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Time-Invariant Instability Problems

  • W. B. Krätzig
Part of the International Centre for Mechanical Sciences book series (CISM, volume 342)

Abstract

As elaborated in Chapter 1 and 2, time-invariant responses can be computed successively by utilization of the tangent stiffness relation
$$ {K_T} \cdot \mathop V\limits^ + = P = {F_i} \to \mathop V\limits^ + = K_T^{ - 1} \cdot \left( {P - {F_i}} \right) $$
(3.1)
with
  • K T the tangent stiffness matrix due to (1.31, 1.32),

  • the increment of the nodal degrees of freedom,

  • P the total applied nodal loads and

  • F i the internal nodal forces due to (1.31, 1.32).

Keywords

Cylindrical Shell Critical Load Bifurcation Point Load Path Primary Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References Chapter 3

  1. 3.1
    Thompson, J.M.T., Hunt, G.W.: A General Theory of Elastic Stability, John Wiley & Sons Ltd., London 1973.MATHGoogle Scholar
  2. 3.2
    Eckstein, U.: Nichtlineare Stabilitätsberechnung elastischer Schalentragwerke. Technical Report No. 83–3, Institute for Struct. Eng., Ruhr-University, Bochum 1983.Google Scholar
  3. 3.3
    Pflüger, A.: Stabilitätsprobleme der Elastostatik. 2nd edition, Springer-Verlag, Berlin 1964.CrossRefMATHGoogle Scholar
  4. 3.4
    Krätzig, W.B.: Eine einheitliche statische und dynamische Stabilitätstheorie für Pfadverfolgungsalgorithmen in der numerischen Festkörpertnechanik. ZAMM 69 (1989) 7, 203–213.CrossRefGoogle Scholar
  5. 3.5
    Stein, E., Wagner, W., Wriggers, P.: Grundlagen nichtlinearer Berechnungsverfahren in der Strukturmechanik. In: Nichtlineare Berechnungen im Konstruktiven Ingenieurbau, E. Stein (ed.), 1–53. Springer-Verlag, Berlin 1989.CrossRefGoogle Scholar
  6. 3.6
    Mittelmann, H.-D., Weber, H.: Numerical Methods for Bifurcation Problems — A Survey and Classification. In: Bifurcation Problems and their Numerical Solution H.-D. Mittelmann, H. Weber (eds.), 1–45. Birkhäuser-Verlag, Basel 1980.CrossRefGoogle Scholar
  7. 3.7
    Riks, E., Brogan, F.A., Rankin, C.C.: Numerical Aspects of Shell Stability Analysis. In: W.B. Krätzig, E. Onate (eds.): Computational Mechanics of Nonlinear Response of Shells, 125–151. Springer-Verlag, Berlin 1990.CrossRefGoogle Scholar
  8. 3.8
    Koiter, W.T.: Over de stabiliteit van het elastisch evenwicht, Dr.-Thesis, Delft 1945. English Translation: On the stability of elastic equilibrium. Stanford Univ., Dept of Aeronaut. and Astronaut., Report AD 704142, Palo Alto 1970.Google Scholar
  9. 3.9
    Brendel, B.: Zur geometrisch nichtlinearen Elastostatik. Dr.-Ing. Dissertation, University of Stuttgart 1979.Google Scholar
  10. 3.10
    Jürcke, R.K., Krätzig, W.B., Wittek, U.: Stabilitätsverhalten axialbelasteter Kreiszylinderschalen mit Regelimperfektionen nach DAST 013. Technical Report No. 83–4, Institute for Struct. Eng., Ruhr-University, Bochum 1983.Google Scholar
  11. 3.11
    Budiansky, B., Hutchinson. J.W.: Dynamic Buckling of Imperfection-Sensitive Systems. In: Proc. 11th IUTAM Congress Munic, 636–651, Springer-Verlag, Berlin 1964.Google Scholar
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    Budiansky, B., Hutchinson, J.W.: Buckling: Progress and Challenge. In: Trends in Solids Mechanics, J.F. Besseling, A.M.A. van der Heijden (eds.), 93–116, Delft University Press, Sijthoff & Noordhoff, Delft 1979.Google Scholar
  13. 3.13
    Jürcke, R.K.: Zur Stabilität und Imperfektionsempfindlichkeit elastischer Schalentragwerke. Technical Report No. 85–5, Inst. f. Struct. Eng., Ruhr-University, Bochum 1985.Google Scholar
  14. 3.14
    Choong, K.K., Hangai, Y.: Path-switching in bifurcation analysis by using line search and generalized inverse. Space structures 4, Th. Telford Ltd, London 1993.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • W. B. Krätzig
    • 1
  1. 1.Ruhr-University BochumBochumGermany

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