具有强制扭转轴的挠曲扭转屈曲及相关问题

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Mathematics and Mechanics of Solids Pub Date : 2024-05-10 DOI:10.1177/10812865241239647
Ciprian D Coman, Andrew P Bassom
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引用次数: 0

摘要

本文从渐近简化的角度讨论了具有连续弹性侧向约束和自由端施加横向点荷载的悬臂梁的经典侧向扭转不稳定性。我们的主要目标之一是提供临界屈曲载荷的分析近似值及其与各种关键非尺寸组的关系。本研究的第一部分涉及双对称梁受约束绕位于剪切中心轴上方任意高度的固定轴旋转的情况。第二部分研究的是横梁,其整个长度上都有一个连续的弹性侧向约束。假定约束的刚度[公式:见正文](说)是有限的,第二种情况下的屈曲方程由侧向位移和扭转角的两个耦合四阶微分方程系统来描述。我们证明,与[公式:见正文]一样,第一部分讨论的问题提供了上述系统的外解法;我们还利用匹配渐近法导出了次导阶外近似的相关边界条件。我们的理论发现通过与全屈曲问题的直接数值模拟比较得到了证实。
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Flexural–torsional buckling with enforced axis of twist and related problems
The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, [Formula: see text] (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as [Formula: see text], the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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