An unconditionally stable time integration method with controllable dissipation for second-order nonlinear dynamics

This paper proposes a two-sub-step time integration method with controllable dissipation to solve nonlinear dynamic problems. The proposed method has second-order accuracy, unconditional stability and zero-order overshoots. In addition, different from most existing time integration methods, the present method is self-starting, and initial acceleration vector is not required. Importantly, the well-known BN-stability theory for first-order nonlinear dynamics is employed to design algorithmic parameters; thus, the present method is BN-stable, or unconditionally stable for nonlinear dynamics. The present method can give stable and accurate predictions for nonlinear problems in which some excellent methods such as the trapezoidal rule and the ρ_∞-Bathe method fail. A few representative nonlinear numerical examples show that the proposed method enjoys advantages in accuracy, stability and energy conservation compared with the trapezoidal rule and the ρ_∞-Bathe method.