New Insights into a Three-Sub-Step Composite Method and Its Performance on Multibody Systems

This paper develops a new implicit solution procedure for multibody systems based on three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward interpolation formula). The is second-order accurate, and the effective stiffness matrices of first two sub-steps are same. In this work, algorithmic parameters further optimized to minimize its local truncation error. Theoretical analysis shows that both undamped damped systems, unconditionally stable, controllably dissipative, third-order has no overshoots. Additionally, all three same, leading matrix being factorized only once in step linear systems. Then, implementation present presented, which position constraint equation strictly satisfied. advantages accuracy, stability, energy conservation validated by some benchmark dynamic problems.