Smart composite plate shape control using piezoelectric materials
Elshafei, Mostafa Adnan
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In the present work, the shape control of fiber reinforced composite plate with embedded piezoelectric actuators is investigated. A finite element formulation is developed for modeling a laminated composite plate that has distributed piezoelectric actuators and sensors subjected to both mechanical and electrical loads. A simple, higher order, shear deformation theory with Hamilton's principle is used to formulate the equations of motion. The model represents the parabolic distribution of transverse shear stresses and the non linearity of in-plane displacements across the thickness. The model is valid for both segmented and continuous and the non linearity of in-plane displacements across the thickness. The model is valid for both segmented and continuous piezoelectric elements, which can be either surface bonded or embedded in the laminated plate. A four-node, bilinear, isoparametric, rectangular element with seven degrees of freedom at each node is developed. The electric potential is treated as a generalized electric coordinate like the generalized displacement coordinates at the mid-plane of the actuator layers. For shape control, an optimization algorithm, based on a finite element technique, is presented for an optical applied voltage to each actuator to minimize the error between the desired shape and the actual shape. The error (objective) function is the mean square of the error between the point in the actual surface and the corresponding point in the desired surface. Based on these techniques, two computer programs have been developed, an finite element modeling of a composite plate with piezoelectric actuators and an optimization model of the actuator voltages for shape control. The present work demonstrate the feasibility of the application of the piezoelectric actuators for the shape control of composite plates used in aerospace structures.
Aeronautical and Astronautical Engineering
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