Characterization of anisotropic, non-homogeneous plates with piezoelectric inclusions

A formulation for the determination of the stiffness, the dielectric and the piezoelectric properties of arbitrarily anisotropic and non-homogeneous laminated composite plates is presented. The linear elastic problem of a sample fibre, an ideal line through the thickness of the plate, is solved in terms of influence coefficients for both the generalized deformations (i.e. linear and angular strains of the plate) and the warping unknowns. The generalized deformations and the warping unknowns, as well as their plane-wise spatial derivatives, are preserved in analytical form. The in- and out-of-plane warping displacements are described by means of arbitrary one-dimensional finite elements, accounting for the full three-dimensional material constitutive law; as a consequence, the desired level of accuracy can be achieved in the determination of interlaminar and intralaminar stresses and strains. The primary result is represented by the stiffness parameters of a general plate, which implicitly account for plane stress effects and for both interlaminar and intralaminar equilibrium and compatibility. Secondary results are represented by the full three-dimensional strain and stress fields due to the local internal force and moment fluxes. The extension to the inclusion of laminæ of piezoelectric materials in the lamination sequence of the plate is addressed. Numerical examples related to the mechanical and piezoelectric characterization of laminated plates are discussed.