Skip to main content
SpringerLink
Log in
Book cover

IUTAM Symposium on Discretization Methods in Structural Mechanics pp 115–122Cite as

Nonlinear Structural Dynamic Analysis by A Discontinuous Galerkin Finite Element Method

  • Conference paper

  • 277 Accesses

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 68))

Abstract

This paper discusses computational aspects of the discontinuous Galerkin (DG) finite element method as applied to nonlinear structural dynamic problems, by which displacements and velocities are approximated as piecewise bilinear functions in space-time and may be discontinuous at the discrete time levels. Both implicit and explicit iterative algorithms for solving the resulting system of coupled equations are derived. An h-adaptive procedure based on the Zienkiewicz-Zhu error estimate using the SPR technique is described. Numerical examples are provided to show the suitability of the DG method for nonlinear structural dynamics.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Babuska, I: Courant element: before and after, in Krizek, M., Neittaanmäki, P. and Stenberg, R. (eds.), Finite Element Methods, fifty years of the Courant element, 37–52, (1993).

    Google Scholar 

  2. Belytschko, T. and Tabbara, M.: H-adaptive finite element methods for dynamic problems, with emphasis on localization, Int.j. numer. methods eng., 36, 4245–4265, (1993).

    Article  MATH  Google Scholar 

  3. French, D. A.: A space-time finite element method for the wave equation, Comput. Methods Appl. Mech. Engrg. 107, 145–157, (1993).

    Article  MathSciNet  MATH  Google Scholar 

  4. Hughes, T. J. R. and Hulbert, G.: Space-time finite element methods for elastodynamics: Formulations and error estimates, Comput. Meth. Appl. Mech. Engrg. 66, 339–363, (1988).

    Article  MathSciNet  MATH  Google Scholar 

  5. Hulbert G. and Hughes, T. J. R.: Space-time finite element methods for second order hyperbolic equations, Comput. Methods Appl. Mech. Engrg. 84, 327–348, (1990).

    Article  MathSciNet  MATH  Google Scholar 

  6. Hulbert, G.: Space-time finite element methods for second-order hyperbolic equations, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1989.

    Google Scholar 

  7. Hulbert, G.: Time finite element methods for structural dynamics, Int. j. numer. methods eng. 33, 307–331, (1992).

    Article  MathSciNet  MATH  Google Scholar 

  8. Johnson, C: Discontinuous Galerkin finite element methods for second order hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 107, 117–129, (1993).

    Article  MathSciNet  MATH  Google Scholar 

  9. Klisinki, M. and Moström, A.: On stability of multi-time step integration procedures, (submitted to J. of Engineering Mechanics) (1995).

    Google Scholar 

  10. Li, X. D.: Adaptive finite element procedures in structural dynamics, Ph.D. Thesis, Publ. 96:2, Dept. of Structural Mechanics, Chalmers University of Technology, Göteborg, Sweden, 1996.

    Google Scholar 

  11. Li, X. D. and Wiberg, N.-E.: Structural dynamic analysis by a time-discontinuous Galerkin finite element method, Int.j. numer. methods eng., 39, 2131–2152, (1996).

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, X. D. and Wiberg, N.-E.: Implementation and adaptivity of a space-time finite element method in structural dynamics, (1997), (to appear in Comput. Meth. Appl. Mech. Engrg.).

    Google Scholar 

  13. Peric, D., Yu, J. and Owen, D. R. J.: On error estimates and adaptivity in elasto-plastic solids: application to the numerical simulation of strain localization in classical and Cosserat continua, Int. j. numer. methods eng., 37, 1351–1379, (1994).

    Article  MathSciNet  MATH  Google Scholar 

  14. D. R. J. Owen, E. Oñate and E. Hinton (Eds.): Computational Plasticity, Fundamentals and Applications, CIMNE, Barcelona, 1997.

    MATH  Google Scholar 

  15. Wiberg, N.-E. and Li, X. D.: A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis, Int.j. numer. methods eng., 37, 3583–3603,(1994).

    Article  MathSciNet  Google Scholar 

  16. Wiberg, N.-E. and Möller, P.: Formulation and solution of hierarchical finite element equations, Int.j. numer. methods eng., 37, 1213–1233, (1988).

    Article  Google Scholar 

  17. Zienkiewicz, O. C. and Zhu, J. Z.: A simple error estimator and adaptive procedure for practical engineering analysis, Int j. numer. methods eng., 24, 333–357, (1987).

    Article  MathSciNet  Google Scholar 

  18. Zienkiewicz, O. C. and Zhu, J. Z.: The superconvergent patch recovery and a posteriori error estimates, Part 1: The recovery technique; Part 2: Error estimates and adaptivity, Int.j. numer. methods eng., 33, 1331–1382, (1992).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Structural Mechanics, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    N.-E. Wiberg

  2. Department of Mechanical Engineering, Linköping Institute of Technology, S-581 83, Linköping, Sweden

    X. D. Li

Authors
  1. N.-E. Wiberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. X. D. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Strength of Materials, Vienna University of Technology, Austria

    H. A. Mang

  2. Institute of Lightweight Structures and Aerospace Engineering, Vienna University of Technology, Austria

    F. G. Rammerstorfer

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Wiberg, NE., Li, X.D. (1999). Nonlinear Structural Dynamic Analysis by A Discontinuous Galerkin Finite Element Method. In: Mang, H.A., Rammerstorfer, F.G. (eds) IUTAM Symposium on Discretization Methods in Structural Mechanics. Solid Mechanics and its Applications, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4589-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4589-3_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5942-8

  • Online ISBN: 978-94-011-4589-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation