An efficient method for train–track–substructure dynamic interaction analysis by implicit-explicit integration and multi-time-step solution

Abstract

Abstract In this work, a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train–track–substructure (TTS) system. It is called implicit-explicit integration and multi-time-step solution method (abbreviated as mI-nE-MTS method). The TTS system is divided into train–track subsystem and substructure subsystem. Considering that the root cause of low efficiency of obtaining TTS solution lies in solving the algebraic equation of the substructures, the high-efficient Zhai method, an explicit integration scheme, can be introduced to avoid matrix inversion process. The train–track system is solved by implicitly Park method. Moreover, it is known that the requirement of time step size differs for different sub-systems, integration methods and structural frequency response characteristics. A multi-time-step solution is proposed, in which time step size for the train–track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand, namely the time spent for m implicit integral steps is equal to n explicit integral steps, i.e., mI = nE as mentioned above. The numerical examples show the accuracy, efficiency, and engineering practicality of the proposed method.

Keywords

• Train–track dynamic interaction
• Substructure system
• Implicit integration
• Explicit integration
• Multi-time-step solution
• Railway engineering