翼截面柱体的弯曲问题

On the St. Venant Flexure Problem for Cross Sections of a Series of Symmetrical Airfoils

摘要: 本文讨论一系列对称翼截面柱体的弯曲问题,柱体空端锁甲外力的方向与主题的对称面垂直.这问题一般可简化为寻找三个平面挑和函数,其中两个函数给出边界值,另一函数给出边界上法向的微商.我们设法将这些调和函数的边界值表达为複变函数的实数或虚数部分,这样所得的复变函数在柱体截面内常会表现有奇异点.本方法中的一个重要内容为：如何削去这些奇异点.本文求得问题的精确普遍解,其中含一个参数,可用来调节截面的厚度.本文最后给出一个例子,阐明求应力函数、扭转厚度及湾区中心的步骤,给出受扭转和弯曲时沿截面边界上剪切的分布情况.

Abstract: This paper deals with the problem of flexure cantilever beam with a symmetrical airfoil cross.The loading is applide at the free end ai right angles to the plane of symmetrical as shown in fig.1.The material is assumed to be homegeneus and isotropic,and the body forces are assumed to be negligble.In general,such a beam will twist as bend.