矩形悬臂薄板的解析解

首先把弹性薄板弯曲问题的控制方程表示成为Hamilton正则方程,然后利用辛几何方法对全状态相变量进行分离变量,求出其本征值后,再按本征函数展开的方法求出矩形悬臂薄板的解析解。由于在求解过程中不需要事先人为地选取挠度函数,而是从薄板弯曲的基本方程出发,直接利用数学的方法求出可以满足其边界条件的这类问题的解析解,使得问题的求解更加理论化和合理化。文中的最后还给出了计算实例来验证本文所采用的方法以及所推导出的公式的正确性。

Analytical solution for rectangular thin cantilever plate

In this paper,the theoretial solution for the elastic cantilever rectangular thin plate is derived by symplectic geometry method.Firstly,the basic equations for elastic thin plate are transferred into Hamilton canonical equations.And then the whole variables are separated and also the eigenvalues are obtained by the symplectic geometry method.Finally,according to the method of eigen function expansion in the symplectic geometry,the explicit solutions for the elastic cantilever rectangular thin plate are presented.Due to the basic elasticity equations of the thin plate are only used and it is not needed prior to select the deformation function arbitrarily.Therefore,the solution is reasonable and theoretical.In order to proof the correcness of formulations,numerical results are also presented to comparing with that of the other reference.