## 6 Conclusions  
This paper proposed an accurate and efficient framework for analyzing the mechanical characteristics of a wire rope with a complex structure, and also provided a practical method to quantitatively evaluate the performance of a complex wire rope with wire breakage. First, an accurate 3D geometry modeling method for a wire rope with a complex structure has been proposed. Second, the material properties of the wire constituting the rope have been tested to facilitate the building of the finite element model of the wire rope. Third, the most feasible element type in the finite element analysis of a wire rope with a complex structure has been investigated. Then, the finite element model of the wire rope with a complex structure is built, and the mechanical characteristics of a 6 \(\times\) K31 WS + FC wire rope are  
Figure 23: Stress distribution in the middle cross-section of the wire rope with a tensile force of 30 kN in cases (**a**), cases (**b**), cases (**c**), cases (**d**), cases (**e**), cases (**f**), cases (**g**), cases (**h**), cases (**i**), cases (**j**), cases (**k**) and cases (**l**).  
Figure 22: The cross-section area and the maximum stress of the wire rope along different wire-breaking conditions.  
figured out, with its effectiveness having been validated by theoretical analysis. Finally, a quantitative relation of the number and location of broken wires with the mechanical characteristics of the wire rope is thoroughly analyzed. The approach proposed in this work can facilitate the optimization of the structure of the wire rope, such as lay angle, lay direction, wire radius, etc., and it also can provide valuable data for reliability and maintenance evaluation of the wire rope in practical operation. The main conclusions of this work are as follows:  
(1) C3D8R is an appropriate element type, and it is advisable for it to be adopted in finite element analysis of wire ropes with complex structures in terms of computational accuracy, efficiency, and convergence.  
(2) The maximum stress cross-section appears at both ends of a 6 \(\times\) K31 WS + FC wire rope regardless of whether there is a broken wire. Thus, we should carefully check the region at both ends of the wire rope when examining the wire rope condition.  
(3) The number and location of the broken wires have a great influence on the maximum stress of the wire rope. A small cross-section area decrease could induce a dramatic increase in the maximum stress. Thus, the wire rope must be carefully examined and analyzed before it can be continued to be used when there is wire breakage.  
(4) Stress distribution in the middle cross-section of the wire rope reveals that the stress of the remaining wires in the strand with broken wires is less than that of the wires in the same position in the intact strands. This phenomenon indicates the bearing capacity of the strand has been weakened, especially when the number of broken wires increases.  
Conceptualization, Q.D.; Software, K.Y.; Formal analysis, K.Y.; Resources, J.G.; Writing-review & editing, K.Y., Q.D., M.S. and F.Y. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the Foundation Enhancement Program for National Defense Science and the Fundamental Research Funds for the Central Universities (Grant Nos. 307202 QBZ0206 and 3072022 CF0218).  
Not applicable.  
Data Availability Statement: Data available on request due to privacy.  
The authors declare no conflict of interest.