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Computational Concepts for Kinetic Instability Problems

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 342))

Abstract

In order to decide upon the stability of a certain time-dependent response \( \bar X = \left\{ {\bar V,\bar V} \right\} \) we now continue with section 1.5.

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References Chapter 5

  1. Müller, P.C.: Stabilität und Matrizen. Springer-Verlag, Berlin 1977.

    MATH  Google Scholar 

  2. Krätzig, W.B., Li, L.-Y.: On rigorous stability conditions for dynamic quasi-bifurcations. Int. J. Solids Struct. 29 (1992) 1, 97–104.

    Article  Google Scholar 

  3. Krätzig, W.B., Quian, Y.-y.: On stability conditions for nonlinear static and dynamic buckling responses. In: Nonlinear Computational Mechanics, P. Wriggers, W. Wagner (eds.), Springer-Verlag, Berlin 1991.

    Google Scholar 

  4. Meirowitch, L.: Methods of Analytical Dynamics. McGraw Hill, New York 1970.

    Google Scholar 

  5. Hagedorn, P.: Nichtlineare Schwingungen. Akademische Verlagsgesellschaft, Wiesbaden 1978.

    MATH  Google Scholar 

  6. Bolotin, V.V.: The dynamic stability of elastic systems. Holden-Day, San Francisco 1964.

    MATH  Google Scholar 

  7. Basar, Y., Eller, C., Krätzig, W.B.: Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures. Computational Mechanics, 2 (1987), 89–98.

    Article  MATH  Google Scholar 

  8. Eller, C.: Lineare und nichtlineare Stabilitätsanalyse periodisch erregter, viskoelastischer Strukturen. Techn. Report No. 88–2, Inst. for Struct. Eng., Ruhr-University, Bochum 1988.

    Google Scholar 

  9. Basar, Y., Eller, C., Krätzig, W.B.: Finite element procedures for the nonlinear stability analysis of arbitrary shell structures. Computational Mechanics 6 (1990), 157–166.

    Article  MATH  Google Scholar 

  10. Eller, C., Krätzig, W.B.: Numerische Stabilitätsanalyse linear und nichtlinear deformierbarer, parametererregter Schalentragwerke. Ing.-Archiv 59 (1989), 345–356.

    Article  MATH  Google Scholar 

  11. Mathies, H.G., Nath, C.: Dynamische Stabilität nichtlinearer Systeme mit periodischer Erregung, dargestellt am Beispiel der großen Windanlage. ZAMM 64 (1984), T67 - T69.

    Google Scholar 

  12. Ziegler, H.: Principles of Structural Stability. Birkhiiuser Verlag, Basel 1977.

    Book  MATH  Google Scholar 

  13. Krätzig, W.B., Eller, C.: Numerical Algorithms for Nonlinear Unstable Dynamic Shell Responses. Computers & Structures, 44 (1992) No. 1/2, 263–271.

    Article  Google Scholar 

  14. Kleiber, M., Kotula, W., Saran, M.: Dynamic quasi-bifurcations in structures subjected to step-loadings. In: Finite Element Methods for Nonlinear Problems, K. J. Bathe et al. (eds.), 529–538. Springer-Verlag Berlin 1986.

    Google Scholar 

  15. Quante, R.: Dynamic Stability Analysis of Elasto-viscoplastic Shell Structures under Time-dependent Loading. Techn. Report No. 92–2, Inst. f. Structural Engineering, Ruhr-University, Bochum 1992.

    Google Scholar 

  16. Willems, J.L.: Stability Theory of Dynamical Systems. Th. Nelson & Sons Ltd., London 1970.

    Google Scholar 

  17. Quante, R., Krätzig, W.B.: Dynamic Stability of Elasto-plastic Shell Structures. In: Computational Plasticity, J. Owen et al. (eds.), 1811–1822, Pineridge Press, Swansea 1992.

    Google Scholar 

  18. Hopf, E.: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems. Berichte d. Math.-Phys. Klasse, Sächs. Akad. d. Wissensch., Leipzig, 94 (1942), 1–22.

    Google Scholar 

  19. Zurmühl, R., Falk, S.: Matrizen und ihre Anwendungen. Vol. 1/ Vol. 2, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1984/1986.

    Google Scholar 

  20. Leipholz, H.: Stabilitätstheorie. B.G. Teubner, Stuttgart, 1968.

    Google Scholar 

  21. Huseyin, K.: Vibrations and Stability of Multiple Parameter Systems. Noordhoff International Publishing, Alphen aan den Rijn, 1978.

    MATH  Google Scholar 

  22. Basar, Y., Krätzig, W.B., Nawrotzki, P.: Nonlinear Dynamic Stability Analysis of Shell Structures under Nonconservative Loads. Engineering Systems Design and Analysis, Vol. 5, ASME 1992, 143–148.

    Google Scholar 

  23. Basar, Y., Ding, Y.: Finite-rotation Elements for the Non-linear Analysis of Thin Shell Structures. Int. J. Solids Structures Vol. 26 (1990), No. 1, 83–97.

    Article  MATH  Google Scholar 

  24. Krätzig, W.B., Nawrotzki, P.: Dynamische Stabilitätsanalyse bewegungsabhängig belasteter, mechanischer Strukturen. ZAMM 73 (1993) 4, T199 - T202.

    MATH  Google Scholar 

  25. Argyris, J., Mlejnek, H.-P.: Die Methode der Finiten Elemente; Bd. 3: Einführung in die Dynamik. Vieweg, Braunschweig, 1988.

    Google Scholar 

  26. Schweizerhof, K.: Nichtlineare Berechnung von Tragwerken unter verformungsabhängiger Belastung mit finiten Elementen. Bericht Nr. 82–2, Institut für Baustatik, Universität Stuttgart, 1982.

    Google Scholar 

  27. Schräpel, H.-D.: Zur Äquivalenz der klassischen Stabilitätskriterien der Elastomechanik bei nichtkonservativen Kräften. Ingenieur-Archiv 60 (1989), 83–91.

    Article  MATH  Google Scholar 

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Kratzig, W.B., Nawrotzki, P. (1995). Computational Concepts for Kinetic Instability Problems. In: Kounadis, A.N., Krätzig, W.B. (eds) Nonlinear Stability of Structures. International Centre for Mechanical Sciences, vol 342. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4346-9_11

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  • DOI: https://doi.org/10.1007/978-3-7091-4346-9_11

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82651-5

  • Online ISBN: 978-3-7091-4346-9

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