Isoperimetric Inequalities in Stability Problems

Kobelev, V. V.

doi:10.1007/978-94-010-9577-8_60

V. V. Kobelev²

Part of the book series: NATO ASI Series ((NSSE,volume 231))

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Summary

The isoperimetric inequalities for the problem of determining the shape of a compressed column that has minimum weight and can withstand a given load, without loss of stability are treated. Two new isoperimetric inequalities, arizing in the problems of stability optimization, are proved: 1) the optimal column has the largest buckling load among all the columns with the same weight and clamped ends; 2) the optimal generalized Pfluger column has the largest buckling load among all generalized Pfluger columns with the same weight.

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Institute for Problems in Mechanics, Russian Academy of Science, 117526, Moscow, Russia
V. V. Kobelev

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V. V. Kobelev
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Essen University, Germany
G. I. N. Rozvany (Professor of Structural Design) (Professor of Structural Design)

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Kobelev, V.V. (1993). Isoperimetric Inequalities in Stability Problems. In: Rozvany, G.I.N. (eds) Optimization of Large Structural Systems. NATO ASI Series, vol 231. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9577-8_60

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DOI: https://doi.org/10.1007/978-94-010-9577-8_60
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9579-2
Online ISBN: 978-94-010-9577-8
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