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Shear deformation in thick auxetic plates

机译:厚板中的剪切变形

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This paper aims to understand the effect of auxeticity on shear deformation in thick plates. Three models for the shear correction factor of plates as a function of Poisson's ratio were proposed: an analytical model, a cubic fit model and a modified model. Of these three, the cubic fit model exhibits the best accuracy over the entire range of Poisson's ratio from -1 to 0.5. The extent of shear deformation is herein investigated using the example of uniformly loaded circular plates. It was found that the maximum deformation of such plates based on Mindlin theory approximates to those according to Kirchhoff theory when the Poisson's ratio of the plate material is highly negative. When the Poisson's ratio of the plate material is -1 and the edge of the plate is simply supported, the calculation of the maximum deflection by Mindlin theory simplifies into that by Kirchhoff theory. These results suggest that auxeticity reduces shear deformation in thick plates, permitting the use of classical plate theory for thick plates only if the plate material is highly auxetic.
机译:本文旨在了解膨胀性对厚板剪切变形的影响。提出了三种剪力校正系数随泊松比变化的模型:解析模型,三次拟合模型和改进模型。在这三个模型中,三次拟合模型在从-1到0.5的整个泊松比范围内均显示出最佳的精度。本文以均匀加载的圆形板为例研究了剪切变形的程度。发现当板材料的泊松比高度为负时,基于Mindlin理论的这种板的最大变形近似于根据Kirchhoff理论的板。当板材的泊松比为-1且仅支撑板材的边缘时,根据Mindlin理论计算的最大挠度会简化为根据Kirchhoff理论进行的计算。这些结果表明,膨胀性减小了厚板的剪切变形,仅当板材料具有高膨胀性时才允许将经典板理论用于厚板。

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