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Lateral-torsional Buckling of Beams Under Combined Loading: A Reappraisal of Papkovitch–schaefer Theorem

Author(s):
Medium: journal article
Language(s): English
Published in: International Journal of Structural Stability and Dynamics, , n. 1, v. 7
Page(s): 55-79
DOI: 10.1142/s0219455407002186
Abstract:

Lateral-torsional buckling of elastic structures under combined loading is considered in this paper. Closed-form solutions are available for a specific range of loading. More generally, approximation of the buckling curve (limit of the stable domain in the loading parameters space) is investigated from the stationary property of the Rayleigh's quotient. The approximation is then compared to a numerical approach, namely the iterative method of Vianello and Stodola. Closed-form solutions give upper bounds with relative error less than 0.2%. It is shown that the stable domain in the loading parameters space is convex. The Papkovitch–Schaefer theorem is extended from previous theoretical works of Plaut,12despite the nonlinear dependence of the equilibrium equations on the loading parameters for the one-dimensional system. The boundary of the stable domain is clearly nonlinear, but this nonlinearity is weak. It is shown that Dunkerley's lower bound is relevant for the two structural cases considered, and the maximum relative error induced by such a lower bound is lower than 2%.

Structurae cannot make the full text of this publication available at this time. The full text can be accessed through the publisher via the DOI: 10.1142/s0219455407002186.
  • About this
    data sheet
  • Reference-ID
    10353170
  • Published on:
    14/08/2019
  • Last updated on:
    14/08/2019
 
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