Abstract

A unified plate model predicting the buckling behaviors is proposed by incorporating both surface and size effects into the general third-order plate theory (GTPT). From the minimum potential energy principle, the governing equations are implemented with presenting the corresponding boundary conditions. Analytic buckling loads for rectangular nanoplates are obtained by considering different boundary conditions. The surface effects, size effects and geometric sizes of nanoplates on the plate instability loads are discussed by using four types of single crystalline metallic nano-materials, gold, silver, copper and nickel. The study reveals that the GTPT is more accurate in predicting the buckling behaviors of nanoplates than the Reddy’s plate theory when surface effects are considered due to the fact that the GTPT can freely satisfy the strain condition on plate surfaces. Further discussion shows that the nonlocal strain gradient GTPT predicts a higher critical buckling load of a nanoplate with increasing high order scale parameter while a lower critical buckling load with increasing nonlocal parameter than the classical GTPT. Moreover, it is found that the increasing in length-to-thickness ratios of the nanoplates enhances the influence of surface effects on the critical buckling loads.

Graphical abstract

A nanoplate with significant surface stresses and the effects on dimensionless critical buckling load factor

中文翻译：

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基于一般三阶剪切变形板理论的纳米板弹性屈曲，包括尺寸效应和表面效应

摘要

通过将表面和尺寸效应结合到通用的三阶板理论（GTPT）中，提出了一种预测板屈曲行为的统一板模型。从最小势能原理出发，通过给出相应的边界条件来实现控制方程。通过考虑不同的边界条件获得矩形纳米板的分析屈曲载荷。通过使用四种类型的单晶金属纳米材料，金，银，铜和镍，讨论了纳米板对板的不稳定性载荷的表面效应，尺寸效应和几何尺寸。研究表明，当考虑表面效应时，由于GTPT可以自由满足板表面的应变条件，因此GTPT在预测纳米板的屈曲行为方面比Reddy板理论更准确。进一步的讨论表明，与传统的GTPT相比，非局部应变梯度GTPT预测高阶尺度参数增加时纳米板的临界屈曲载荷较高，而随着非局部参数增加而预测出较低的临界屈曲载荷。此外，发现纳米板的长度/厚度比的增加增强了表面效应对临界屈曲载荷的影响。进一步的讨论表明，与传统的GTPT相比，非局部应变梯度GTPT预测高阶尺度参数增加时纳米板的临界屈曲载荷较高，而随着非局部参数增加而预测出较低的临界屈曲载荷。此外，发现纳米板的长度/厚度比的增加增强了表面效应对临界屈曲载荷的影响。进一步的讨论表明，与传统的GTPT相比，非局部应变梯度GTPT预测高阶尺度参数增加时纳米板的临界屈曲载荷较高，而随着非局部参数增加而预测出较低的临界屈曲载荷。此外，发现纳米板的长度/厚度比的增加增强了表面效应对临界屈曲载荷的影响。

图形概要

具有显着表面应力的纳米板及其对无因次临界屈曲载荷因子的影响