正交异性圆环壳应力状态的渐近分析

本文导出了另一组正交异性壳的基本方程。方程含三个复值变量ｋ１、ｋ２和，复值量的实部分别是中面的曲率变化和扭率。在旋转壳轴对称变形情况下，通过引入复值变量，方程组直接转化为一个二阶常微分方程。的实部代表子午线元素的转角。对于正变异性圆环壳，假定轴对称荷载沿径线方向接任意规律分布，得出了方程的渐近解。计算了壳中的应力和位移。

The Asymptotic Analysis for the Stresses in Orthotropic Toroidal Shells under Axially symmetric Loads

In this paper another set of basic equations for orthotropic shells was derived. The equations contain three complex variables of which the real parts are the changes of curvatures and twist for middle surface respectively. In the case where the deformations of rotational shells are axially symmetric, the set of equations reduces to a second-order differential equation directly by introducing the complex variable, of which the real part represents the angle by which an element of the meridian rotates. Axial symmetric loads are assumed to be distributed arbitrarily along the meridian and the asymptotic solution of the equation for orthotropic toroidal shells is obtained with the stresses and displacements thus calculated.