Theoretic Solution of Rectangular Thin Plate on Foundation With Four Edges Free by Symplectic Geometry Method

The theoretic solution for rectangular thin plate on foundation with four edges free was derived by symplectic geometry method.In the analysis proceeding,the elastic foundation was presented by the Winkler model.Firstly,the basic equations for elastic thin plate were transferred into Hamilton canonical equations.The symplectic geometry method was used to separate the whole variables and eigenvalues were obtained simultaneously.Finally,according to the method of eigen function expansion,the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees were developed.Since the basic elasticity equations of thin plate is only used and it is not need to select the deformation function arbitrary.Therefore,the solution is theoretical and reasonable.In order to show the correction of formulations derived,a numerical example was given to demonstrate the accuracy and convergence of the current solution.