弹性地基上矩形薄板问题的Hamilton正则方程及解析解  

HAMILTON CANONICAL EQUATIONS AND THE ANALYTICAL SOLUTION FOR RECTANGULAR THIN PLATE ON ELASTIC FOUNDATION

作　　者：钟阳[1] 张永山[2] 

机构地区：[1]大连理工大学土木学院,大连116024 [2]广州大学土木学院,广州510405

出　　处：《固体力学学报》2005年第3期325-328,共4页Chinese Journal of Solid Mechanics

摘　　要：利用辛算法求出弹性地基上矩形薄板问题的解析解,将弹性地基视为双参数弹性地基,直接从弹性矩形薄板的控制方程推导出了问题的Ham ilton正则方程,为求出任意边界条件下问题的理论解奠定了基础,并且通过算例验证了文中所采用方法的正确性.The Hamilton canonical equations and the theoretical solution for rectangular thin plate on foundation with four free edges are derived by symplectic geometry method. Firstly, the basic equations for elastic thin plate on elastic foundation are transferred into Hamilton canonical equations. Then the whole variables are separated and 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 a rectangular thin plate on the foundation with four free edges are presented. Numerical results based on the solution are compared with that in literature to clarify the correctness of the solution.

关 键 词：弹性薄板 弹性地基 HAMILTON正则方程 辛算法 解析解 双参数弹性地基 弹性矩形薄板 板问题 任意边界条件 方程推导 

分 类 号：TU339[建筑科学—结构工程]