Improved Electromechanical Response in Laminated Piezoelectric Plates Using a Zigzag Theory

Abstract

The zigzag theories are a class of the shear deformation theories that combine the accuracy of the layerwise theories and the efficiency of the equivalent single-layer theories. A nine variable zigzag theory is presented in this work for the laminated piezoelectric plates. Unlike any existing zigzag theory, the transverse shear boundary conditions on the lateral surfaces are not imposed. The theory satisfies interlaminar continuity of displacements and transverse shears stresses. A variational principle is used in deriving governing equations. Bending responses have been obtained under sinusoidal and uniformly applied mechanical and electromechanical loads. Three-dimensional (3D) exact elasticity and piezoelasticity solutions have been used to assess the accuracy of the present theory for a number of simply supported rectangular laminated composite and piezoelectric plates. The transverse shear stress relaxation condition at the boundary surfaces has led to improved predictions in the displacements, stresses, and electric field entities. Present theory is also compared with a number of shear deformation theories to illustrate how significantly the responses get improved due to the transverse shear relaxation.