Finite element formulation for passive shape control of thin composite plates with integrated piezoelectric layer

Abstract

The Hamilton’s principle for piezoelectric materials and the strain displacement relations based on the classical laminate theory’s kinematics of deformation are utilized in deriving the piezoelectroelastic finite element equations of motion. Lagrange interpolation functions for in-plane displacement and Hermite cubic shape functions (conforming type) for transverse deflection are implemented through a four noded rectangular element. The formulation does not account voltage as the nodal degree of freedom. The computer code developed for composite plates with integrated piezoelectric sensors and actuator layers has been extensively validated for piezoelectric behaviour, static deflection and free vibration. The laminate deflection suppressed depends on the magnitude of the voltage applied, and this is a passive method of shape control. The effect of fibre orientation, stacking sequence and number of plies has been part of the numerical exercise on passive shape control. © Springer Science + Business Media B.V. 2008.