Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

Details Confirmation of Lagrange Hypothesis for Twisted Elastic Rod Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

2011-11-30

arxiv.org/abs/1111.7093v1

Physics

Mathematical Physics

4 pages

Scientific paper

10.1007/s00158-012-0773-9

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. The Lagrange hypothesis, that the optimal rod possesses the constant cross-section was abandoned for Euler buckling problem. 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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