纯弯曲下薄壁圆柱壳屈曲的非线性分析

为解决薄壁圆柱壳在纯弯曲下由于横截面的椭圆化而引起的屈曲几何非线性问题. 基本假设是改良的Brazier 简单理论,把圆柱壳的纯弯曲变形简化成一个两阶段的过程,分别求得纵向弯曲变形应变能和横截面变形应变能,然后利用最小势能原理求出作用力矩与杆端旋转角度的关系,最后分析可知:壳体长度参数越小,对应的圆柱壳壁越薄,非线性的影响越大;剪力大小参数越小,边界条件对椭圆化变形影响越小,非线性的影响越大.

NONLINEAR BENDING RESPONSE OF THIN-WALLED CYLINDRICAL SHELLS UNDER PURE BENDING

This paper focuses on solving the problem of geometrically nonlinear buckling of thin-walled cylin- drical shells under pure bending with the cross-section tending to be oval-shaped. The basic hypothesis is based on the modified Brazier simple theory that the deformation of a shell under pure bending can be simplified as a two-stage process. By the two-stage process, the longitudinal bending strain energy and the cross-sectional deformation strain energy are obtained. The relationship between the end-rotation and the applied moment is obtained through the principle of the minimum potential energy. It is shown that: the smaller the shell length parameters and the thinner the corresponding cylindrical shell wall, the greater the impact of nonlinearity will be; the smaller the shear length parameters and the smaller the effect of the boundary conditions on the deformation leading to oval section shape, the greater the impact of nonlinearity will be.