Skip to main content
Book cover

Encyclopedia of Continuum Mechanics pp 1–12Cite as

Analytical Stability Considerations in Lightweight Design

  • 154 Accesses

Synonyms

Beams; Bifurcation buckling; Critical loads; Plates; Shells; Stability limit

Definitions

Lightweight structures are thin walled and/or slender; hence, they are prone to the occurrence of structural instabilities under various loading conditions. In this chapter analytical equations for estimating the critical loads of some important structures, such as beams, plates, and cylindrical shells, are presented. All equations discussed are based on a static stability criterion and limited to linear elastic material behavior.

Stability Criteria and Post-buckling Behavior

Depending on the stiffness of the structure and the loading conditions, different forms for the loss of structural stability can be observed involving bifurcation of equilibria, snap-through, snapback, and flutter instabilities. Reaching the plastic limit load can also be considered as an occurrence of a structural instability but is not further discussed within this chapter.

Bifurcation of equilibrium is...

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  • Bažant Z, Cedolin L (2010) Stability of structures – elastic, inelastic, fracture and damage theories. World Scientific Publishing Co. Pte. Ltd., Singapore

    CrossRef  Google Scholar 

  • Donnell L (1932) A new theory of buckling of thin cylinders under axial pressure. ASME Trans 56: 795–806

    Google Scholar 

  • Flügge W (1932) Die Stabilität der Kreiszylinderschale. Ingenieur-Archiv 3:463–506

    CrossRef  Google Scholar 

  • Hertel H (1986) Leichtbau. Springer, Berlin

    MATH  Google Scholar 

  • Lee S, Manuel F, Rossow E (1968) Large deflections and stability of elastic frames. J Eng Mech Div 94:521–548

    Google Scholar 

  • Pflüger A (1975) Stabilitätsprobleme der Elastostatik, 3rd edn. Springer, Berlin

    CrossRef  Google Scholar 

  • Rammerstorfer F, Daxner T (2009) Berechnungs und Designkonzepte für den Leichtbau. In: Degischer H, Lüftl S (eds) Leichtbau – Prinzipien, Werkstoffauswahl und Fertigungsvarianten. Wiley-VCH, Weinheim, pp 14–43, Copyright Wiley-VCH Verlag GmbH & Co. KGaA. (Figures partially reproduced with permission.)

    Google Scholar 

  • Ziegler F (1998) Technische Mechanik der festen und flüssigen Körper. Springer, Wien

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Lightweight Design and Structural Biomechanics, TU Wien, Vienna, Austria

    Melanie Todt & Franz G. Rammerstorfer

Authors
  1. Melanie Todt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Franz G. Rammerstorfer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Melanie Todt .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Prof. Dr. Andreas Öchsner

Section Editor information

  1. Institut für Leichtbau und Struktur-Biomechanik, TU Wien, Wien, Austria

    Franz G. Rammerstorfer

  2. Institut für Leichtbau und Struktur-Biomechanik, TU Wien, Wien, Austria

    Melanie Todt

  3. Institut für Leichtbau und Struktur-Biomechanik, TU Wien, Wien, Austria

    Isabella C. Skrna-Jakl

Rights and permissions

Reprints and Permissions

Copyright information

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

About this entry

Verify currency and authenticity via CrossMark

Cite this entry

Todt, M., Rammerstorfer, F.G. (2018). Analytical Stability Considerations in Lightweight Design. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_7-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_7-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering