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Analysis of Newmark Explicit Integration Method for Nonlinear Systems

Published online by Cambridge University Press:  05 May 2011

S.-Y. Chang ,
Y.-C. Huang  and
C.-H. Wang
S.-Y. Chang*
Affiliation:
Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan 10608, R.O.C.
Y.-C. Huang*
Affiliation:
Department of Construction Management, Hwa Hsia Institute of Technology, Taipei, Taiwan 23568, R.O.C.
C.-H. Wang*
Affiliation:
CSIRO Division of Sustainable Ecosystems, 37 Graham Road, Highett, Victoria 3190, Australia
*
*Professor
**Associate Professor
***Research Scientist
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Abstract

Numerical properties of the Newmark explicit method in the solution of nonlinear systems are explored. It is found that the upper stability limit is no longer equal to 2 for the Newmark explicit method for nonlinear systems. In fact, it is enlarged for stiffness softening and is reduced for stiffness hardening. Furthermore, its relative period error increases with the increase of the step degree of nonlinearity for a given value of the product of the natural frequency and the time step. It is also verified that the viscous damping determined from an initial stiffness is effective to reduce displacement response in the solution of a nonlinear system as that for solving a linear elastic system. All the theoretical results are confirmed with numerical examples.

Keywords

Step degree of nonlinearityStabilityAccuracy
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 4 , December 2006 , pp. 321 - 329
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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