Numerically Stable Integrated Simulation Method with Different Time Steps for Coupled Dynamic Systems

Compared with monolithic simulation methods, integrated simulation methods are suitable for the simulation of multiphysical fields and large-scale structural dynamic systems since they allow for decomposing the entire system into several subsystems, the behavior of which can be numerically captured through the use of independent finite element analysis tools. However, there still lacks a robust integrated simulation method that can be easily implemented within existing analysis tools and ensures that different subsystems stably utilize different integration schemes and time steps. To this end, based on the previously developed numerically stable integrated simulation method, this study develops an integrated simulation method where different time steps (DTS) can be used in multiple substructures. The stability criteria of this method are theoretically derived using an amplification matrix method suitable for subsystems and verified with a four-degrees-of-freedom (DOF) spring-mass-damper model. The analysis results demonstrate that the proposed method expands the stability boundary when conditionally stable explicit integration schemes are used. Furthermore, when unconditionally stable implicit integration schemes are used, they achieve unconditional numerical stability. The accuracy of this approach is also evaluated, revealing that it inherits second-order accuracy. Two application examples considering soil-structure interaction (SSI) are provided to demonstrate the feasibility and applicability of the proposed method in existing finite element tools, as well as its advantages in terms of computation time.