{"title":"The tallest column problem: New first integrals and estimates","authors":"Teodor M. Atanackovic","doi":"10.1016/j.crme.2019.09.001","DOIUrl":null,"url":null,"abstract":"<div><p>We analyze the problem of finding the shape of the tallest column. For the system of equations that determine the optimal shape we construct a variational principle and two new first integrals. From the first integrals we are able to determine, analytically, the size of the cross-sectional area of the optimal column at the bottom, as well as the corresponding bending moment and curvature of the elastic line. Our result for critical load is compared with the results obtained by other methods.</p></div>","PeriodicalId":50997,"journal":{"name":"Comptes Rendus Mecanique","volume":"347 9","pages":"Pages 626-631"},"PeriodicalIF":1.0000,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.crme.2019.09.001","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mecanique","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1631072119301366","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze the problem of finding the shape of the tallest column. For the system of equations that determine the optimal shape we construct a variational principle and two new first integrals. From the first integrals we are able to determine, analytically, the size of the cross-sectional area of the optimal column at the bottom, as well as the corresponding bending moment and curvature of the elastic line. Our result for critical load is compared with the results obtained by other methods.
期刊介绍：
The Comptes rendus - Mécanique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
The journal publishes original and high-quality research articles. These can be in either in English or in French, with an abstract in both languages. An abridged version of the main text in the second language may also be included.
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