Sumplectic Superposition Solutions For Two Kinds Of Bending Problems Of Orthotropic Rectangular Thin Plates With One Edge Clamped

The bending problem of orthotropic rectangular thin plate under a uniform load with one edge clamped and the other three edges free is studied by the symplectic superposition method.Firstly,the Hamiltonian system corresponding to the thin plate equation is derived,and the original bending problem is decomposed into three subproblems by analyzing the boundary conditions,two of them are bending problems with two opposite edges slidingly supported,and the other is bending problem with one edge simply supported and the opposite edge slidingly supported.Secondly,the solutions in the form of series of the three subproblems are obtained respectively by the symplectic elasticity method,and then the symplectic superposition solution of the original bending problem is obtained by the superposition of the above three solutions of the subproblems.In Addition,the bending problem of orthotropic rectangular thin plate with point-supported at two adjacent corners and clamped at the opposite edge under uniformly load is also studied by the symplectic superposition method.By analyzing the boundary conditions,the original bending problem is decomposed into three subproblems which are two opposite edges simply supported problems,and then the analytical solutions of the three sub-problems are obtained respectively by using the symplectic elasticity method.Next,the symplectic superposition solution of the bending problem is obtained by superposing the solutions of the three subproblems.Finally,the correctness of the two kinds of symplectic superposition solutions are verified by specific examples,respectively.