Dynamic analysis framework of train-bridge system based on improved Gauss precise integration method

With the assumption that the displacement of any moment can be determined by the motion of its two adjacent time steps with the help of a Hermite interpolating function, an improved Gauss precise integration method is constructed to solve the structural nonlinear problems, in which the Duhamel term of a state equation of a precise time-integration method is expanded in terms of 3-node Gauss integration method. On the basis of the improved method, an efficient analysis framework for the dynamic interaction analysis of a train-bridge system is proposed. The train-bridge system consists of train subsystems and bridge subsystems, and both of them are established with the finite element method. The rigid component assumption is introduced to the train subsystem, the mode superposition method is applied to the bridge subsystem to reduce the degrees-of-freedom, and the dynamic interaction between two subsystems is expressed with nonlinear virtual forces. A 4-axle vehicle passing through a simply-supported beam with a 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 traditional Newmak-β method, respectively. The numerical results show that the improved Gauss precise integration method not only avoids the solution of linear equations but also improves the time interval of integration, comparing with Newmak-β method, and the framework shows good effectiveness in application.