基于离散时间传递矩阵法的变截面刚构桥-地震时程分析方法

Seismic Dynamic Time-history Analysis Method of Rigid Frame Bridge with Variable Cross-section Based on the Discrete Time Transfer Matrix Method

摘要:

为提高变截面刚构桥地震动力时程分析的计算效率,提出了基于离散时间传递矩阵法的时程算法。首先,从欧拉梁的动平衡方程出发,结合逐步时间积分法的线性化方法,基于离散时间传递矩阵法推导了欧拉梁的单元传递矩阵;然后,将变截面刚构桥离散为平面杆系结构,依据张量变换原理将单元状态矢量转换至整体坐标系下,借助分叉点处的协调条件和平衡条件建立了离散体系的整体传递矩阵;最后,借助数值仿真软件,考虑地震荷载的多点输入影响,采用逐步数值迭代求解的方式实现了变截面刚构桥的地震动力时程分析。以某变截面刚构桥为算例完成仿真计算,并与有限元法就数值计算精度和计算效率进行了对比讨论,分析结果论证了本文所提算法的有效性和高效性。

关键词:变截面刚构桥; 地震动力时程分析; 离散时间传递矩阵法; 逐步时间积分法

Abstract:

In order to improve the calculation efficiency of the seismic dynamic time-history analysis for rigid frame bridge with variable cross-sections, a calculation method was established based on the discrete time transfer matrix method. Firstly, employing the linearization method of step-by-step time integration method, the element transfer matrix was derived based on the dynamic equilibrium equation of Euler beam, whose transverse displacement was described by modal coordinates. Secondly, according to the principle of tensor computation, the construction method of the whole transfer matrix for the discrete system of rigid frame bridge with variable cross-sections was derived by means of the coordination matrix and the equilibrium matrix at the bifurcation point. Finally, utilizing the numerical simulation software, the seismic dynamic time-history analysis of rigid frame bridge with variable cross-sections under multiple-support seismic inputs was realized using numerical iteration. Taking a rigid frame bridge with variable cross-sections as an example, the reliability and high computational efficiency of the proposed method were verified by the numerical results as compared to the finite element method.

Key words:rigid frame bridge with variable cross-section; seismic dynamic time-history analysis; discrete time transfer matrix method; step-by-step integration method