Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T03:04:01.974Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Get access

Abstract

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
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Chang, S. Y., “Explicit Pseudodynamic Algorithm with Unconditional Stability,” Journal of Engineering Mechanics, ASCE, 128, pp. 935–947 (2002).Google Scholar
2. Chang, S. Y., “An Explicit Method with Improved Stability Property,” International Journal for Numerical Method in Engineering, 77, pp. 1100–1120 (2009).Google Scholar
3. Chang, S. Y., “A New Family of Explicit Method for Linear Structural Dynamics,” Computers & Structures, 88, pp. 755–772 (2010).Google Scholar
4. Chang, S. Y., “A Family of Non-Iterative Integration Methods with Desired Numerical Dissipation,” International Journal of Numerical Methods in Engineering, 100, pp. 62–86 (2014).Google Scholar
5. Chang, S. Y., “Dissipative, Non-Iterative Integration Algorithms with Unconditional Stability for Mildly Nonlinear Structural Dynamics,” Nonlinear Dynamics, 79, pp. 1625–1649 (2015).Google Scholar
6. Chen, C. and Ricles, J. M., “Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory,” Journal of Engineering Mechanics, 134, pp. 676–683 (2008).Google Scholar
7. Chang, S. Y., “Family of Structure-Dependent Explicit Methods for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 140, 06014005 (2014).Google Scholar
8. Gui, Y., Wang, J. T., Jin, F., Chen, C. and Zhou, M. X., “Development of a Family of Explicit Algorithms for Structural Dynamics with Unconditional Stability,” Nonlinear Dynamics, 77, pp. 1157–1170 (2014).Google Scholar
9. Chang, S. Y., “A Loading Correction Scheme for A Structure-Dependent Integration Method,” Journal of Computational and Nonlinear Dynamics, 12, 011005 (2017).Google Scholar
10. Chen, C. and Ricles, J. M., “Stability Analysis of Direct Integration Algorithms Applied to Nonlinear Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 134, pp. 703–711 (2008).Google Scholar
11. Chen, C. and Ricles, J. M., “Stability Analysis of Direct Integration Algorithms Applied to MDOF Nonlinear Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 136, pp. 485–495 (2010).Google Scholar
12. Newmark, N. M., “A Method of Computation for Structural Dynamics,” Journal of Engineering Mechanics Division, ASCE, 85, pp. 67–94 (1959).Google Scholar
13. Chang, S. Y., “Accurate Representation of External Force in Time History Analysis,” Journal of Engineering Mechanics, ASCE, 132, pp. 34–45 (2006).Google Scholar
14. Goudreau, G. L. and Taylor, R. L., “Evaluation of Numerical Integration Methods in Elasto-Dynamics,” Computer Methods in Applied Mechanics and Engineering, 2, pp. 69–97 (1972).Google Scholar
15. Belytschko, T. and Hughes, T. J. R., Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland (1983).Google Scholar