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Nonlinear analysis of cantilever rods due to terminal moments

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Summary

In this paper an analytical procedure for the nonlinear analysis of a cantilever rod subjected to terminal moments is presented. According to this method the nonlinear equilibrium differential equations of the deformed rod are decoupled, and an exact solution by elliptic integrals is obtained, when: i) the initial rod is a helix with kinetic symmetry so that the principal moments of inertia of the cross-section are equal, and ii) the unstressed rod is a straight one with constant initial twist.

Übersicht

Es wird ein analytisches Verfahren für die nichtlineare Analyse eines beidseitig gelagerten Balkens unter der Belastung von Randmomenten eingeführt. Gemäß dieser Methode werden die nichtlinearen Gleichgewichts-Differentialgleichungen des unverformten Balkens entkoppelt. Eine exakte Lösung in Form von elliptischen Integralen wird erhalten, wenn 1) der ungespannte Balken spiralförmig mit kinetischer Symmetrie ist, so daß die Hauptträgheitsmomente des Querschnitts gleich sind, 2) der ungespannte Balken gerade ist und eine konstante Anfangsdrehung besitzt.

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References

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Authors and Affiliations

  1. Department of Mathematics, Athens

    D. E. Panayotounakos

  2. Department of Theoretical and Applied Mechanics, National Technical University of Athens, 5. K. Zographou Street, Zographou Athens, 625, Greece

    P. S. Theocaris

Authors
  1. D. E. Panayotounakos
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  2. P. S. Theocaris
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Panayotounakos, D.E., Theocaris, P.S. Nonlinear analysis of cantilever rods due to terminal moments. Ing. arch 49, 73–79 (1980). https://doi.org/10.1007/BF02627748

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  • DOI: https://doi.org/10.1007/BF02627748

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