Computational Mechanics

, Volume 55, Issue 3, pp 455–468 | Cite as

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

Original Paper


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.


Composite scheme Linear and non-linear dynamics Optimal parameters 


  1. 1.
    Bathe KJ, Baig MMI (2005) On a composite implicit time integration procedure for nonlinear dynamics. Comput Struct 83:2513–2524Google Scholar
  2. 2.
    Bathe KJ (2007) Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Comput Struct 85:437–445CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bathe KJ, Noh G (2012) Insight into an implicit time integration scheme for structural dynamics. Comput Struct 98–99:1–6CrossRefGoogle Scholar
  4. 4.
    Kuhl D, Crisfield MA (1999) Energy-conserving and decaying algorithms in non-linear structural dynamics. Int J Numer Meth Eng 45:569–599CrossRefMATHMathSciNetGoogle Scholar
  5. 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 67:87–110CrossRefMATHMathSciNetGoogle Scholar
  6. 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 67:367–385CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover Publications, New YorkMATHGoogle Scholar
  8. 8.
    Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div 85:67–94Google Scholar
  9. 9.
    Matias Silva WT, Mendes Bezerra L (2008) Performance of composite implicit time integration scheme for nonlinear dynamic analysis. Math Probl Eng 2008:1–17CrossRefGoogle Scholar
  10. 10.
    Wagner W (1990) A finite element model for nonlinear shells of revolution with finite rotations. Int J Numer Meth Eng 29:1455–1471CrossRefMATHGoogle Scholar
  11. 11.
    Wagner W, Gruttmann F (1994) A simple finite rotation formulation for composite shell elements. Eng Comput 11:145–176CrossRefMathSciNetGoogle Scholar
  12. 12.
    Chung J, Hulbert GM (1993) A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-Alpha Method. J Appl Mech 60:371–375CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Hilber HM, Hughes TJR, Taylor RL (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng Struct Dynam 5:283–292CrossRefGoogle Scholar
  14. 14.
    Lewis DI, Simo JC (1994) Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups. J Nonlinear Sci 4:253–299CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Wagner W, Private communication with Prof. Rolf Lammering, HSU HamburgGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für BaustatikKarlsruher Institut für TechnologieKarlsruheGermany

Personalised recommendations