Skip to main content
SpringerLink
Log in

Improved formulations of the CR and KR methods for structural dynamics

  • Technical Papers
  • Published:
Earthquake Engineering and Engineering Vibration Aims and scope Submit manuscript

Abstract

Although the Chen-Ricles (CR) method and the Kolay-Ricles (KR) method have been applied to conduct pseudodynamic tests, they have both been found to have some adverse numerical properties, such as conditional stability for stiffness hardening systems and an unusual overshoot in the steady-state response of a high-frequency mode. An improved formulation for each method can be achieved by using a stability amplification factor to boost the unconditional stability range for stiffness hardening systems and a loading correction term to eliminate the unusual overshoot in the steady-state response of a high-frequency mode. The details for developing improved formulations for each method are shown in this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bathe KJ (1996), Finite Element Procedure in Engineering Analysis, Englewood Cliffs, N.J., USA: Prentice-Hall, Inc.

    Google Scholar 

  • Belytschko T and Hughes TJR (1983), Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland.

    Google Scholar 

  • Chang SY (2002), “Explicit Pseudodynamic Algorithm with Unconditional Stability,” Journal of Engineering Mechanics, ASCE, 128(9): 935–947.

    Article  Google Scholar 

  • Chang SY (2006), “Accurate Representation of External Force in Time History Analysis,” Journal of Engineering Mechanics, ASCE, 132(1): 34–45.

    Article  Google Scholar 

  • Chang SY (2007a), “Improved Explicit Method for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 133(7): 748–760.

    Article  Google Scholar 

  • Chang SY (2007b), “Enhanced, Unconditionally Stable Explicit Pseudodynamic Algorithm,” Journal of Engineering Mechanics, ASCE, 133(5): 541–554.

    Article  Google Scholar 

  • Chang SY (2010), “A New Family of Explicit Method for Linear Structural Dynamics,” Computers & Structures, 88(11-12): 755–772.

    Article  Google Scholar 

  • Chang SY (2012), “Discussion of Paper 'Real-Time Hybrid Testing Using the Unconditionally Stable Explicit CR Integration Algorithm' by Cheng Chen, James M. Ricles, Thomas M. Marullo and Oya Mercan, Earthquake Engineering and Structural Dynamics 2009; 38: 23–44,” Earthquake Engineering and Structural Dynamics, 41: 1061–1063.

    Article  Google Scholar 

  • Chang SY (2014a), “Family of Structure-Dependent Explicit Methods for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 140(6): 06014005.

    Article  Google Scholar 

  • Chang SY (2014b), “A Family of Non-Iterative Integration Methods with Desired Numerical Dissipation,” International Journal of Numerical Methods in Engineering, 100(1): 62–86.

    Article  Google Scholar 

  • Chang SY (2015a), “Dissipative, Non-Iterative Integration Algorithms with Unconditional Stability for Mildly Nonlinear Structural Dynamics,” Nonlinear Dynamics, 79(2): 1625–1649.

    Article  Google Scholar 

  • Chang SY (2015b), “Discussion of Paper ‘Development of a Family of Unconditionally Stable Explicit Direct Integration Algorithms with Controllable Numerical Energy Dissipation’ by Chinmoy Kolay and James M. Ricles, Earthquake Engineering and Structural Dynamics 2014; 43: 1361–1380,” Earthquake Engineering and Structural Dynamics, 44(2): 325–328.

    Article  Google Scholar 

  • Chang SY (2015c), “A General Technique to Improve Stability Property for a Structure-Dependent Integration Method,” International Journal for Numerical Methods in Engineering, 101(9): 653–669.

    Article  Google Scholar 

  • Chen C and Ricles JM (2008), “Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory,” Journal of Engineering Mechanics, ASCE, 134(8): 676–683.

    Article  Google Scholar 

  • Goudreau GL and Taylor RL (1972), “Evaluation of Numerical Integration Methods in Elasto-Dynamics,” Computer Methods in Applied Mechanics and Engineering, 2: 69–97.

    Article  Google Scholar 

  • Hilber HM and Hughes TJR (1978), “Collocation, Dissipation, and ‘Overshoot’ for Time Integration Schemes in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, 6: 99–118.

    Article  Google Scholar 

  • Kolay C and Ricles JM (2014), “Development of a Family of Unconditionally Stable Explicit Direct Integration Algorithms with Controllable Numerical Energy Dissipation,” Earthquake Engineering and Structural Dynamics, 43(9): 1361–1380.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Taipei University of Technology, NTUT Box 2653, No. 1, Section 3, Jungshiau East Road, Taipei, 10608, Taiwan

    Shuenn-Yih Chang

Authors
  1. Shuenn-Yih Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuenn-Yih Chang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, SY. Improved formulations of the CR and KR methods for structural dynamics. Earthq. Eng. Eng. Vib. 17, 343–353 (2018). https://doi.org/10.1007/s11803-018-0445-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11803-018-0445-x

Keywords

Search

Navigation