Study On Anisotropic Plate Under Hamiltonian System

In this paper, Applying the Hamiltonian systemic theory tothe analytic solutions for solving bending problem of anisotropicplate.The first part main introduces the theory of the Hamiltoniansystem,there are three forms of classical mechanics equations ofmotion,they are different in form, they are different both in analyticsolution and numerical solution.Also introduces the related basicknowledge of Hamiltonian system mathematical foundation insymplectic geometry space.The second part is the introduction of the bending problem oforthotropic plate into the Hamiltonian system.The basic idea isthis:first the anisotropic plate bending problems under the Lagrangesystem is transformed into the Hamiltonian system by the dualtransformation. then get the he corresponding Hamilton dualequation,then get the dual equation solution of eigenvalue andeigenvector by using the method of separation of variables,then get eigenfunction-vector expansion through the boundary condition.lastthe analytic-al solutions of the bending of Orthotropic plates arederived.And this method is extended to anisotropic plate bendingproblems in general.in this paper,the method is from the basic equations of elasticmechanics into the Hamiltonian system. the equation derived in thisdissertation is simple in form.In solving problems do not assumethat the deflection function. The Hamilton dual equation to solve thedeflection function, and then we can get the solution of the problem.