基于离散时间传递矩阵法的变截面梁地震时程分析方法研究

为提高变截面梁地震动力求解的计算效率，提出了基于离散时间传递矩阵法的时程分析方法。首先，从欧拉梁的偏微分振动方程出发，基于逐步时间积分法的线性化方法并结合张量变换原理，建立了变截面梁的动力时程计算方法；其次，考虑地震动激励的非一致输入效应，采用数值迭代求解的方式建立了变截面梁地震动力时程分析的离散时间传递矩阵算法；最后，编制了数值仿真计算程序，并结合具体算例进行了算法的有效性和高效性验证。算例结果表明:在采用相同计算模型的前提下，离散时间传递矩阵法不仅能够在计算精度方面与有限元法保持一致，同时还拥有更高的计算效率。

Seismic dynamic time-history analysis method of beam with variable cross-section based on the discrete time transfer matrix method

In order to improve the computational efficiency of seismic dynamic solution of a beam with variable cross-section, a time-history analysis method based on the discrete time transfer matrix method was proposed. Firstly, based on the partial differential vibration equation of Euler-Bernoulli beam, employing the linearization method of the step-by-step time integration and combining with the tensor transformation principle, the dynamic time-history analysis method of beam with variable cross-section was established. Secondly, considering the inconsistency input effect of ground motion excitation, the discrete time transfer matrix algorithm for seismic dynamic time-history analysis of beam with variable cross-section was established by the numeric iteration method. Finally, by means of computer program, the validity and efficiency of that method were verified. The results are as follows. Compared to the FEM, the proposed method not only has almost the same calculation accuracy but also a higher computational efficiency under the premise of adopting the same calculation model.