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A Levy-type solution for buckling analysis of micro-plates considering the small length scale

机译：考虑小长度尺度的微板屈曲分析的Levy型解决方案

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摘要

In this paper, a Levy-type solution based on the modified couple stress theory is developed to study the buckling behaviors of micro-plates. Based on this theory, length scale parameter is considered to capture the size effect of rectangular micro-plates. Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain the stability equations and corresponding boundary conditions. Different boundary conditions with two opposite edges simply supported and arbitrary boundary conditions along the other edges are considered. To illustrate the new model, both uniaxial and biaxial loads are applied and the critical buckling loads are defined for over a wide range of thickness, different length scale parameters and various boundary conditions. To show the accuracy of the formulations, present results are compared with available results in literature for specific cases and a very good agreement is observed. Results reveal that the critical buckling load increases as the length scale parameter increases especially when the thickness of the micro-plates becomes in order of length scale parameter and this effect is more significant for free boundary condition.
机译：本文提出了一种基于修正耦合应力理论的Levy型解，以研究微板的屈曲行为。基于此理论，长度标尺参数被认为是捕获矩形微板的尺寸效应。利用最小势能和邻近平衡准则获得稳定性方程和相应的边界条件。考虑简单支撑两个相对边缘的不同边界条件，以及沿其他边缘的任意边界条件。为了说明该新模型，同时应用了单轴和双轴载荷，并针对较大的厚度范围，不同的长度比例参数和各种边界条件定义了临界屈曲载荷。为了显示配方的准确性，将当前结果与文献中特定情况下的现有结果进行比较，并观察到非常好的一致性。结果表明，临界屈曲载荷随着长度尺度参数的增加而增加，特别是当微板的厚度按长度尺度参数的顺序变化时，这种影响在自由边界条件下更为明显。

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