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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Effect of an elastic substrate on buckling of free-standing nanocolumns
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Effect of an elastic substrate on buckling of free-standing nanocolumns

机译：弹性基底对自支撑纳米柱屈曲的影响

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摘要

This paper studies the buckling problem of nanowires (NWs) and carbon nanotubes (CNTs) freely standing on a substrate and subjected to distributed axial loads. NWs and CNTs are modeled as elastic nanocolumns and due to their high Young's modulus, the substrate is reasonably considered as an elastic foundation. The junction between the nanocolumn and substrate is described by a rotational spring. A new approach is suggested to solve the stability of axially-loaded nanocolumns with a rotational spring junction. An approximation expression for the critical load with high accuracy is derived in closed form. The results are confirmed for a rectangular Ag NW by FEM. Numerical results of the critical length of NWs and CNTs under their own weight are presented in graphs and tables. Obtained results indicate that the critical length is sensitive to small Young's modulus of the elastic substrate and becomes insensitive for enough large Young's modulus of the elastic substrate. When the rotational spring stiffness is sufficiently large, the case reduces to a free-standing NW on a rigid foundation.
机译：本文研究了纳米线（NWs）和碳纳米管（CNTs）在基体上自由站立并承受轴向分布载荷的屈曲问题。 NW和CNT被建模为弹性纳米柱，由于它们的高杨氏模量，因此可以将其合理地视为弹性基础。纳米柱和基底之间的连接由旋转弹簧描述。建议一种新方法来解决带有旋转弹簧结的轴向加载纳米柱的稳定性。以封闭形式导出高精度的临界载荷的近似表达式。通过FEM对矩形Ag NW的结果进行了确认。图表和表格中显示了自重作用下NW和CNT的临界长度的数值结果。所得结果表明，临界长度对弹性基材的小的杨氏模量敏感，而对于足够大的弹性基材的杨氏模量则不敏感。当旋转弹簧刚度足够大时，外壳会减小到在刚性基础上的独立NW。

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