基于有限元-向量式有限元的斜拉桥非线性振动计算方法

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (3) : 129-138.

论文

王涛1，胡宇鹏2，张兴标1，刘德贵1

作者信息 +

Nonlinear vibration calculation method for cable-stayed bridge based on finite element & vector form finite element method

WANG Tao1, HU Yupeng2, ZHANG Xingbiao1, LIU Degui1

Author information +

文章历史 +

摘要

向量式有限元法本质上是考虑几何非线性的有限元显式动力时程积分方法。阐述了向量式有限元的基本原理，对比了向量式有限元与基于单元随动坐标系的非线性有限元动力计算方法的相同点与差别，开发了使用杆、梁单元的有限元-向量式有限元统一算法框架的计算程序。使用该程序建立了大跨度斜拉桥计算模型，首先，使用非线性有限元法计算了斜拉桥的静力状态与动力特性，计算了列车-桥梁耦合动力作用下桥梁的振动；然后，使用向量式有限元计算了斜拉桥在拉索突然断裂状态下的非线性振动；最后，计算了在列车-桥梁耦合动力作用下，拉索发生断裂时，桥梁与列车的振动状态。结果表明：使用向量式有限元可以简单可靠地直接模拟斜拉桥在破坏状态下的非线性振动状态；列车运行至跨中附近时，若斜拉桥跨中最长拉索突然发生断裂，对其它拉索的安全性影响不大，离断裂拉索越远的拉索受到的影响越小，但拉索突然断裂会对桥上行驶中列车的安全性造成威胁。本文为大跨度斜拉桥在破坏状态下的非线性振动分析提供了新的解决方案。

Abstract

Vector form finite element method in essence is an explicit dynamic time-history integration method by considering geometric nonlinearity. The basic principle of vector finite element was described. The similarities and differences between the vector form finite element method and the nonlinear finite element method dynamic calculation based on co-rotational formulation element coordinate system are compared. A program for calculating the unified algorithm framework of finite element and vector form finite element using link and beam elements was developed. It makes up for the shortcomings of the two calculation methods. The calculation model of the long-span cable-stayed bridge was established by using the program. Firstly, the nonlinear finite element method was used to calculate the static state and dynamic characteristics of the cable-stayed bridge, and the vibration of the bridge under the coupled dynamic action of train and bridge was calculated. Then, the nonlinear vibration characteristics of cable-stayed bridge under the condition of sudden cable fracture are calculated by using vector form finite element method. Finally, the vibration state of the bridge and the train when the cable breaking under train-bridge coupled dynamic effect was calculated. The results show that, the nonlinear vibration of cable-stayed bridges under failure can be simulated directly and reliably by using vector form finite element method. When the train runs near the mid-span, if the longest cable breaks suddenly in the mid-span of a cable-stayed bridge, the safety of other cables is not affected much, and the further away from the broken cables, the less affected the cables are. The sudden fracture of the cable can pose a threat to the safety of the moving train. This paper provides a new technical scheme for nonlinear vibration analysis of long-span cable-stayed Bridges under failure condition.

导出引用

王涛1，胡宇鹏2，张兴标1，刘德贵1. 基于有限元-向量式有限元的斜拉桥非线性振动计算方法[J]. 振动与冲击, 2022, 41(3): 129-138

WANG Tao1, HU Yupeng2, ZHANG Xingbiao1, LIU Degui1. Nonlinear vibration calculation method for cable-stayed bridge based on finite element & vector form finite element method[J]. Journal of Vibration and Shock, 2022, 41(3): 129-138

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