一般旋转壳在轴对称变形下的复变量方程

Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution

本文在Love-Kirchhoff的假定下,求得了一般旋转壳在轴对称变形下的复变量方程.当旋转壳是圆截面环壳时,这些方程简化为F.Tlke(1938),R.A.Clark(1950)和B.B.HOBOm^JIOB(1951)的方程.当平均半径(?)比环截面半径a大得很多时,求得了细环壳的复变量方程,当这个细环壳的截面是圆形时,简化作为作者(1979)的圆截面的细环壳复变量方程,我们列出了椭圆截面的细环壳复变量方程.当椭圆截面近似于圆截面时,该方程在形式上和圆细环壳方程基本相同.

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirch-hoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F. T61ke(1938)[3], R. A. Clark (1950)[4]and B. B. HoBo-OB(1961)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex varaible may be simplified into the equation for slender ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slender circular ring shells given by this author(1979)[6]. If the form of elliptic cross section is near a circle, then the equation of slender ring shell with near-circle elliptic cross section may be reduced to the complex variable equation similar in form for circular slender ring shells.