A non-iteration partitioned method with a sliding window for large-scale time-variant vehicle-track-bridge systems

A Non-Iterative Partitioned method with Sliding Window (NP-SW) is proposed for efficiently solving time-variant dynamic systems such as Vehicle-Rail-Bridge Systems (VRBS). In contrast to conventional approaches that retain the entire rail domain, NP-SW confines rail computation to a sliding window aligned with the vehicle's position, thereby significantly reducing the problem scale while preserving high accuracy of dynamic responses. To accommodate the sliding window mechanism in the NP-SW method, the windowed multi-partitioned structural analyzers and the interface solver were formulated. Specifically, Boolean matrices were determined to relate the global rail matrices to their localized windowed matrices, and the subdomain-interface mappings were formulated accordingly. By shifting the time-variant interface from the vehicle-rail interface to the rail-bridge interface, the system's inherent time dependency is preserved. From a numerical and theoretical perspective, the stability, efficiency, accuracy, and hybrid integration schemes of the NP-SW method are investigated based on a VRBS (i.e., a single-car vehicle, a rail-sleeper-ballast track model, and a multi-span simply supported bridge). Under an appropriate selection of window length, the energy drift of the NP-SW method maintained an extremely low and negligible level across different train speeds and integration schemes. For the eight-span simply-supported beam bridge example, the NP-SW method can reduce the computational time by a factor of 277 compared to the global rail simulation while maintaining consistency about 95% for all in-window dynamic response results within the entire calculation time. The efficiency and accuracy advantages of the NP-SW method becomes more pronounced for large-scale dynamic systems.