## 5 Simulation Experimental Results and Discussions
### Structural Configurations of Topology Optimization and Results of Geometric Reconstruction  
Table 9 presents the TO structural configurations and their geometric reconstruction results obtained from orthogonal experiments via hexahedral and tetrahedral meshes. According to Table 9, it can be seen that, based on the recommended standards for influencing factors proposed in Section 3, the orthogonal experiments resulted in high-performance TO structural configurations. Subsequently, the obtained TO structural configurations were reconstructed according to the geometric reconstruction criteria and the geometric reconstruction approach by the FEA on the reconstructed models using a tetrahedral mesh size of 2 mm. The obtained results are provided in Table 10. The analyses reveal that the maximum stress of the reconstructed gooseneck chain primarily occurs in the stress singularity and stress concentration areas around the ear flange and the bolt connection hole. Since the maximum stress values in these areas do not reflect the actual situation and are not the focus of the present study, after removing the stress singularity and stress concentration regions, the neck of the gooseneck chain became the main maximum stress region. Compared with the hexahedral mesh, the recommended standards for influencing factors based on the tetrahedral mesh lead to more stable structural configurations in orthogonal experiments that eventually converge to the global optimal solution, thus confirming the effectiveness of the recommended standards.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mesh Type**} & \multirow{2}{*}{**Level No.**} & \multicolumn{3}{c}{**Factor Level**} \\ \cline{3-5}  & & **C** & **D** & **E** \\ \hline \multirow{3}{*}{Hexahedral} & 1 & 1.75 & 4.6 & 3 \\  & 2 & 2 & 4.8 & 3.5 \\  & 3 & 2.5 & 5 & 4 \\ \hline \multirow{3}{*}{ Tetrahedral} & 1 & 3.5 & 5.2 & 2.5 \\  & 2 & 4 & 5.6 & 3 \\ \cline{1-1}  & 3 & 4.5 & 6 & 3.5 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Factors and levels utilized in the orthogonal experimental design.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Hexahedral**} & \multicolumn{3}{c}{** Tetrahedral**} \\ \cline{2-7}  & **C** & **D** & **E** & **C** & **D** & **E** \\ \hline \multirow{2}{*}{\(1\)} & 1.75 & 4.80 & 4.00 & 3.5 & 6.0 & 3.0 \\  & 1.75 & 5.00 & 3.50 & 3.5 & 5.2 & 2.5 \\  & 1.75 & 4.60 & 3.00 & 3.5 & 5.6 & 3.5 \\  & 2.00 & 5.00 & 4.00 & 4.0 & 5.2 & 3.0 \\  & 2.00 & 4.80 & 3.00 & 4.0 & 6.0 & 3.5 \\  &  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Hexahedral Mesh**} & \multicolumn{2}{c}{**Tetrahedral Mesh**} \\ \cline{2-5}
**No.** & **Structural** & **Geometric** & **Structural** & **Geometric** \\  & **Configuration** & **Configuration** & **Configuration** & **Configuration** \\ \hline
1 & & & & \\
2 & & & & \\
3 & & & & \\
4 & & & & \\
5 & & & & \\
6 & & & & \\
7 & & & & \\
8 & & & & \\
9 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 9: TO structural configurations and geometric reconstruction results from orthogonal experiments via hexahedral and tetrahedral meshes.