An unconditionally stable two-sub-step composite method with controllable dissipation for nonlinear systems

Time integration methods are widely employed to predict transient responses of dynamic systems. Implicit and explicit methods possess their own advantages and disadvantages. In general, explicit methods are more efficient than implicit methods, but implicit methods can be designed to be unconditionally stable, hence the selection of step sizes only considers accuracy requirements. The implicit TR has strictly second-order accuracy and unconditional stability, and it can preserve energy for linear conservative systems. But for wave propagation and stiff systems, the TR is not effective since it cannot damp out unwanted information. To this end, dissipative α-methods were developed. For improving the single-step α-methods' accuracy, linear multi-step methods and the multi-sub-step methods were proposed. The linear multi-step methods are not self-starting, so another method has to be used to solve the initial steps. The multi-sub-step methods are self-starting, and they have been quickly developed since 2005. After the two-sub-step Bathe method was proposed, some other multi-sub-step methods were developed. In this context, this paper proposes an unconditionally stable and controllably dissipative two-sub-step composite method for dynamic systems, named as the Two-sub-step Generalized Central Difference (TGCD) method [1].