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Assessments of Structure-Dependent Integration Methods with Explicit Displacement and Velocity Difference Equations

Published online by Cambridge University Press:  17 July 2017

S. Y. Chang and
T. H. Wu
S. Y. Chang*
Affiliation:
Department of Civil EngineeringNational Taipei University of TechnologyTaipei, Taiwan
T. H. Wu
Affiliation:
Department of Civil EngineeringNational Taipei University of TechnologyTaipei, Taiwan
*
Corresponding author (changsy@ntut.edu.tw)

Abstract

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A family of structure-dependent integration methods has been proposed by Gui et al. for time integration. Although it has desirable numerical properties, such as unconditional stability, explicit formulation and second-order accuracy, it has some adverse properties, such as a poor capability to capture structural nonlinearity, an overshoot in a high frequency steady- state response and a weak instability in the high frequency response of nonzero initial conditions. The causes of these adverse properties are explored. A poor capability to capture structural nonlinearity may originate from the convergence rate of 1 in velocity error. This family method has an overshoot in a high frequency steady-state response and this overshoot can be eliminated by adding a load-dependent term into the displacement difference equation. It is also analytically verified that the family method generally has no weak instability. However, the special member with λ = 4, i.e., CR explicit method, is shown to have a weak instability. Thus, it must be prohibited from practical applications although many applications of this method were found in the literature.

Keywords

Forced vibration responseLocal truncation errorOvershootingWeak instability

Information

Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018, pp. 771 - 778
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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