圆锥壳方程的二次渐近解

本文由旋转壳的一对二阶常微分方程得出圆锥壳的复变量方程,利用渐近积分法推导出方程的一次近似解和二次近似解。二次近似解达到薄壳理论所具有的精度,一次近似解也具有足够精度。对于所取算例,本文解的计算结果与已有的Kelvin函数解的结果符合良好。但本文解为有限形式的简单表达式,便于计算应用。

Asymptotic Solution of the Second Degree for the Equation of Conical Shells

In the present paper, the complex equation of conical shells has been obtained in terms of two ordinary differential equations of the second order for shells of revolution. The first and second approximations of the solution have been derived by asymptotic integration of the equation. The second approximation of the solution is of the same accuracy as theory of thin shells, and the first approximation is also sufficiently precise for engineering computation. The expressions of the solution take simple and finite forms, so are convenient for use in engineering computation. For numerical example, the results obtained by use of the present solution are in good agreement with those of the exact solution expressed in terms of Kelvin function.