HAMILTONIAN SOLUTION SYSTEM FOR THIN PLATES AND ITS VARIATIONAL PRINCIPLE

The Hamiltonian solution system is generalized to the thin plate problems. Firstly, the Hamiltonian dual differential equations for thin plates are derived. Then, the functional expression of Hamiltonian variational principle, Π_H, is obtained. Differing from those proposed in related reference, the deflection w, the rotation Ψ_x, the moment M_x and the equivalent shear force V_x are taken as the dual variables; For thin plate problems, both elimination and addition of variables are needed when the Hamiltonian functional Π_H is derived using the Hellinger-Reissner functional Π_HR. The process is different from that used in the thick plate problems, where only elimination is utilized. The theoretical achievements of the Hamiltonian system for thin plates provide new effective tools for analytical and finite element solutions of thin plates.