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Confirmation of Lagrange hypothesis for twisted elastic rod

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Abstract

The history of structural optimization as an exact science begins possibly with the celebrated Lagrange problem: to find a curve which by its revolution about an axis in its plane determines the rod of greatest efficiency (Lagrange 1868). The Lagrange hypothesis, that the optimal rod possesses the constant cross-section was abandoned for Euler buckling problem (Tadjbakhsh and Keller, J Appl Mech 29:159–164, 1962). In this Article the Lagrange hypothesis is proved to be valid for Greenhill’s problem of torque buckling. The corresponding isoperimetric inequality is affirmed.

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References

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Authors and Affiliations

  1. MUHR und BENDER KG, Central Development, Attendorn, Germany

    Vladimir Kobelev

  2. University of Siegen, Siegen, Germany

    Vladimir Kobelev

Authors
  1. Vladimir Kobelev
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Correspondence to Vladimir Kobelev.

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Kobelev, V. Confirmation of Lagrange hypothesis for twisted elastic rod. Struct Multidisc Optim 46, 155–157 (2012). https://doi.org/10.1007/s00158-012-0773-9

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  • DOI: https://doi.org/10.1007/s00158-012-0773-9

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