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Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates

机译：剪切变形矩形板弯曲分析的精确混合经典解

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摘要

The thin plate model leads to a differential equation of fourth-order, while the mixed first-order shear deformation plate is modeled by a system of differential equations of second-order. The first model does not provide a very good analysis of shear deformity in plates in which the thickness-to-length ratio is relatively large. Nevertheless, the latter is more difficult and much more accurate. In this paper, the relationships between the findings of the two models allowing shear deformation results to be obtained from the results of classical thin theories are displayed without using any shear correction factors. The exact solutions are presented for bending of six types of rectangular plates having two opposite edges simply supported, and the other two edges may be quite general. The accuracy of the present model is demonstrated via problems for which the exact solutions and numerical results are available, and solutions are also presented as benchmark solutions for researchers to use in checking their numerical thick plate solutions.
机译：薄板模型导致四阶微分方程，而混合的一阶剪切变形板由二阶微分方程组建模。第一个模型不能很好地分析厚度与长度之比较大的板的剪切变形。然而，后者更困难并且更准确。在本文中，显示了两个模型的发现之间的关系，该关系允许从经典薄理论的结果获得剪切变形结果，而无需使用任何剪切校正因子。提出了精确的解决方案来弯曲六种类型的矩形板，这些矩形板的两个相对边缘简单地支撑着，另外两个边缘可能很普通。通过可得到精确解和数值结果的问题证明了本模型的准确性，并且还提出了解决方案作为基准解决方案，供研究人员用来检查其数值厚板解决方案。

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