Coupling Composite Schemes With Different Time Steps for Multi-Scale Structural Dynamics

Simulating the dynamics of structural systems containing both stiff and flexible parts with a time integration scheme that uses a uniform time-step for the entire system is challenging because of the presence of multiple spatial and temporal scales in the response. We present, for the first time, a multi-time-step (MTS) coupling method for composite time integration schemes that is well suited for such stiff-flexible systems. Using this method, the problem domain is divided into smaller subdomains that are integrated using different time-step sizes and/or different composite time integration schemes to achieve high accuracy at a low computational cost. In contrast to conventional MTS methods for single-step (SS) schemes, a key challenge with coupling composite schemes is that multiple constraint conditions are needed to enforce continuity of the solution across subdomains. We develop the constraints necessary for achieving unconditionally stable coupling of the composite ρ∞-Bathe schemes and prove this property analytically. Further, we conduct a local truncation error (LTE) analysis and study the period elongation and amplitude decay characteristics of the proposed method. Lastly, we demonstrate the performance of the method for linear and nonlinear stiff-flexible systems to show that the proposed MTS method can achieve higher accuracy than existing methods for time integration, for the same computational cost.