基于4变量精确平板理论的剪切效应分析

Shear Effect Analysis on Plates Based on the 4-Variable Refined Plate Theory

由于中厚板壳结构或者复合材料板壳结构中横向剪切模量与面内伸缩模量之比较低,剪切效应对其结构力学行为的影响较为严重.该文基于4变量精确平板理论(refined plate theory,RPT),对平板弯曲过程中的剪切效应进行了分析和讨论.首先对RPT进行了简要的介绍,然后以受横向均布载荷的四边简支矩形板为例,进行了无量纲的数值计算,着重讨论了平板的几何尺寸和性质对其剪切效应的影响:剪切效应随着厚度增加而加强,尤其是当宽厚比小于10以后,剪切效应会迅速加强;剪切效应随横向剪切模量与面内伸缩模量的比值减小而增强;在同种条件下,"剪切"挠度在正交各向异性板中的比重始终大于其在各向同性板中的比重,并且平板越厚或者长宽比越大,两种板的剪切效应差异性越大;各向同性板中的剪切效应受长宽比的变化表现得更加敏感,其"剪切"挠度比重随长宽比的增大而持续减小,而正交各向异性板中的"剪切"挠度比重则呈现出先减小后增大的趋势.研究结果可为提高板壳结构弯曲分析的准确性提供参考.

For moderately thick plates or composite plates, due to the low ratio of the transverse shear modulus to the in-plane extension modulus, the shear effects signify much to the mechanical behavior of structures. Based on the 2-variable refined plate theory （ RPT）, the discnssion about the shear effects on the bending of plates was carried out. The RPT was introduced briefly at first, then numerical examples of simply supported rectangular plates subjected to uniformly distributed load were given, with a focus on the geometry and property effects on the shear effects. The shear effects increase with the plate thickness, especially dramatically when the width-thickness ratio is less than 10; the shear effects increase with the ratio of the transverse shear modulus to the in-plane extension modulus; under the same condition, the proportion of the ＂shear＂ deflection in the orthotropic plate is always larger than that in the isotropic plate, and the difference of shear effects between these 2 kinds of plates becomes more significant with the increase of the thickness or the aspect ratio; the shear effects in the isotropic plates are more sensitive to the aspect ratios, and the proportion of the ＂shear＂ deflection in the isotropic plate decreases with the aspect ratio, but decreases first and increases later in the orthotropic plate.