A high precision direct integration scheme for nonlinear dynamic systems

Kuinian Li, Anthony P Darby

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Based on the high precision direct (HPD) integration scheme for linear systems, a high precision direct integration scheme for nonlinear (HPD-NL) dynamic systems is developed. The method retains all the advantages of the standard HPD scheme (high precision with large time-steps and computational efficiency) while allowing nonlinearities to be introduced with little additional computational effort. In addition, limitations on minimum time step resulting from the approximation that load varies linearly between timesteps are reduced by introducing a polynomial approximation of the load. This means that, in situations where a rapidly varying or transient dynamic load occurs, a larger time-step can still be used while maintaining a good approximation of the forcing function and, hence, the accuracy of the solution. Numerical examples of the HPD-NL scheme compared with Newmark's method and the fourth-order Runge-Kutta (Kutta 4) method are presented. The examples demonstrate the high accuracy and numerical efficiency of the proposed method.
Original languageEnglish
Article number041008
Number of pages10
JournalJournal of Computational and Nonlinear Dynamics
Volume4
Issue number4
Early online date24 Aug 2009
DOIs
Publication statusPublished - Oct 2009

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