On the tallest column
type: Item
instance of: scholarly article
title: On the tallest column
zbMATH Open document ID: 1246.74040
author: Yu V. Egorov
published in: Comptes Rendus. Mécanique. Académie des Sciences, Paris
publication date: 2011-07-29T00:00:00Z
review text: The problem of the strongest heavy column subject to elastic instability was formulated by \textit{F. I. Niordsen} [Q. Appl. Math. 23, 47--53 (1965; Zbl 0127.16103)]. Their solution was successively questioned by \textit{S. J. Cox} and \textit{C. M. McCarthy} [SIAM J. Math. Anal. 29, No. 3, 547--554 (1998; Zbl 0913.34072); ibid. 31, No. 4, 940--940 (2000; Zbl 0957.34073)] who remarked that the existence of an optimal column cannot be granted in advance. In the present paper the author shows, with arguments of monotonicity, that the solution exists and is unique. The result is interesting, but a restrictive assumption on the quadratic relationship between the area of the cross-section and its moment of inertia excludes a wide class of technically relevant cases.
reviewed by: Piero Villaggio
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74G25
Mathematics Subject Classification ID: 74G30
zbMATH DE Number: 5934037
zbMATH Keywords: min-max problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: monotonicity
MaRDI profile type: Publication
full work available at URL: j.crme.2010.05.001
OpenAlex ID: W2109849179
DOI: 10.1016/J.CRME.2010.05.001
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description: scientific article; zbMATH DE number 5934037