A novel explicit-implicit time integration method for solving time-dependent finite element equation: The Versa-δ method

In this paper, we present a novel explicit-implicit time integration method for solving dynamic problems. The proposed method is designed to easily switch between explicit and implicit forms by adjusting certain control parameters. The remaining control parameters are optimized to ensure that the method would deliver a flawless performance in both forms. This method uses two sub-steps per time step and can directly be used as a first-order and a second-order method, with high capability to suppress spurious responses. The consistency, stability, numerical damping, order of accuracy, amplitude decay, and period elongation are later analyzed for both explicit and implicit forms. Additionally, the proposed method is compared specifically with other widely-used methods with two sub-steps, including both explicit and implicit approaches. Examples are also provided to demonstrate the method's practicality.