Winkler‐Pasternak foundation effect on the buckling loads of arbitrarily rigid or restrained supported nonlocal beams made of different FGM and porosity distributions

IF 2.3 4区工程技术 Q1 MATHEMATICS, APPLIED

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-10-20 DOI:10.1002/zamm.202300569

Büşra Uzun, Mustafa Özgür Yaylı

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引用次数: 0

Abstract

Abstract The present research investigates lateral stability of a functionally graded nanobeam using Eringen's differential nonlocal elasticity model under rigid (clamped, pinned, free) and deformable (lateral, rotational restraints) boundary conditions. Sigmoid and power law have been employed as grading laws to study the influence of the material distribution on the snap‐buckling analysis of a nanobeam with arbitrary boundary conditions. Moreover, Fourier sine series with Stokes’ transformation are employed to investigate the effects of boundary conditions on the stability response of nanobeams embedded in a Pasternak foundation. A parametric study has been performed to investigate the effect of deformable boundaries, Pasternak foundation and small‐scale parameters on the stability response of the nanobeam and the results have been presented in a series of tables and figures. It has been observed that consideration of the small‐scale parameter, Pasternak foundation, deformable boundaries and functionally grading index (of sigmoid and power‐law) are essential while analyzing the static stability response. The obtained analytical results may be used as benchmarks in future researches of functionally graded nanobeams embedded in an elastic medium.

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Winkler - Pasternak地基对由不同FGM和孔隙率分布构成的任意刚性或受限支承非局部梁屈曲荷载的影响

摘要本研究利用Eringen微分非局部弹性模型研究了刚性(夹紧、钉住、自由)和变形(侧向、旋转约束)边界条件下功能梯度纳米梁的横向稳定性。采用s型律和幂律作为分级律，研究了材料分布对任意边界条件下纳米梁的屈曲分析的影响。此外，采用Stokes变换的傅里叶正弦级数研究了边界条件对纳米梁嵌入帕斯捷尔纳克地基稳定性响应的影响。对变形边界、帕斯捷尔纳克基础和小尺度参数对纳米梁稳定性响应的影响进行了参数化研究，并将结果以一系列表格和图表的形式呈现出来。在分析静稳定性响应时，考虑小尺度参数、帕斯捷尔纳克基础、变形边界和功能分级指标(s型和幂律)是必不可少的。所得的分析结果可为今后弹性介质中功能梯度纳米梁的研究提供参考。

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来源期刊

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 数学-力学

CiteScore

3.30

自引率

8.70%

发文量

199

审稿时长

3.0 months

期刊介绍： ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.