Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 3341-3358 |
Number of pages | 18 |
Journal | Nonlinear Dynamics |
Volume | 105 |
Early online date | 11 Aug 2021 |
DOIs | |
Publication status | Published - 1 Sept 2021 |
Bibliographical note
Funding Information:The support of the National Natural Science Foundation of China (11872090) is gratefully acknowledged.
Keywords
- BN-stability
- Controllable dissipation
- Nonlinear systems
- Truly self-starting
- Two-sub-step