圆板有限转动弯曲问题解的唯一性

The Uniqueness of Solutions in the Bending Problem of Circular Plates with, Finite Rotation

本文在较为一般的情形下证明了圆板有限转动弯曲问题轴对称解的唯一性.首先基于有限转动弹性圆板的 Reissner 方程,并且考虑了边缘弹性支承的非线性边界条件,建立了非线性两点边值问题,其次在适当的条件下证明了解的唯一性,给出了两个新的结果.特别地,在 von Karman方程的情形下本文结论可以退化到文[2]和[6]中的相应结论.最后还给出了 karman 方程解的唯一性.

In this paper,the uniqueness of solutions in the bending problem ofcircular plates with finite rotation is proved in ordinary cases.First,the nonlinear boundary conditions in the elastical supported edge are considered,and the nonlinear two-point boundary value problem is formulated.Next,the uniqueness of solutions is proved under proper conditions,and two new conclusions are obtained.In the special case of Karman'stheequations,the conclusions of this paper return to those correspondingto related literature.