A nonconforming generalized H-R mixed finite element is developed for
static and dynamic analysis of piezoelectric composite laminated plates.
The overall structure is solved discretely using 8-node hexahedral nonconforming
solid elements, discarding many of the artificial assumptions in the plate
and shell theories. The displacement and stress can be obtained directly
through linear equations, including potential and electric displacement. The
-continuous
polynomial shape function commonly for the displacement methods is used to represent
the displacement variables and stress variables, and the nonconforming term is introduced
into the interior of the elements, which allows it to show better numerical performance
than the similar conforming elements. The displacement and stress boundary conditions
are introduced simultaneously so that the actual out-of-plane stress results are obtained
at the free boundary. The free-vibrational characteristic equations for piezoelectric
laminated plates are derived by combining the nonconforming generalized H-R mixed
variational principle with Hamiltonian principle. The accuracy of the present method
is verified by analyzing several representative numerical examples of laminated plates.