An integrated explicit–implicit algorithm for vehicle–rail–bridge dynamic simulations

The dynamic interaction between the vehicle, rail, and bridges presents a huge computational challenge, especially for reliability analysis based on Monte Carlo simulations. In this study, an integrated algorithm is proposed for the vehicle–rail–bridge dynamic interaction problem. This algorithm divides the system into two subdomains, i.e. the vehicle–rail subdomain and the bridge subdomain. The vehicle–rail subdomain and the bridge subdomain are integrated by the Zhai algorithm and the Newmark-β algorithm, respectively. The integrated algorithm allows different time steps (or multitime steps) to be used for the two domains: a large time step for the bridge subdomain and a smaller one for the vehicle–rail subdomain. The stability region of the proposed algorithm was found through the two-degree-of-freedom model problem, when a single time step is used in both subdomains. The accuracy of the algorithm was numerically investigated through the two-degree-of-freedom model. The vehicle–rail–bridge vibration excited by rail irregularities and earthquakes was simulated using the multitime step algorithm. The effect of the time step ratio (ratio of the large time step to the small time step) on the accuracy of the vehicle–rail–bridge responses was investigated. It has been shown that the time step ratio of less than 50 produces vehicle–rail–bridge responses in an accurate manner for engineering purposes. The multitime step algorithm can solve the vehicle–rail–bridge problem 20 times faster than the single time step algorithms that are conventionally used in the vehicle–rail–bridge simulations. This multitime step algorithm provides an efficient alternative for solving the dynamic interaction between vehicle–rail and large-scale civil structures.