四边任意支承条件下弹性矩形薄板弯曲问题的解析解

利用辛几何法推导出了四边为任意支承条件下矩形薄板弯曲的解析解。在分析过程中首先把矩形薄板弯曲问题表示成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四边为任意支承条件下矩形薄板弯曲的解析解。由于在求解过程中并不需要人为的事先选取挠度函数，而是从弹性矩形薄板弯曲的基本方程出发，直接利用数学的方法求出问题的解析解，使得这类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方法的正确性。

Theoretic Solution for Rectangular Thin Plate with Arbitrary Boundary Conditions By Symplectic Geometry Method

The analytical solution for a rectangular thin plate with arbitrary boundary conditions is derived. The basic equations for elastic thin plate are transformed into Hamilton canonical equations, And then the symplectic geometry method is adopted to separate the whole variables and the eigenvalues are obtained. According to the technology of eigen function expansion, the explicit solution can be presented. It is unnecessary to select the deformation function, thus the solution conforms to the requirement, a numerical example verifies the aualidity.