Bending analysis of nanobeams based on the integral form of nonlocal elasticity using the numerical Rayleigh-Ritz technique

IF 1.4 4区工程技术 Q3 ENGINEERING, MECHANICAL

Journal of Strain Analysis for Engineering Design Pub Date : 2022-02-22 DOI:10.1177/03093247221076249

M. F. Oskouie, R. Ansari, H. Rouhi

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引用次数: 2

Abstract

The nonlocal theory is commonly applied for nanomaterials due to its capability in considering size influences. Available studies have shown that the differential version of this theory is not suitable for some problems such as bending of cantilever nanobeams, and the integral version must be used to avoid obtaining inconsistent results. Therefore, an attempt is made in this paper to propose an efficient variational formulation based on the integral nonlocal model for the analysis of nanobeams. The formulation is developed in a general form so that it can be used for arbitrary kernel functions. The nanobeams are modeled using the Bernoulli-Euler beam theory, and their bending behavior is analyzed. Derivation of governing equations is performed according to an energy-based approach. Also, a numerical approach based on the Rayleigh-Ritz method is developed for the solution of problem. Moreover, the results of integral and differential models are compared. It is revealed that by the proposed numerical solution, the paradox in the behavior of nanocantilever is resolved.

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基于非局部弹性积分形式的纳米梁弯曲分析

非局部理论由于其考虑尺寸影响的能力而被广泛应用于纳米材料。已有研究表明，该理论的微分版本不适用于悬臂纳米梁弯曲等问题，必须使用积分版本以避免得到不一致的结果。因此，本文试图提出一种基于积分非局部模型的有效变分公式来分析纳米梁。该公式以一般形式发展，因此它可以用于任意核函数。采用伯努利-欧拉梁理论对纳米梁进行了建模，并对其弯曲性能进行了分析。根据基于能量的方法推导控制方程。同时，提出了基于瑞利-里兹法的数值求解方法。并对积分模型和微分模型的计算结果进行了比较。结果表明，所提出的数值解解决了纳米反杠杆行为中的悖论。

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

Journal of Strain Analysis for Engineering Design 工程技术-材料科学：表征与测试

CiteScore

3.50

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Strain Analysis for Engineering Design provides a forum for work relating to the measurement and analysis of strain that is appropriate to engineering design and practice. "Since launching in 1965, The Journal of Strain Analysis has been a collegiate effort, dedicated to providing exemplary service to our authors. We welcome contributions related to analytical, experimental, and numerical techniques for the analysis and/or measurement of stress and/or strain, or studies of relevant material properties and failure modes. Our international Editorial Board contains experts in all of these fields and is keen to encourage papers on novel techniques and innovative applications." Professor Eann Patterson - University of Liverpool, UK This journal is a member of the Committee on Publication Ethics (COPE).