Symplectic Superposition Solution For Bending Problem Of An Orthotropic Rectangular Thin Plate With Two Adjacent Edges Clamped And Its Opposite Point-supported At A Corner

The Hamiltonian canonical equation of the bending problem of a uniformly load-ed orthotropic rectangular thin plate with two adjacent edges clamped and its opposite point-supported at a corner is studied,and the eigenvalues and eigenfunctions of the Hamiltonian operator with two opposite sides simply supported are obtained.Firstly,according to the symplectic orthogonality and completeness of the eigenfunctions,the general solution of the Hamiltonian canonical equation with two opposite sides simply supported is calculated.Then,we obtain the symplectic superposition solution of the original bending problem by the symplectic superposition method.Finally,in order to prove the correctness of the symplectic superposition solution,we calculate the deflections and bending moments values at some points of the bending problems of isotropic rect-angular plates and orthotropic rectangular plates by using the symplectic superposition solution obtained in this paper.