SEPARABLE K-CANONICAL EQUATION OF PIEZOELECTRICITY AND EXPLICIT SYMPLECTIC METHOD FOR LAMINATED PLATES

In the application of symplectic numerical methods to Hamiltonian systems, it is important to recognize that a nearby Hamiltonian is approximately conserved for exponentially long times. The numerical result of separable differential equation is very accurate by using the symplectic numerical methods. Based on the modified Hellinger-Reissner (H-R) variational principle of piezoelectricity，Hamiltonian four-node rectangular element matrix was constructed in this paper. Then the separable K-canonical formulation of the Hamiltonian element was derived by exchanging the row-column of Hamiltonian element formulation. Finally, the explicit symplectic schemes was employed to solve the static problem of piezoelectric material laminated plate. The numerical examples show that the explicit symplectic method can be applied to the large-scale differential equation.