Time-Invariant Instability Problems

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


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


Cylindrical Shell Critical Load Bifurcation Point Load Path Primary Path 
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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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