最高列问题:新的第一积分和估计

IF 1 4区工程技术 Q4 MECHANICS Comptes Rendus Mecanique Pub Date : 2019-09-01 DOI:10.1016/j.crme.2019.09.001

Teodor M. Atanackovic

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引用次数: 0

摘要

我们分析找出最高柱的形状的问题。对于确定最优形状的方程组，我们构造了一个变分原理和两个新的一等积分。从第一个积分中，我们可以解析地确定底部最优柱的横截面积大小，以及相应的弯矩和弹性线的曲率。并与其他方法得到的结果进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The tallest column problem: New first integrals and estimates

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.

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来源期刊

Comptes Rendus Mecanique 物理-力学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

12 months

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.