HAMILTONIAN VARIATIONAL PRINCIPLE WITH ARBITRARY PARAMETERS FOR THIN PLATES

The Hamiltonian variational principle and its functional ∏_H(w,M_x,Ψ_x,V_x) for thin plates are generalized and a new Hamiltonian variational principle with two optional parameters, η₁ and η₂, and its functional ∏_Hη1η2(w,M_x,Ψ_x,V_x) are developed. In the derivation process, the Hellinger-Reissner variational principle and functional∏_HR(w,M) for thin plates are developed into a new Hellinger-Reissner variational principle with one optional parameter η₁ and a functional∏_HRη1(w,M), respectively. With variable elimination method (variables M_y and M_xy are eliminated), variable substitution and multiplier method (variables Ψ_x and V_x are added), the Hamiltonian functional with two optional parameters for thin plates,∏_Hη1η2(w,M_x,Ψ_x,V_x is derived from the functional ∏_HRη1(w,M). The variational principle with parameters is the combined form of various variational principles, and it establishes close relationships among these variational principles. By rational selection and evaluation of the parameters η₁ and η₂, many degenerative forms of the functional with parameters can be obtained. This provides an effective tool to develop various finite element models.