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A multilayered plate theory with transverse shear and normal warping functions

机译：具有横向剪切和法向变形功能的多层板理论

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摘要

A multilayered plate theory taking into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear, the fifth to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho-Parmerter and ( a modified version of) Beakou-Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal stretching, are also considered. These theories, which use the same kinematic field with different warping functions, are compared to analytical solutions for the bending of simply supported plates. Various plates are considered, with special focus on low length-to-thickness ratios: an isotropic plate, two homogeneous orthotropic plates with ply orientation of 0 degrees and 5 degrees, a [0/c/0] sandwich panel and a [-45/0/45/90]s composite plate. Results show that models are more accurate if their kinematic fields (i) depend on all material properties (not only the transverse shear stiffnesses), (ii) depend on the length-to-thickness ratios and (iii) present a coupling between the x and y directions. (C) 2015 Elsevier Ltd. All rights reserved.
机译：提出了一种考虑了横向剪切和正常拉伸的多层板理论。该理论基于具有五个翘曲函数的七个未知运动场。四个变形函数与横向剪切有关，第五个变形函数与正常拉伸有关。翘曲函数是从精确的三维解发布的。它们与为简单支撑的弯曲问题在特定点计算的横向剪力和法向应力的变化有关。保留了Reddy，Cho-Parmerter和Beakou-Touratier理论（的修改版本）进行比较。还考虑了这些理论的扩展版本，它们能够处理正常的拉伸。这些理论使用相同的运动场并具有不同的翘曲函数，并将这些理论与简单支撑板弯曲的解析解进行了比较。考虑使用各种板，特别关注低的长度/厚度比：各向同性板，两个均一的正交各向异性板（层方向为0度和5度），[0 / c / 0]夹心板和[-45 / 0/45/90] s复合板。结果表明，如果模型的运动场（i）取决于所有材料特性（不仅取决于横向剪切刚度），（ii）取决于长度与厚度之比，并且（iii）在x之间存在耦合，则模型更准确。和y方向。 （C）2015 Elsevier Ltd.保留所有权利。

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