum stress was reduced to 262.7 MPa after optimization, indicating a significant reduction of 20.13% and staying far from the material's yield strength. The maximum displacement was also reduced by 6.97% after optimization. Finally, under the other two typical operating conditions after optimization, the strength and stiffness performance of the bus body frame were improved to varying degrees. The results above validate the effectiveness of the optimization method. In the actual operation of buses, low-frequency vibrations are often more dangerous than high-frequency vibrations. Therefore, this study focuses on analyzing the first ten mode frequencies of the bus body frame. Under the dynamic modal simulation test, a comparison of the mode frequencies before and after optimization is presented in Table 6. It is observed that after optimization, each mode frequency increases by less than 1 Hz, with \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Order** & **Initial Value (Hz)** & **Optimized Value (Hz)** & **Change (Hz)** \\ \hline
1 & 5.97 & 6.44 & 0.47 \\
2 & 8.71 & 8.82 & 0.11 \\
3 & 10.57 & 10.63 & 0.06 \\
4 & 11.27 & 11.32 & 0.05 \\
5 & 12.35 & 12.57 & 0.22 \\
6 & 13.59 & 13.65 & 0.06 \\
7 & 13.67 & 14.59 & 0.92 \\
8 & 15.92 & 15.97 & 0.05 \\
9 & 18.62 & 18.92 & 0.30 \\
10 & 19.41 & 19.68 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the first ten modal frequencies before and after optimization. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multicolumn{2}{c}{**Maximum Stress (MPa)**} & \multirow{2}{*}{**Change**} & \multicolumn{2}{c}{**Maximum Displacement (mm)**} & \multirow{2}{*}{**Change**} \\ \cline{2-2} \cline{4-6}  & **Initial Value** & & & **Initial Value** & & **Optimized Value** \\ \hline Horizontal bending & 220.7 & 207.3 & \(-\)6.07\% & 7.723 & 6.116 & \(-\)20.81\% \\ \hline Ultimate torsion & 348.6 & 300.6 & \(-\)13.77\% & 28.401 & 23.658 & \(-\)16.70\% \\ \hline Emergency braking & 305.6 & 262.4 & \(-\)14.14\% & 10.045 & 8.084 & \(-\)19.52\% \\ \hline Emergency cornering & 328.9 & 262.7 & \(-\)20.13\% & 13.408 & 12.474 & \(-\)6.97\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of maximum stress and displacement for four typical operating conditions before and after optimization. the first mode frequency increasing to 6.44 Hz. Moreover, the overall modal frequencies range between 6.44 Hz and 19.68 Hz, and each mode frequency increases steadily without any significant abrupt changes. This observation indicates a well-connected and stable overall structure of the bus body frame.