用弹性力学方法研究平夹支圆板的稳定问题

本文用数学弹性稳定理论导出圆板弹性稳定问题的基本方程，对于平夹支圆板，由Ｈ变换给出位移及其偏导数的级数式，直接求得问题的解析解，数值计算的结果表明，弹性力学方法注得的薄圆板临界载荷低于经典板理论的结果，而这两种理论所反应的临界载荷与板的厚径比、泊松比之间的变化关系也略有不同。

A Study of Stability Problem of Circular Plate with Clamped Edge Based on the Theory of Elasticity

n this paper, the governing equations of the stability problem of a circular plate are derived on the basis of the mathematical stability theory of elasticity.For a circular plate with clamped edge,the analytical solution is directly obtained by use of the H-transformation. The numerical results show that the critical load from the mathematical stability theory of elasticity is slightly lower than that from the classical plate theory. The rates of change of the critical loads with the size and Poisson's ratio of the plate from both of theory are slightly different.