## 1 Introduction
Its fracture will greatly impact the normal use of cable-stayed bridges. Finite element analysis is a good way to study how a cable-stayed bridge works mechanically. The finite element analysis method can more clearly analyze the structure's mechanical properties in a complex environment. Through the finite element simulation, we can better understand the changing rules of the structure under special working conditions. [PERSON] et al. [24] proposed a modified elastic support method based on the Karopov reduction method. The stability analysis of the double-tower double-plane cable-stayed bridge tower with a large stiffness tower, a small tower span ratio, and small cable spacing can be carried out in the elastic range. [PERSON] et al. [25] compared four methods for calculating the response of cable-stayed bridges after cable breakage: linear static, nonlinear static, linear dynamic, and nonlinear dynamic analysis methods. The bridge's dynamic response after a cable break is thought to be smaller the closer the broken cable is to the cable tower. [PERSON] and [PERSON] [26] studied the dynamic response and dynamic magnification factor of cable fracture by nonlinear dynamic analysis and proposed the corresponding theoretical model. It is suggested that the dynamic magnification factor (DAF) of the main girder's bending moment at its worst position is generally less than 2.0, while the DAF of the cable force and tower bending moment at its worst position is higher than 2.0. [PERSON] and [PERSON] [27] proposed a structural vulnerability assessment method based on the influence degree C of a damage scenario on structural performance and the ratio M of the damage scenario to the total scale of the structural system. Taking the minimum buckling safety factor \(\lambda\) and the maximum stress safety factor \(\mu\) of the main girder as the structural performance parameters, the vulnerability analysis of cable-stayed bridge broken cable damage scenarios at different locations was carried out, which provides a reference for the selection of monitoring content and sensor layout in structural health monitoring. [PERSON] and [PERSON] [28] suggested a framework for evaluating the reliability of long-span cable-stayed bridges after a cable break, and they also came up with a new bridge service limit state that focused on the overall safety and performance of traffic on the bridge after a cable break. Through the similarity ratio theory and stiffness similarity principle, the finite element analysis method is applied to the laboratory scale model. By simulating the unique working conditions of the broken cable, the structure's performance change was studied and analyzed, and good results were found. Through the combination of model testing and finite element analysis, [PERSON] and [PERSON] [29] put forward the influence of cable breakage on the structural behavior of cable-stayed bridges, such as internal force, displacement, and ultimate bearing capacity. The corresponding indicators for cable-stayed bridge cable replacement were provided. [PERSON] et al. [30] established a laboratory finite element model to simulate the fracture process of stay cables. Using the finite element model, theoretical and experimental analyses were used to look at the cable force and the bridge's natural frequency in depth. [PERSON] et al. [31] established a cable-stayed bridge segment scale model to study the distribution law of cable force, girder stress, and deflection under different cable-breaking conditions and girder damage conditions. They summarized the influence of cable failure and girder damage on the static change of a cable-stayed bridge. [PERSON] et al. [32] used a scale model of a single-sided cable-stayed bridge and strain measurements in different places on the bridge deck to find out how much or how little tension was lost in the stay cables. The finite element analysis method was applied to practical engineering projects.