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Improved shear correction factors for deflection of simply supported very thick rectangular auxetic plates
International Journal of Mechanical and Materials Engineering Pub Date : 2016-11-25 , DOI: 10.1186/s40712-016-0065-z
T. C. Lim

The first-order shear deformation theory (FSDT) for plates requires a shear correction factor due to the assumption of constant shear strain and shear stress across the thickness; hence, the shear correction factor strongly influences the accuracy of the deflection solution; the third-order shear deformation theory (TSDT) does not require a correction factor because it facilitates the change in shear strain across the plate thickness. This paper obtains an improved shear correction factor for simply supported very thick rectangular plates by matching the deflection of the Mindlin plate (FSDT) with that of the Reddy plate (TSDT). As a consequence, the use of the exact shear correction factor for the Mindlin plate gives solutions that are exactly the same as for the Reddy plate. The customary adoption of 5/6 shear correction factor is a lower bound, and the exact shear correction factor is higher for the following: (a) very thick plates, (b) narrow or long plates, (c) high Poisson’s ratio plate material, and (d) highly patterned loads, while the commonly used shear correction factor of 5/6 is still valid for the following: (i) marginally thick plates, (ii) square plates, (iii) negative Poisson’s ratio materials, and (d) uniformly distributed loadings.

中文翻译:

改进的剪切校正系数,用于简单支撑的非常厚的矩形厚板的挠度

板的一阶剪切变形理论(FSDT)需要剪力校正因子,这是因为假设整个厚度方向上的剪应力和剪应力恒定。因此,剪切校正因子极大地影响了挠度解的精度。三阶剪切变形理论(TSDT)不需要校正因子,因为它有助于在整个板厚上改变剪切应变。通过匹配Mindlin板(FSDT)和Reddy板(TSDT)的挠度,可以得到简单支撑的非常厚的矩形板的改进的剪切校正系数。因此,对Mindlin板使用精确的剪切校正因子可得出与Reddy板完全相同的解。通常采用5/6剪切校正因子是一个下限,
更新日期:2016-11-25
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