A Scalable Multiple-Time-Step Efficient Numerical Algorithm for Wind–Road Vehicle–Train–Bridge Dynamic Simulations

Abstract

During the past two decades, more and more rail-cum-road bridges have been built to meet the ever-increasing demand of highway and railway transportation in China. The rail-cum-road bridges are expected to withstand multiple types of loadings during normal operation, including wind, road vehicle, and train. Accurate quantifications of the coupling dynamics among bridge, road vehicle, and train are essential to ensure the safety and reliability of rail-cum-road bridges during their lifetime. The present study develops an analytical framework to simulate the complex wind–road vehicle–train–bridge (WRVTB) system. In addition, a scalable multiple-time-step (SMTS) algorithm is proposed to overcome the computational efficiency issue of traditional single-time-step (STS) algorithms for solving the WRVTB interaction. The SMTS algorithm utilizes domain decomposition techniques to enable a fine and a coarse time-step to be assigned for a road vehicle–train subsystem and bridge subsystem, which greatly improves the computational efficiency for solving the WRVTB interaction. A numerical simulation of coupled WRVTB analysis is conducted based on a prototype rail-cum-road bridge to demonstrate the computational efficiency and accuracy of the proposed method. The results indicate that both the MTS and the SMTS algorithms are able to achieve better accuracy and efficiency simultaneously in comparison with the STS algorithm. Although the SMTS algorithm does not exhibit obvious superiority over the MTS algorithm in terms of the overall accuracy and computational efficiency, the major advantage of the proposed SMTS algorithm over the MTS algorithm is the flexibility. When the SMTS algorithm is adopted, a refined time-step can be assigned to a subsystem of interest, while relatively coarse time-steps can be assigned to the remaining subsystems. As such, the desired accuracy of the subsystem of interest is guaranteed at a low computational cost.