Confirmation of Lagrange Hypothesis for Twisted Elastic Rod
Mathematical Physics
2016-11-04 v1 math.MP
Optimization and Control
Exactly Solvable and Integrable Systems
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. 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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Cite
@article{arxiv.1111.7093,
title = {Confirmation of Lagrange Hypothesis for Twisted Elastic Rod},
author = {V. Kobelev},
journal= {arXiv preprint arXiv:1111.7093},
year = {2016}
}
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4 pages