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 time-steps 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.
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e-mail: kuinian.li@wits.ac.za
e-mail: absapd@bath.ac.uk
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October 2009
Research Papers
A High Precision Direct Integration Scheme for Nonlinear Dynamic Systems
Kuinian Li,
Kuinian Li
School of Civil and Environmental Engineering,
e-mail: kuinian.li@wits.ac.za
University of the Witwatersrand, Johannesburg
, 2050 Johannesburg, South Africa
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Antony P. Darby
Antony P. Darby
Department of Architecture and Civil Engineering,
e-mail: absapd@bath.ac.uk
University of Bath
, Bath, BA2 7AY, UK
Search for other works by this author on:
Kuinian Li
School of Civil and Environmental Engineering,
University of the Witwatersrand, Johannesburg
, 2050 Johannesburg, South Africae-mail: kuinian.li@wits.ac.za
Antony P. Darby
Department of Architecture and Civil Engineering,
University of Bath
, Bath, BA2 7AY, UKe-mail: absapd@bath.ac.uk
J. Comput. Nonlinear Dynam. Oct 2009, 4(4): 041008 (10 pages)
Published Online: August 25, 2009
Article history
Received:
May 29, 2008
Revised:
February 3, 2009
Published:
August 25, 2009
Citation
Li, K., and Darby, A. P. (August 25, 2009). "A High Precision Direct Integration Scheme for Nonlinear Dynamic Systems." ASME. J. Comput. Nonlinear Dynam. October 2009; 4(4): 041008. https://doi.org/10.1115/1.3192129
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