## 3 Finite Element Model of a 6 \(\times\) K31 WS + FC Wire Rope
### Pre-Processing of the Finite Element Model
#### 3.2.2 Mesh Setup  
To improve the efficiency and convergence of the proposed finite element model, the seeding edges method is used and the wire rope is carefully gridded. The number of seeds on the end face and generatrix of each wire is 12 and 300, respectively. The neutral axis algorithm is adopted to generate an inertratic grid for the model, which is meshed into a hexahedron element with 402,135 nodes and 308,800 elements, as shown in Figure 8.  
To find the most suitable element type in the analysis of the wire rope, a model with 1/6 pitch of a 6 \(\times\) K31 WS + FC wire rope loaded by axial strain \(\varepsilon\) = 0.01 is established, which is depicted in Figure 9.  
The contact properties are identical, as specified in Section 3.2.1. The simulation results of six feasible element types are listed in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Element** \\ **Type** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Severe** \\ **Discontinuous** \\ **Iterations** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Time (s)** \\ **Elements** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Elements** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Nodes** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Maximum** \\ **Stress (MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Maximum** \\ **Deformation (mm)** \\ \end{tabular} } \\ \hline C3D8 & 0 & \(1.34\times 10^{3}\) & \(5.69\times 10^{5}\) & \(1.09\times 10^{6}\) & \(1.35\times 10^{3}\) & \(8.82\times 10^{-2}\) \\ C3D8R & 0 & \(1.39\times 10^{3}\) & \(5.69\times 10^{5}\) & \(1.09\times 10^{6}\) & \(1.18\times 10^{3}\) & \(1.10\times 10^{-1}\) \\ C3D8I & 0 & \(1.27\times 10^{3}\) & \(5.69\times 10^{5}\) & \(1.55\times 10^{6}\) & \(1.53\times 10^{3}\) & \(9.397\times 10^{-2}\) \\ C3D8S & 0 & \(1.43\times 10^{3}\) & \(5.69\times 10^{5}\) & \(1.09\times 10^{6}\) & \(1.37\times 10^{3}\) & \(8.82\times 10^{-2}\) \\ C3D20 & 7 & \(4.18\times 10^{3}\) & \(1.72\times 10^{6}\) & \(3.80\times 10^{6}\) & \(1.42\times 10^{3}\) & \(9.17\times 10^{-2}\) \\ C3D20R & 5 & \(3.55\times 10^{3}\) & \(1.05\times 10^{6}\) & \(2.40\times 10^{6}\) & \(1.42\times 10^{3}\) & \(8.64\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysis results of 6 feasible element types.  
Figure 8: Refined finite element mesh of a 6 \(\times\) K31 WS + FC wire rope.  
Figure 9: Constraints and boundary conditions in 1/6 pitch of a 6 \(\times\) K31 WS + FC wire rope.  
In Table 4, the model meshed by quadratic elements C3D20 and C3D20R have a much greater number of elements and nodes than the other element types. Moreover, the excessive elements and nodes of C3D20 and C3D20R caused severe discontinuous iterations during the calculation. The aforementioned reasons make the analysis efficiency of C3D20 and C3D20R much lower than other types of elements, while the values of maximum stress and maximum deformation do not show many differences. In addition, the solution time of quadratic elements is about three times longer than that of linear elements. Thus, C3D20 and C3D20R are not suitable for the finite element simulation of a 6 \(\times\) K31 WS + FC wire rope. Although the hourglass effect is well suppressed by the additional degrees of freedom in C3D8I, it can cause greater stress and deformation. The rigidity of C3D8S and C3D8 is too large. All three types of elements, C3D8I, C3D8S, and C3D8, are not consistent with the actual material properties of the wire rope. As for C3D8R, it overcame the shortcomings of the above element types in the finite element simulation of a 6 \(\times\) K31 WS + FC wire rope and had good computational efficiency and accuracy, so it is adopted in the following analysis.