Shape Control of Composite Plates with Distributed Piezoelectric Actuators in a Three-Dimensional Formulation

Based on the method of sampling surfaces, a hybrid finite-element model is developed for a three-dimensional analysis of laminated composite plates with piezoelectric patches. According to this method, the sampling surfaces inside the layers and piezoelectric patches parallel to the middle surface are selected, and displacements and electric potentials of these surfaces are introduced as unknown functions. The sampling surfaces are located inside the layers and patches at the nodes of Chebyshev polynomials that allows one to obtain numerical solutions asymptotically approaching the solutions of electroelasticity as the number of sampling surfaces tends to infinity. A method to determine the optimal voltages applied to the electrodes of piezoelectric patches that makes it possible to bring the plate to the desired shape by using the inverse piezoelectric effect is proposed.