The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis

IF 4.2 Q2 NANOSCIENCE & NANOTECHNOLOGY
A. Naderi
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引用次数: 1

Abstract

This paper studies buckling problem of square nano-plates under uniform biaxial pressure through using three-dimensional nonlocal elasticity theory. Equations of stability are solved analytically for square nano-plates with simple supports using a Navier-type method. Critical buckling stress is presented for nano square plates with different thickness-length and nonlocal parameter-length ratios. The critical buckling stress is also reported using different local (classical) and nonlocal two-dimensional plate theories constructed essentially based on some simplifying assumptions. Comparison of the results of two-dimensional and three-dimensional theories for both local and nonlocal cases shows that the nonlocal two-dimensional plate theories are not as accurate as the local two-dimensional ones. This issue however reveals importance of the nonlocal three-dimensional solutions. Finally, through comparison of the numerical results with those obtained from molecular dynamic simulations, the value of the nonlocal parameter is calibrated for square graphene sheets. This parameter can be also used for the other nonlocal three-dimensional mechanical analyses of square graphene sheets to find accurate solutions.
方形石墨烯片三维非局部弹性分析的非局部参数:精确屈曲分析
本文利用三维非局部弹性理论研究了方形纳米板在双轴均匀压力下的屈曲问题。采用navier型方法解析求解了具有简单支撑的方形纳米板的稳定性方程。给出了不同厚度-长度和非局部参数-长度比的纳米方形板的临界屈曲应力。用不同的局部(经典)和非局部二维板理论也报道了临界屈曲应力,这些理论基本上是基于一些简化的假设。将二维和三维理论在局部和非局部情况下的计算结果进行比较,结果表明非局部二维板理论的计算精度不如局部二维板理论。然而,这个问题揭示了非局部三维解的重要性。最后,通过与分子动力学模拟结果的比较,对方形石墨烯片的非局部参数进行了标定。该参数也可用于方形石墨烯片的其他非局部三维力学分析,以找到准确的解。
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
CiteScore
6.00
自引率
1.70%
发文量
24
期刊介绍: Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems is a peer-reviewed scientific journal published since 2004 by SAGE Publications on behalf of the Institution of Mechanical Engineers. The journal focuses on research in the field of nanoengineering, nanoscience and nanotechnology and aims to publish high quality academic papers in this field. In addition, the journal is indexed in several reputable academic databases and abstracting services, including Scopus, Compendex, and CSA's Advanced Polymers Abstracts, Composites Industry Abstracts, and Earthquake Engineering Abstracts.
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