Static electromechanical response of smart composite/sandwich plates using an efficient finite element with physical and electric nodes

Abstract

An efficient quadrilateral element, recently developed by the authors, based on an improved zigzag theory is assessed for the static electromechanical response of hybrid plates with electroded piezoelectric sensors and actuators. The theory accounts for the transverse normal strain due to the electric field in the approximation of deflection. The electric potential is approximated as layerwise quadratic across the thickness. By introducing an electric node in the element for the electric potentials of the electroded piezoelectric surfaces, the equipotential condition of such surfaces is modelled very efficiently. The electric potential degrees of freedom (DOF) corresponding to the quadratic component of the electric potential distribution are associated with the four physical nodes to allow for the inplane electric field induced due to direct piezoelectric effect. The requirement of C1 continuity of interpolation functions of the deflection is circumvented by employing the improved discrete Kirchhoff constraint technique. The finite element (FE) formulation is validated by comparing the results with other available results in the literature. Comparison of the present results for static response of a variety of piezoelectric bimorph, hybrid composite and sandwich plates, with 3D analytical and FE solutions and those of other available elements establishes that the present element is accurate, robust and computationally efficient.