An Accurate, Controllably Dissipative, Unconditionally Stable Three-Sub-Step Method for Nonlinear Dynamic Analysis of Structures

An implicit truly self-starting time integration method for nonlinear structural dynamical systems is developed in this paper. The proposed method possesses unconditional stability, second-order accuracy, and controllable dissipation, and it has no overshoots. The well-known BN-stability theory is employed in the design of algorithmic parameters, ensuring that the proposed method can stably solve nonlinear structural dynamical systems without restricting the time step size. The spectral analysis shows that compared to existing second-order accurate time integration methods, the proposed method enjoys a considerable advantage in low-frequency accuracy. For nonlinear problems where the currently popular Generalized-α method and ρ∞-Bathe method fail, the proposed method shows strong stability and accuracy. Further, for nonlinear problems in which all methods' results are convergent, the proposed method has greater accuracy, efficiency, and energy-conservation capability.