复合材料薄壳最佳缠绕状态的研究

A Study of the Optimum Twisting State of Shell Twisted with Fibre Composite and Its Application

用张量分析及微分几何对旋转曲面上的测地线微分方程及斜驶线微分方程进行了研讨。纤维缠绕除满足短程线的环向缠绕 (周向缠绕 ) ,并考虑到对纤维缠绕结构 ,提高其层间剪切强度是提高纤维缠叠层构件整体破坏强度的主要途径 ,而对纤维缠绕构件 ,采用横跨交叉编织是提高层间剪切强度的一种方法。根据这种计算的思路 ,对某叶环复合材料环壳的缠绕方式采用环形周向缠绕加环跨交叉缠绕的方法 ,优于美国采用的单纯环向缠绕方法。建议的环形周向缠绕和环跨交叉缠绕均是在满足短程线方程的前提下进行的。叶环缠绕完全可按环跨交叉缠绕及周向缠绕相结合的程序进行重叠缠绕。本文还证明了旋转柱面上的测地线方程、螺旋线方程以及斜驶线方程三者的一致性。

The differential equation of geodesic and the differential equation of inclined path of revolutionary curved surface have been studied by using tensor analysis and differential geometry. For fibre circumferential shell twist, besides satisfying the toroidal twist (circumferential twist) of the shortest path, and also considering the fibre twisting structure, increasing the interlayer shear strength is the main method for increasing the global breaking strength of the layered component twisted with fibre. But for fibre twisting component using cross twist is an alternative method to increase interlayer shear strength. Based on this idea the combination of toroidal twisting and cross twisting for the composite shell twisting is a better method than the simple toroidal twisting method used in the United States of America. The precondition for the toroidal twisting and cross twisting suggested above is to satisfy the shortest path equation. The present parper has also proved the consistence of geodesic equation, solenoidal equation and inclined path equation on the revolutionary cylinder. The shell twisting has already been used in a variety of structures.