Abstract: Based on the nonlinear FEM computational theory of co-rotational (CR) formulation, a Newmark-β nonlinear FEM dynamic time-history algorithm for the structures of truss and beam was proposed. The geometric nonlinearity of the structures could be considered in the time-history calculation. The real displacement and internal force of the elements could be obtained by calculating the element extension and by deducting the rigid body displacement of the structure. The calculation principles of the geometric nonlinearity dynamic program were elaborated. A calculation program was developed and the FEM model was established. The comparison was carried out between the example and the calculation results of the ANSYS. The results show that the difference of the calculation results between the program and ANSYS on nonlinear static and dynamic time-history is very small, and the program is faster than ANSYS, which is applicative for large amplitude vibration calculation of truss and beam structures.

Key words: bridge engineering, FEM program, co-rotational formulation, geometric nonlinearity, dynamic time-history, stayed cable

摘要： 基于CR列式非线性有限元计算理论，提出了针对杆、梁结构的Newmark-β非线性有限元动力时程积分算法,在动力时程计算中，可以考虑结构的几何非线性效应，通过计算单元伸长并 扣除结构刚体位移得到单元的实际变形和内力；阐述了非线性有限元动力时程计算程序的计算原理,开发了计算程序，建立有限元模型；通过算例与ANSYS的计算结果进行了对比。结果表明： 程序非线性静力与动力时程计算结果与ANSYS差别很小，且计算速度更快，程序算法正确可靠，适用于杆、梁结构大幅度非线性振动的计算。

关键词: 桥梁工程, 有限元程序, CR列式, 几何非线性, 动力时程, 斜拉索