A refined hybrid plate theory for composite laminates with piezoelectric laminae

In this paper, a refined theory of laminated composite plates with piezoelectric laminae is developed. The equations of motion of the theory are developed using an energy principle. This formulation is based on linear piezoelectricity, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The theory developed herein is hybrid in the sense that an equivalent single-layer theory is used for the mechanical displacement field, whereas the potential function for piezoelectric laminae is modeled using a layerwise discretization in the thickness direction. For the equivalent single layer, the third-order shear deformation theory of Reddy is used. This hybrid feature is good in that it demonstrates a way in which multilayered smart skin piezoelectric structures may be analysed to accommodate multiple voltage inputs and/or sensor outputs.