轴对称正交异性圆环壳的齐次完全渐近解

承受轴对称载荷的正交异性圆环壳的静力分析,归结为求解一非齐次二阶复变量方程.当所含参数μ较大时,常采用渐近解法.因方程含一阶转点,所以求全域一致有效且达到薄壳理论精度的完全渐近解较为困难.过去,齐次解只求到一级近似.本文采用广义Airy函数方法,求出了高级近似.这样,轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开.

Fully Asymptotic Soultion of the Orthotropic Toroidal Shells under Axisymmetric Loading

The asymptotic analysis for the stresses in orthotropic toroidal shells under axisymmetic loading becomes to solve an inhomogeneous second-order diffential equation in complex form. It is good to use the asymptotic method when the parameter u takes a large value. However,it is difficult to find the uniformly valid and fully asymptotic solution within the accuracy of theory of thin shells because of the turning point in the equation. So far only first-order approximation for the homogeneous solution is found. In present paper the high-order approximation to the homogeneous solution is found by use of a class of generalized Airy functions. Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.