Electro-mechanical response of piezoelectric laminated plates using finite element methods

The idea of 'smart structures' is relatively new. One of the many available types of materials for sensors and actuators which serve as the active structural element in smart structures, is the piezoelectric material. Due to complexities in satisfying the equations of equilibrium and boundary conditions, exact solutions to such problems are not available and finite element techniques are often used. As a viable alternative to time-consuming and expensive complete three-dimensional analysis, an efficient combination of in-plane two-dimensional analysis and quasi-three-dimensional analysis can be used. The objective of this research is to incorporate constitutive equations of piezoelectrics into the finite element analysis to determine the electro-mechanical response of plates with piezoelectric layers.; In inplane analysis, the plate is modelled using nine-node isoparametric plane stress elements. The electro-mechanical response of plates with piezoelectric patches is investigated. It is found that shape of the piezoelectric actuator patches depends on the desired stress fields, however sharp comers in the patches result in high stress gradients and should thus be avoided. The application of electric field to induce stress in plates can be effectively used to achieve stress attenuation. The finite element technique is also used to detect deflections in plates under bending loads.; Since these laminated plates consist of distinct layers, the interlaminar response and delamination characteristics of the laminated plates are of importance. The quasi-three-dimensional analysis technique models the through-the-thickness cross-section of the laminate using two-dimensional element with three degrees of freedom at each node. High interlaminar stress gradients in the vicinity of electrodes and at the edges of surface mounted piezoelectric layers, could result in possible delamination of the plate. This analysis shows that delamination detection and suppression can be achieved using appropriate electric fields on embedded piezoelectric layers.; This dissertation addresses the finite element formulation and some aspects of the conceptual basis for design issues of surface mounted and embedded piezoelectric layers in laminated plates.