Model and Algorithm for Track Element and Vehicle Element

Abstract

With rapid development of the high-speed railways, the train traveling at a high-speed will induce great dynamic stress on the track structure and strong vibration of the vehicle, which directly affects train operation safety and comfort. In this chapter, the track element model and the vehicle element model with 15 nodes and 26 degrees of freedom are proposed. By adopting the finite element method and the Lagrange equation, the stiffness matrix, mass matrix and damping matrix for the track element and the vehicle element are deduced. The train-track-subgrade coupling system will be discretized into finite vehicle elements and track elements, in which the track-subgrade system is simulated as a series of track elements and the train as vehicle elements. In the process of computation, it only needs to generate the global stiffness matrix, global mass matrix and global damping matrix of the track-subgrade system once. And in the following computation of each time step, it only needs to assemble the stiffness matrix, mass matrix and damp matrix of the vehicle element into the global stiffness, mass and damping matrices of the track-subgrade system. Therefore, computational efficiency is largely improved.