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New static and dynamic analyses of macro and nano FGM plates using exact three-dimensional elasticity in thermal environment

机译：在热环境中使用精确的三维弹性对宏观和纳米级FGM板进行新的静态和动态分析

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摘要

In this article, the static and dynamic behaviors of macro and nano inhomogeneous plates made of functionally graded materials (FGMs) have been investigated based on three-dimensional elasticity theory in combination with the nonlocal theory of Eringen. Variation of deflection along the thickness has been considered as the result of three-dimensional analysis. The governing equations have been derived and developed considering the nonlocal theory for nano-scale plates. Conveniently, the results of macro-sized plates were concluded by neglecting the small scale effects. The results were compared with the some related papers available in the literature. Since the three-dimensional elasticity has been applied, the obtained results are more accurate than other plate theories. In addition, if the plate is subjected to thermal loading, only the results of three-dimensional analysis will be correct. Since the nonlocal analysis has been assumed, the small-scale effects and related parameters have been studied for the nano-scale plates. Finally, the effects of some other important parameters have been surveyed on the results, such as the size of plate, loading, FGM parameters, and boundary conditions.
机译：本文基于三维弹性理论并结合Eringen的非局部理论，研究了功能梯度材料（FGM）制成的宏观和纳米非均质板的静态和动态行为。作为三维分析的结果，已经考虑了沿厚度的挠度变化。考虑到纳米级板的非局部理论，已经推导并发展了控制方程。方便地，忽略小规模效应即可得出大尺寸板的结果。将结果与文献中的一些相关论文进行了比较。由于已应用三维弹性，因此获得的结果比其他板理论更准确。另外，如果板承受热负荷，则只有三维分析的结果才是正确的。由于已经假设了非局部分析，所以已经研究了纳米级板的小规模效应和相关参数。最后，调查了一些其他重要参数对结果的影响，例如板的尺寸，载荷，FGM参数和边界条件。

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