Hamiltonian System Theory Applied Research In The Plate Bending Problem

In this paper, the application of Hamiltonian systematic theory in plate bending problem is studied. The governing equations of the problem are derived in Hamiltonian form by using variable substitution and variational principle. Then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem. The result can be derived by analytical method. While in traditional elasticity mechanics, we make our best to eliminate the unknown variables and can get the simplest equation in a brief form. At the same time, the rank of equation is increased, so we cannot solve the equation by direct method and have to resort to semi-converse method.The detailed research and derivation for thin plate bending are carried out by means of Hamiltonian systematic theory in this paper. The results are effective and accurate. Extending thin plate bending problems to thick plate bending problems, we get the analytical solution for thick plate with two opposite edges simply supported. Several computational examples in the paper are of practical values to engineering applications.