Three-dimensional train–track–bridge coupled dynamics model based on the explicit finite element method

In this paper, a train-track-bridge coupled dynamics modeling and coupling method was proposed. The coupled dynamic system was modeled separately with multiple subsystems by finite element method and the three-dimensional nonlinear wheel-rail contact relationship was used to account for non-linearity. Using explicit numerical methods and coupling the subsystems by the load term on the right end of the dynamic equations, repetitive iteration in the dynamic response solution process was avoided. Thus, a simplified the solution of nonlinear dynamic models can be achieved in limited time. In order to meet the requirement of diagonalization of the mass matrix in the algorithm, the modal superposition method was adopted. In the solution method proposed in this study, only a set of mass, damping, and stiffness matrices of the subsystem structure need to be established for solution instead of building the total matrix of the coupled dynamic system. Thus, greatly reduce the dynamic system matrix dimension for periodic train-track-bridge coupled dynamic systems. The train-track-bridge coupled dynamics model proposed in this paper is suitable to model various track and bridge structures, the wheel-rail contact relationship used is closer to reality and has more accuracy in describing the force state between wheel and rail. Besides, the unit size, number of modalities and numerical integration step size required in the calculation of each subsystem have been determined based on numerical experiments. Using the established dynamics model, the effects of the commonly used bound and separation ballastless track structures on the train operation safety was analyzed employing single-sample and multi-samples analysis. The calculation results demonstrated that the separation model is preferable for the prediction of train operation safety.