Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Computational Dynamics

  • Peter BetschEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_22-1



Computational dynamics refers to the numerical solution of the time evolution equations pertaining to specific dynamical systems. In continuum mechanics, the time evolution equations typically come in the form of initial boundary value problems (IBVP). The numerical solution of the partial differential equations associated with the IBVP relies on the discretization of the original problem in space and time. The discretization process translates the underlying infinite-dimensional problem to a finite-dimensional (or discrete) system of algebraic equations which is amenable to a computer-based numerical solution.


Continuum mechanics embraces both fluid and solid mechanics. The focus of the present work is on computational solid dynamics, leaving aside the separate branch of computational fluid dynamics. The main task of computational solid dynamics is the...

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  1. Betsch P, Janz A, Hesch C (2018) A mixed variational framework for the design of energy-momentum schemes inspired by the structure of polyconvex stored energy functions. Comput Methods Appl Mech Eng 335:660–696MathSciNetCrossRefGoogle Scholar
  2. Crisfield M (1997) Non-linear finite element analysis of solids and structures. Advanced topics, vol 2. John Wiley & Sons, ChichesterGoogle Scholar
  3. Gonzalez O (1996) Time integration and discrete Hamiltonian systems. J Nonlinear Sci 6:449–467MathSciNetCrossRefGoogle Scholar
  4. Gonzalez O (2000) Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Comput Methods Appl Mech Eng 190(13-14):1763–1783MathSciNetCrossRefGoogle Scholar
  5. Gonzalez O, Stuart A (2008) A first course in continuum mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Groß M, Betsch P, Steinmann P (2005) Conservation properties of a time FE method. Part IV: higher order energy and momentum conserving schemes. Int J Numer Methods Eng 63:1849–1897CrossRefGoogle Scholar
  7. Hughes T (2000) The finite element method. Dover Publications, MineolazbMATHGoogle Scholar
  8. Krenk S (2009) Non-linear modeling and analysis of solids and structures. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Lew A, Mata P (2016) A brief introduction to variational integrators. In: Betsch P (ed) Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics, CISM courses and lectures, chap 5, vol 565, Springer, chap 5, pp 201–291CrossRefGoogle Scholar
  10. Marsden J, Ratiu T (1999) Introduction to mechanics and symmetry, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  11. Newmark N (1959) A method of computation for structural dynamics. J Eng Mech Div ASCE 85:67–94Google Scholar
  12. Romero I (2012) An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics. Comput Mech 50(5):603–610MathSciNetCrossRefGoogle Scholar
  13. Romero I (2016) High frequency dissipative integration schemes for linear and nonlinear elastodynamics. In: Betsch P (ed) Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics, CISM courses and lectures, vol 565, Springer Nature, Springer, chap 1, pp 1–30Google Scholar
  14. Simo J, Tarnow N (1992) The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Z angew Math Phys (ZAMP) 43:757–792CrossRefGoogle Scholar
  15. Wood W (1990) Practical time-stepping schemes. Oxford Applied Mathematics and Computing Science Series, Clarendon Press, OxfordGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany

Section editors and affiliations

  • René de Borst
    • 1
  1. 1.Department of Civil and Structural EngineeringUniversity of SheffieldSheffieldUK