# 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
### Dynamic Modal Simulation Results  
The modal analysis of the hydrogen fuel cell city bus body frame was conducted using Optistruct software 2018 (Altair, Troy, MI, USA, 2018), and the first 16 natural frequencies were extracted. Among them, the first six natural frequencies were found to be close to 0, indicating that the first six modes of the bus body frame are rigid modes, resulting in rigid displacements that are not relevant for the analysis in this study. Therefore, the first six natural frequencies were omitted from further consideration. Table 3 shows the natural frequencies for the first 10 modes of the modal analysis, with the lowest natural frequency being 5.97 Hz, which satisfies the low-frequency vibration requirements of the bus body frame.  
Figure 10: Displacement contour plot under emergency cornering condition.  
\begin{table}
\begin{tabular}{c c} \hline
**Order** & **Frequency/Hz** \\ \hline
1 & 5.97 \\
2 & 8.71 \\
3 & 10.57 \\
4 & 11.27 \\
5 & 12.35 \\
6 & 13.59 \\
7 & 13.67 \\
8 & 15.92 \\
9 & 18.62 \\
10 & 19.41 \\ \hline \end{tabular}
\end{table}
Table 3: Frequencies of the bus body’s first ten modes.  
Figure 9: Stress contour plot under emergency cornering condition.  
As shown in Figure 11, under the ultimate torsion condition, the maximum stress value has been reduced from the original 348.6 MPa to 300.6 MPa, which is now below the yield strength of the Q345 material (345 MPa). This indicates that the optimized bus body frame can meet the strength requirements for this condition. Additionally, as depicted in Figure 11, the maximum displacement has decreased from the original 28.401 mm to 23.658 mm, further enhancing the stiffness performance of the bus body frame under this condition.  
Moving on to the emergency cornering condition, as illustrated in Figure 11, the maximum stress value has been reduced from the original 328.9 MPa to 262.7 MPa, which is also below the yield strength of the Q345 material (345 MPa). This shows that the bus body frame has further improved its strength performance under this condition. Furthermore, as shown in Figure 11, the maximum displacement has decreased to 12.474 mm, and it remains within the expected target, satisfying the design stiffness requirements.  
Based on the results obtained from the static simulation tests under these two target conditions, the feasibility and effectiveness of the size optimization method have been demonstrated.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Part ID** & **Initial Value** & **Optimized Value** \\ \hline
1 & 3.0 & 3.2 \\
2 & 2.0 & 3.9 \\
3 & 3.0 & 4.0 \\
4 & 2.0 & 2.6 \\
5 & 1.5 & 1.2 \\
6 & 3.0 & 3.0 \\
7 & 2.0 & 3.0 \\
8 & 5.0 & 3.0 \\  
Figure 11: Stress and displacement contour plots for bus body frame under optimized ultimate torsion and Emergency Cornering Conditions: (**a**) stress contour plot under ultimate torsion condition; (**b**) displacement contour plot under ultimate torsion condition; (**c**) stress contour plot under emergency cornering condition; (**d**) displacement contour plot under emergency cornering condition.