Electric Potential Recovery in Smart Composite Plates
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ORIGINAL RESEARCH
Electric Potential Recovery in Smart Composite Plates Yong‑Min Jeong1 · Jun‑Sik Kim1 Received: 28 April 2020 / Revised: 21 July 2020 / Accepted: 1 September 2020 / Published online: 14 September 2020 © Korean Multi-Scale Mechanics (KMSM) 2020
Abstract A post-processing method is proposed to improve the accuracy of electric potential in smart composite plates. We employ a higher-order plate theory that consists of cubic in-plane and quadratic out-of-plane displacements. Starting from threedimensional piezoelectricity, we systematically develop post-processing and recovery procedures by using three-dimensional piezoelectric equilibrium equations. The method proposed is applied to cross-ply piezoelectric laminates in cylindrical bending. The results obtained are compared to those of exact elasticity. It is observed that the mechanical quantities approach those of elasticity as the plate becomes very thin, whereas the electrical quantities do not. The discontinuity of transverse shear strains plays a crucial role in the prediction of electric potential. Irrespective of the length-to-thickness ratios of plates, the error of electric potential in the higher-order theory is about 10%. This error can be reduced by improving the transverse shear strains via the proposed method. Keywords Electric potential · Smart composite plates · Post-processing
Introduction Piezoelectric materials have had various engineering applications, which can be used either actuator, sensor, or both. The mechanics of piezoelectric materials have been spotlighted in past three decades. They are formulated by embracing piezoelectric constitutive equations into classical variational principle. It is therefore important to understand plate theories and piezoelectric characteristics. One of the failure mechanisms of laminated composite plates is ‘delamination’ that is caused by the transverse stresses. Many plate theories therefore have been developed to accurately predict them [1–4]. Subsequently such plate theories extended to smart composite plates [5–10]. In many researches, mechanical displacements are modeled by polynomials with layer-wise or zigzag functions. For laminated composite plates, these work very well for transverse shear deformation. On the other hands, for smart composite plates, an electric potential has to be modeled as well. In the same way, the potential has been modeled * Jun‑Sik Kim [email protected] 1
by polynomials, layer-wise or zigzag functions. Many researches have focused on mechanical responses for the prescribed electric potential. Even if they have calculated the electric potential, the results obtained are merely compared for various mechanical loading conditions. It is very rare in literature to investigate the effect of transverse strains on the electric potential. Post-process methods have been developed to circumvent a complexity of using higher-order theories [11–14]. The method utilizes the solution of base theories, where displacements are improved by using stress equilibrium equat
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