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

Yi Ji, Yufeng Xing*, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)3341-3358
Number of pages18
JournalNonlinear Dynamics
Volume105
Early online date11 Aug 2021
DOIs
Publication statusPublished - 1 Sep 2021

Keywords

  • BN-stability
  • Controllable dissipation
  • Nonlinear systems
  • Truly self-starting
  • Two-sub-step

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