Vector Form Intrinsic Finite-Element Analysis for Train and Bridge Dynamic Interaction

Abstract

A computationally efficient method is proposed for analyzing train and bridge dynamic interaction responses based on the vector form intrinsic finite-element method. The proposed method does not need to establish a large number of complicated dynamic coupling equations for the train and bridge, in contrast to the traditional finite-element method. A train with multiple cars traveling over a railway bridge with multiple spans was analyzed, and two computational models were considered: two-axle and coach models. The effects of rail irregularity and rail ballast were also considered. In the proposed method, the bridge is modeled as mass particles linked by a series of massless beam elements, and the train is simulated by mass particles. The motions of the mass particles are governed by Newton’s second law, and the central difference scheme is employed to solve the equation of motion for each mass particle. The fictitious reverse-motion procedure is employed to obtain the pure deformations of the massless beam elements, from which the internal forces exerted on the mass particles are evaluated. Assembly of the global stiffness matrix is avoided, and each mass-particle motion is calculated independently, which makes the proposed method easy and efficient. Compared with existing analytical and numerical methods, the proposed method provides simpler modeling of the dynamic interaction between the train and bridge and more efficient computation. Furthermore, the proposed method can yield very accurate results.