In the present work, a novel explicit solution is proposed for obtaining twisting deformation and optimal shape control of smart laminated cantilever composite plates/beams using inclined piezoelectric actuators. The linear piezoelectricity and plate theories were adapted for the analysis. A novel double integral multivariable Fourier transformation method and discretised higher order partial differential unit step function equations were employed. For the first time, an exact solution is developed to analyse electro-mechanical twisting moments in smart composite structures. Since there are no published benchmark results for verification, a series of simple, accurate and robust finite element (FE) analysis models and realistic electro-mechanical coupled FE procedures are developed for the effective prediction of the structural behaviour of the smart laminated piezo-composite structures under arbitrary loads. In addition to the novelty of the explicit solution, more comprehensive FE simulations of smart structures and step-by-step guidelines are discussed. The effect of various parameters including electro-mechanical twisting coupling, layup thickness, actuators size, placement, and inclination angle, electrical voltage, stacking sequence, and geometrical dimension was taken into account. The comparison of results showed an excellent agreement. Unlike the earlier studies, the proposed method does not require the characteristic and trial deflection function to be predetermined.
Macro fiber composite (MFC) actuators developed by the NASA have been increasingly used in engineering structures due to their high actuation power, compatibility, and flexibility. In this study, an efficient two dimensional quadratic multi-layer shell element by using first order shear deformation theory (FOSDT) is developed to predict the linear strain–displacement static deformation of laminated composite plates induced by MFC actuators. FOSDT is adapted from the Reissner–Mindlin plate theory. An eight-node quadratic piezoelectric multi-layer shell element with five degrees of freedom is introduced to prevent locking effect and zero energy modes observed in nine-node degenerated shell element. Two types of MFC actuators are used: (1) MFC-d31 and (2) MFC-d33, which differ in their actuation forces. For result verification, the electro-mechanically coupled quadratic finite element (FE) model is compared with the ABAQUS results in various examples. Comparison of the results showed good agreement. The proposed quadratic FE formulation is simple and accurate, which eliminates the need for costly FE commercial software packages. It was observed that earlier studies have mostly emphasized on the effect of actuation power and MFC fiber orientations on mechanical shape deformation of smart composite plates. In this study, a more comprehensive, in-depth investigation is conducted into host structure performance such as boundary conditions, laminate stacking sequence configuration, and symmetry/asymmetry layups.
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