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A two-variable first-order shear deformation theory considering in-plane rotation for bending, buckling and free vibration analyses of isotropic plates

机译：考虑面内旋转的两变量一阶剪切变形理论，用于各向同性板的弯曲，屈曲和自由振动分析

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This paper presents a two-variable first-order shear deformation theory considering in-plane rotation for bending, buckling and free vibration analyses of isotropic plates. In recent studies, a simple first-order shear deformation theory (S-FSDT) was developed and extended. It has only two variables by separating the deflection into bending and shear parts while the conventional first-order shear deformation theory (FSDT) has three variables. However, the S-FSDT provides incorrect predictions for the transverse shear forces on the insides and the twisting moments at the boundaries except simply supported plates since it does not consider in-plane rotation. The present theory also has two variables but considers in-plane rotation such that it is able to correctly predict the responses of plates with any boundary conditions. Analytical solutions are obtained for rectangular plates with two opposite edges that are simply supported, with the other edges having arbitrary boundary conditions. Numerical results of deflections, stress resultants, buckling loads and natural frequencies are presented with the FSDT, the S-FSDT and the present theory. Comparative studies demonstrate the effects of in-plane rotation and the accuracy of the present theory in predicting the bending, buckling and free vibration responses of isotropic plates.
机译：本文提出了一种考虑面内旋转的两变量一阶剪切变形理论，用于各向同性板的弯曲，屈曲和自由振动分析。在最近的研究中，简单的一阶剪切变形理论（S-FSDT）得到发展和扩展。通过将挠度分为弯曲部分和剪切部分，它只有两个变量，而传统的一阶剪切变形理论（FSDT）具有三个变量。但是，S-FSDT对内部的横向剪切力和边界处的扭转力矩提供了错误的预测，除了简单支撑的板外，因为它不考虑平面内旋转。本理论也有两个变量，但考虑了平面内旋转，因此它能够正确预测在任何边界条件下板的响应。对于具有两个简单支撑的相对边缘的矩形板，而其他边缘具有任意边界条件，则可以获得解析解。 FSDT，S-FSDT和本理论给出了挠度，应力合成，屈曲载荷和固有频率的数值结果。比较研究证明了平面旋转和本理论在预测各向同性板的弯曲，屈曲和自由振动响应方面的准确性。

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