Abstract:A precise Runge-Kutta hybrid integration method with high accuracy is constructed to solve structural nonlinear problems without iteration, in which the Duhamel term of state equation of the precise integration method is expanded in terms of 4-order Runge-Kutta method. Based on the method, an efficient analysis framework for dynamic interaction analysis of train-bridge system is proposed. The train-bridge system consists of a train subsystem and a bridge subsystem, and both subsystems are established by using finite element method. The rigid component assumption is introduced to the train subsystem, while the mode superposition method is applied to the bridge subsystem to reduce the number of degree-of-freedom. The inner nonlinear effect of both subsystems and the dynamic interaction between two subsystems are taken as virtual forces. A 4-axle vehicle passing through the simply supported beam with 32m span at constant speed is taken as a case study. The dynamic analysis of the coupled system is carried out by using the proposed framework and the Runge-Kutta method. The comparison of numerical results shows that the convergent time interval of precise Runge-Kutta hybrid integration method may be greatly larger than that of Runge-Kutta method, and that the proposed framework may be expanded in practice.