Skip to main content
SpringerLink
Log in
Book cover

Festschrift pp 143–150Cite as

Über das Auftreten energieloser Verformungsmoden bei gemischten Finiten Elementen

  • Chapter

  • 149 Accesses

Summary

In this paper a mixed finite element is considered which contains displacements and strains as principal unknowns. However, the results are also applicable on mixed displacement and stress formulations. Based on theorems concerning the rank of matrix products a criterion for the existence of spurious modes on the element level is derived and its implications are discussed.

Zusammenfassung

Es wird ein gemischtes Finîtes Element betrachtet, welches Verschiebungen und Verzerrungen als prinzipielle Unbekannte enthält. Die Ergebnisse können jedoch auch auf gemischte Formulierungen mit Verschiebungen und Spannungen angewendet werden. Mit Hilfe von drei Theoremen über den Rang von Matrixprodukten wird ein Kriterium für das Auftreten energiefreier Verformungsmoden auf Elementebene gewonnen und diskutiert.

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   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

Literatur

  1. Jacquotte, O.P.; Oden, J.T.: Analysis of hourglass instabilities and control in underintegrated finite element methods. Comp. Meth. Appl. Mech. Engng. 44 (1984), 339–363

    Article  MathSciNet  MATH  Google Scholar 

  2. Belytschko, T.; Ong, J.S.-J.; Liu, W.K.: A consistent control of spurious singular modes in 9-node Lagrange elements for the Laplace and Mindlin plate equation. Comp. Meth. Appl. Mech. Engng. 44 (1984), 269–295

    Article  MATH  Google Scholar 

  3. Liu, W.K.; Ong, J.S.-J.; Uras, R.A.: Finite element stabilization matrices — an unification approach. Comp. Meth. Appl. Mech. Engng. 53 (1985), 13–46

    Article  MathSciNet  MATH  Google Scholar 

  4. Wissmann, J.W.; Becker, T.; Möller, H.: Stabilization of the zero-energy modes of under-integrated isoparametric finite elements. Comp. Mech. 2 (1987), 289–306

    Article  MATH  Google Scholar 

  5. Kollmann, F.G.; Mukherjee, S.: A general, geometrically linear theory of inelastic, thin shells. Acta Mech. 57 (1984), 41–67

    Article  MathSciNet  Google Scholar 

  6. Oden, T.J.: Functional analysis. Englewood Cliffs: Prentice Hall 1979

    MATH  Google Scholar 

  7. Deif, A.S.: Advanced matrix theory for scientists and engineers. London: Abacus Press 1982

    MATH  Google Scholar 

  8. Rubinstein, R.; Puuch, E.F.; Atluri, S.N.: An analysis of, and remedies for kinematic modes in hybrid-stress finite elements: Selection of stable, invariant stress fields. Comp. Meth. Appl. Mech. Engng. 38 (1983), 63–92

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Darmstadt, Deutschland

    F. G. Kollmann

Authors
  1. F. G. Kollmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kollmann, F.G. (1988). Über das Auftreten energieloser Verformungsmoden bei gemischten Finiten Elementen. In: Festschrift. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-28742-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-28742-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-926031-60-0

  • Online ISBN: 978-3-662-28742-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation