Post-critical behavior of cantilever simply supported beam on an elastic foundation

IF 2.3 4区工程技术 Q3 MECHANICS

Mechanics Research Communications Pub Date : 2025-06-24 DOI:10.1016/j.mechrescom.2025.104469

Sanja J. Mihok, Armin D. Berecki, Lidija Z. Rehlicki Lukešević

引用次数: 0

Abstract

In this paper, we analyze the stability of a cantilever beam simply supported on a Winkler-type elastic foundation. We examine both the nonlinear and linearized problems, as well as the numerical results of the linearized problem with respect to parameters describing the critical force and foundation stiffness. We prove that, for the unique values of the critical force and foundation stiffness, we obtain exactly one nontrivial solution corresponding to the buckling mode, which is not the case for a simply supported beam on a Winkler-type foundation. We also perform a bifurcation analysis of the nonlinear problem using the Lyapunov–Schmidt reduction method and present the bifurcation pattern.

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弹性基础上悬臂简支梁的后临界性能

本文对温克勒型弹性地基上简支悬臂梁的稳定性进行了分析。我们研究了非线性和线性化问题，以及线性化问题关于描述临界力和基础刚度参数的数值结果。我们证明，对于临界力和基础刚度的唯一值，我们得到了屈曲模态对应的一个非平凡解，而对于winkler型基础上的简支梁则不是这样。我们还利用Lyapunov-Schmidt约简方法对非线性问题进行了分岔分析，并给出了分岔模式。

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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来源期刊

Mechanics Research Communications 物理-力学

CiteScore

4.10

自引率

4.20%

发文量

114

审稿时长

9 months

期刊介绍： Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.