再论圆板轴对称过屈曲问题

A Reinvestigation of Axisymmetric Post-buckling of Thin Circular Plates

从精确的非线性几何关系出发，推导出以过屈曲挠度和径向住移为基本未知量的周边受压圆板轴对称过屈曲问题的控制方程。采用打靶法和位移参数小步延拓法直接数值求解了所得非线性常微分方程边值问题，获得了板进入过屈曲状态后周边压力大范围变化的全局解。计算结果表明，当过屈曲挠度大于５倍板厚以后ｖｏｎ（）方程解与本文解有明显差别。

Based on the exact non-linear geometric eqtiations the governing equations of ax-isymmetric post-buckling problems of circular plates subjected to enplane boundary compres-sores are deduced in terms of the buckled deflections and the radial displacements of theplates. By using shooting method and analytical continuation of small parameters of the de-flections, the obtained non-linear boundary value problems of ordinary differential equationsare solved directly and the global solutions of the buckled state of the plates with largeranges of the boundary compressures are get. The numerical results show that there exists aobvious difference between the present solutions and those of von karman equation when thepost-buckled deflection is 5 times greater than the thickness of the plates.