A refined theory with exponential through-thickness approximation for cross-ply piezoelectric composite laminates with weak interfaces

An equivalent single layer theory for piezoelectric composite laminates with weak interfaces is built by deducing three through-thickness functions in displacement and potential fields from the three-dimensional elasticity equilibrium equations and electrostatics charge equation. It uses exponential approximation through thickness in displacements and potential. The interfacial bonding conditions are characterized by a linear slip law and an electrically semi-permeable assumption, and used to determine the three through-thickness functions. This refined theory shows high accuracy, but use only six displacement and potential variables, the number of which is independent of the number of layers involved. The closed-form solutions of piezoelectric laminates in cylindrical bending subjected to different sets of edge boundary conditions are presented and fill the gaps in literature. The present solutions can predicts the singular effects of stresses near clamped edges.