A new unconditionally stable time integration method for analysis of nonlinear structural dynamics

A. Gholampour, Mehdi Ghassemieh, Mahdi Karimi-Rad

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

Original languageEnglish
Article number021024
Number of pages12
JournalJournal of Applied Mechanics
Volume80
Issue number2
DOIs
Publication statusPublished - Mar 2013
Externally publishedYes

Keywords

  • computational time
  • implicit method
  • nonlinear structural dynamics
  • overshooting effect
  • second order accuracy
  • unconditionally stable method

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