Skip to main content
SpringerLink
Log in
Book cover

Engineering Design Applications pp 1–10Cite as

A Remedy for a Family of Dissipative, Unconditionally Stable Explicit Integration Methods

  • Chapter
  • First Online:

  • 1331 Accesses

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 92))

Abstract

A family of dissipative structure-dependent integration methods has been developed for structural dynamics. In general, this family of methods can integrate favorable numerical properties together, such as the unconditional stability, explicit formulation, second-order accuracy and controllable numerical damping. Due to the unconditional stability and explicit formulation, it is very computationally efficient for solving general structural dynamics problems. However, an adverse high-frequency overshooting behavior in the steady-state response might be generally experienced if this family of methods is applied to carry out the time integration. The cause of this overshoot is explored. It seems that the incomplete formulation of the difference equation for the displacement increment is responsible for this overshoot. Consequently, this overshooting can be completely eliminated after adding an appropriate load-dependent term into the difference equation for the displacement increment.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Chang, S.Y.: Explicit pseudodynamic algorithm with unconditional stability. J. Eng. Mech. ASCE 128(9), 935–947 (2002)

    Article  Google Scholar 

  2. Chang, S.Y.: Improved explicit method for structural dynamics. J. Eng. Mech. ASCE 133(7), 748–760 (2007)

    Article  Google Scholar 

  3. Chang, S.Y.: An explicit method with improved stability property. Int. J. Numer. Method Eng. 77(8), 1100–1120 (2009)

    Article  MathSciNet  Google Scholar 

  4. Chang, S.Y.: A new family of explicit method for linear structural dynamics. Comput. Struct. 88(11–12), 755–772 (2010)

    Article  Google Scholar 

  5. Chang, S.Y.: Development and validation of a new family of computationally efficient methods for dynamic analysis. J. Earthquake Eng. 19(6), 847–873 (2015)

    Article  Google Scholar 

  6. Chen, C., Ricles, J.M.: Development of direct integration algorithms for structural dynamics using discrete control theory. J. Eng. Mech. ASCE 134(8), 676–683 (2008)

    Article  Google Scholar 

  7. Gui, Y., Wang, J.T., Jin, F., Chen, C., Zhou, M.X.: Development of a family of explicit algorithms for structural dynamics with unconditional stability. Nonlinear Dyn. 77(4), 1157–1170 (2014)

    Article  MathSciNet  Google Scholar 

  8. Tang, Y., Lou, M.L.: New unconditionally stable explicit integration algorithm for real-time hybrid testing. J. Eng. Mech. ASCE 143(7), 04017029-1-15 (2017)

    Article  Google Scholar 

  9. Chang, S.Y.: Numerical dissipation for explicit, unconditionally stable time integration methods. Earthquakes Struct. Int. J. 7(2), 157–176 (2014)

    Google Scholar 

  10. Chang, S.Y.: A family of non-iterative integration methods with desired numerical dissipation. Int. J. Numer. Meth. Eng. 100(1), 62–86 (2014)

    Article  Google Scholar 

  11. Chang, S.Y.: Dissipative, non-iterative integration algorithms with unconditional stability for mildly nonlinear structural dynamics. Nonlinear Dyn. 79(2), 1625–1649 (2015)

    Article  Google Scholar 

  12. Chang, S.Y., Tran, N.C., Wu, T.H.: A one-parameter controlled dissipative unconditionally stable explicit algorithm for time history analysis. Sci. Iranica 24(5), 2307–2319 (2017)

    Google Scholar 

  13. Kolay, C., Ricles, J.M.: Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation. Earthq. Eng. Struct. Dyn. 43, 1361–1380 (2014)

    Article  Google Scholar 

  14. Goudreau, G.L., Taylor, R.L.: Evaluation of numerical integration methods in elasto-dynamics. Comput. Methods Appl. Mech. Eng. 2, 69–97 (1972)

    Article  Google Scholar 

  15. Chang, S.Y.: Accurate representation of external force in time history analysis. J. Eng. Mech. ASCE 132(1), 34–45 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Taipei University of Technology, Taipei, Taiwan, ROC

    Shuenn-Yih Chang

  2. Fu Jen Catholic University, New Taipei City, Taiwan, ROC

    Chiu-Li Huang

Authors
  1. Shuenn-Yih Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chiu-Li Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuenn-Yih Chang .

Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany

    Andreas Öchsner

  2. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität, Magdeburg, Germany

    Holm Altenbach

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chang, SY., Huang, CL. (2019). A Remedy for a Family of Dissipative, Unconditionally Stable Explicit Integration Methods. In: Öchsner, A., Altenbach, H. (eds) Engineering Design Applications. Advanced Structured Materials, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-79005-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-79005-3_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-79004-6

  • Online ISBN: 978-3-319-79005-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation