A non-iterative partitioned computational method with the energy conservation property is proposed in this study for calculating a large class of time-variant dynamic systems comprising multiple subsystems. The velocity continuity conditions are first assumed in all interfaces of the partitioned subsystems to resolve the interface link forces. The Newmark integration scheme is subsequently employed to independently calculate the responses of each system based on the obtained link forces. The proposed method is thus divided into two computational modules: multi-partitioned structural analyzers and an interface solver, providing a modular solution for time-variant systems. The proposed method resolves the long-standing problem of iterative computation required in partitioned time-variant systems. More specifically, the proposed method eliminates the need for time-variant matrix formation and the utilization of complex iterative procedures in partitioned computations, which significantly improves computational efficiency. The derivation process and theoretical demonstration of the proposed method are thoroughly presented through a representative example, i.e., a vehicle-rail-sleeper-ballast time-variant system. The proposed method's accuracy, energy conservation property, and efficiency are systematically demonstrated in comparison with the results of the global model, highlighting its superior performance. A more general example provided in Appendix C demonstrates that the proposed method is not confined to the analysis of vehicle-rail-sleeper-ballast systems but applies to other structural dynamic systems.