Shape Control of Composite Plates with Distributed Piezoelectric Actuators in a Three-Dimensional Formulation
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SHAPE CONTROL OF COMPOSITE PLATES WITH DISTRIBUTED PIEZOELECTRIC ACTUATORS IN A THREE-DIMENSIONAL FORMULATION
S. V. Plotnikova and G. M. Kulikov*
Keywords: electroelasticity, composite plate, shape control, finite-element method, method of sampling surfaces 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.
Introduction Smart thin-walled structures with piezoelectric sensors and actuators are currently gaining ever-increasing acceptance in engineering. The use of piezoelectric actuators discretely distributed on external surfaces allows one to give a specified form to a structure and also to compensate for the action of temperature and mechanical loads on it by applying the corresponding voltage to electrodes of piezoelectric lap plates. The difficulty in solving these problems is caused
The Tambov State Technical University, Russia * Corresponding author; e-mail: [email protected]
Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 5, pp. 821-840, September-October, 2020. Original article submitted December 27, 2019; revision submitted July 21, 2020. 0191-5665/20/5605-0557 © 2020 Springer Science+Business Media, LLC
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by the complex distributions of mechanical and electric fields in thin-walled composite structures with piezoelectric lap plates; therefore, the methods of their calculation are refined constantly. The calculation of layered composite plates with piezoelectric lap plates based of the classical Kirchhoff theory was performed in [1], and a satisfactory agreement between theoretical and experimental results for displacements was obtained. In [2, 3], the calculation methods for smart structures with piezoelectric lap plates obtained a further development on the basis of the Mindlin theory of plates. In [4-10], to calculate layered piezoelectric structures, a 6-parameter model considering the transverse compression is used, where displacements vary linearly across their thickness. Elaborated are developed 3D isoparametric 8- and 18-node finite elements with various distributions of electric potential across the thickness the package and piezoelectric actuators. A more general approach is based on the application of 7- [11, 12] and 9-parameter [13, 14] models allowi
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