Skip to main content
SpringerLink
Log in

Enhanced studies on a composite time integration scheme in linear and non-linear dynamics

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

In Bathe and Baig (Comput Struct 83:2513–2524, 2005), Bathe (Comput Struct 85:437–445, 2007), Bathe and Noh (Comput Struct 98–99:1–6, 2012) Bathe et al. have proposed a composite implicit time integration scheme for non-linear dynamic problems. This paper is aimed at the further investigation of the scheme’s behaviour for use in case of linear and non-linear problems. Therefore, the examination of the amplification matrix of the scheme will be extended in order to get in addition the properties for linear calculations. Besides, it will be demonstrated that the integration scheme also has an impact on some of these properties when used for non-linear calculations. In conclusion, a recommendation for the only selectable parameter of the scheme will be given for application in case of geometrically non-linear calculations.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38

Similar content being viewed by others

References

  1. Bathe KJ, Baig MMI (2005) On a composite implicit time integration procedure for nonlinear dynamics. Comput Struct 83:2513–2524

  2. Bathe KJ (2007) Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Comput Struct 85:437–445

    Article  MathSciNet  Google Scholar 

  3. Bathe KJ, Noh G (2012) Insight into an implicit time integration scheme for structural dynamics. Comput Struct 98–99:1–6

    Article  Google Scholar 

  4. Kuhl D, Crisfield MA (1999) Energy-conserving and decaying algorithms in non-linear structural dynamics. Int J Numer Meth Eng 45:569–599

    Article  MATH  MathSciNet  Google Scholar 

  5. Hoff C (1988) Practical performance of the \(\theta _{1}\)-method and comparison with other dissipative algorithms in structural dynamics. Comput Methods Appl Mech Eng 67:87–110

    Article  MATH  MathSciNet  Google Scholar 

  6. Hoff C, Pahl PJ (1988) Development of an implicit method with numerical dissipation from generalized single step algorithm for structural dynamics. Comput Methods Appl Mech Eng 67:367–385

    Article  MATH  MathSciNet  Google Scholar 

  7. Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover Publications, New York

    MATH  Google Scholar 

  8. Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div 85:67–94

    Google Scholar 

  9. Matias Silva WT, Mendes Bezerra L (2008) Performance of composite implicit time integration scheme for nonlinear dynamic analysis. Math Probl Eng 2008:1–17

    Article  Google Scholar 

  10. Wagner W (1990) A finite element model for nonlinear shells of revolution with finite rotations. Int J Numer Meth Eng 29:1455–1471

    Article  MATH  Google Scholar 

  11. Wagner W, Gruttmann F (1994) A simple finite rotation formulation for composite shell elements. Eng Comput 11:145–176

    Article  MathSciNet  Google Scholar 

  12. Chung J, Hulbert GM (1993) A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-Alpha Method. J Appl Mech 60:371–375

    Article  MATH  MathSciNet  Google Scholar 

  13. Hilber HM, Hughes TJR, Taylor RL (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng Struct Dynam 5:283–292

    Article  Google Scholar 

  14. Lewis DI, Simo JC (1994) Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups. J Nonlinear Sci 4:253–299

    Article  MATH  MathSciNet  Google Scholar 

  15. Wagner W, Private communication with Prof. Rolf Lammering, HSU Hamburg

Download references

Author information

Authors and Affiliations

  1. Institut für Baustatik, Karlsruher Institut für Technologie, Karlsruhe, Germany

    S. Klarmann & W. Wagner

Authors
  1. S. Klarmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Wagner.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klarmann, S., Wagner, W. Enhanced studies on a composite time integration scheme in linear and non-linear dynamics. Comput Mech 55, 455–468 (2015). https://doi.org/10.1007/s00466-014-1096-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-014-1096-z

Keywords

Search

Navigation