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- Title
Isoperimetric inequality in the periodic Greenhill Problem of twisted elastic rod.
- Authors
Kobelev, Vladimir
- Abstract
In this article we demonstrate the isoperimetric inequality arising in exactly solvable structural optimization problem of stability under torque load. The Greenhill problem describes the forming of a loop in an elastic bar under torsion. The inequality for infinite rod with periodical cross-section with two types of supports is rigorously verified. The optimal shape of the twisted rod is constant along its length and the optimal shape of cross-section is the equilateral triangle. The technique to demonstrate of isoperimetric inequalities exploits the variational method and the Hölder inequality.
- Subjects
ISOPERIMETRIC inequalities; STRUCTURAL optimization; ELASTIC rods &; wires; TORSION; MECHANICAL engineering
- Publication
Structural & Multidisciplinary Optimization, 2016, Vol 54, Issue 1, p133
- ISSN
1615-147X
- Publication type
Article
- DOI
10.1007/s00158-016-1404-7