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Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

机译：基于非局部Timoshenko束理论的功能梯度纳米束弯曲和屈曲的解析解

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摘要

In this paper, static bending and buckling of a functionally graded (FG) nanobeam are examined based on the nonlocal Timoshenko and Euler-Bernoulli beam theory. This non-classical (nonlocal) nanobeam model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is developed for simply-supported boundary conditions, and exact formulas are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio, various material compositions on the static and stability responses of the FG nanobeam are discussed. Some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed. The results show that the new nonlocal beam model produces larger deflection and smaller buckling load than the classical (local) beam model.
机译：在本文中，基于非局部Timoshenko和Euler-Bernoulli束理论，研究了功能梯度（FG）纳米束的静态弯曲和屈曲。这种非经典（非局部）纳米束模型结合了长度比例参数（非局部参数），可以捕获小比例效应。假设FG纳米束的材料特性在厚度方向上变化。使用最小总势能原理导出控制方程式和相关的边界条件。针对简单支持的边界条件开发了Navier型解，并提出了挠度和屈曲载荷的精确公式。讨论了非局部参数，长宽比，各种材料组成对FG纳米束的静态和稳定性响应的影响。还提供了一些说明性实例以验证本发明的制剂和解决方案。观察到良好的一致性。结果表明，与传统的（局部）梁模型相比，新的非局部梁模型产生更大的挠度和较小的屈曲载荷。

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  • 来源
    《Composite Structures》 |2013年第3期|378-386|共9页
  • 作者

    M. SimSek; H.H. Yurtcu;

  • 作者单位

    Yildiz Technical University, Faculty of Civil Engineering, Department of Civil Engineering, Davutpasa Campus, 34210 Esenler-Istanbul, Turkey;

    Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering, Department of Mathematical Engineering, Davutpasa Campus, 34210 Esenler-lstanbul, Turkey;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    bending; buckling; nonlocal elasticity theory; functionally graded materials;

    机译：弯曲;屈曲非局部弹性理论功能分级材料;

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