四边任意支承条件下弹性矩形厚板辛几何法解析解

利用辛几何法推导出了四边任意支承条件下矩形厚板弯曲的解析解.在分析过程中首先把弹性厚板弯曲问题的简化方程表示为H am ilton正则方程,然后利用辛几何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任意支承条件下矩形厚板弯曲的解析解.由于在求解过程中不需要事先人为选取挠度函数,而是从厚板弯曲的基本方程出发,直接利用数学的方法求出可以完全满足其边界条件的解析解,使得这类问题的求解更加合理.计算实例验证了所采用的方法以及所推导出公式的正确性.

Theoretical solution for rectangular thick plate with arbitrary boundary conditions by symplectic geometry method

The theoretical solution for rectangular thick plate with arbitrary boundary conditions is derived by symplectic geometry method.Firstly,the basic equations for elastic thick plate are transferred into Hamilton canonical equations.Then the symplectic geometry method is used to separate the whole variables and the eigenvalues are obtained.Finally,according to the method of eigen function expansion,the explicit solution for rectangular thick plate with arbitrary boundary conditions is presented.Due to the fact that the basic elasticity equations of thick plate is only used and there is no need to select the deformation function arbitrary,the solution achieved is reasonable.A numerical example testifies the correctness of formulations.