Analysis of smart functionally graded materials using an improved third order shear deformation theory



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Smart materials are very important because of their potential applications in the biomedical, petroleum and aerospace industries. They can be used to build systems and structures that self-monitor to function and adapt to new operating conditions. In this study, we are mainly interested in developing a computational framework for the analysis of plate structures comprised of composite or functionally graded materials (FGM) with embedded or surface mounted piezoelectric sensors/actuators. These systems are characterized by thermo-electro-mechanical coupling, and therefore their understanding through theoretical models, numerical simulations, and physical experiments is fundamental for the design of such systems. Thus, the objective of this study was to perform a numerical study of smart material plate structures using a refined plate theory that is both accurate and computationally economical. To achieve this objective, an improved version of the Reddy third-order shear deformation theory of plates was formulated and its finite element model was developed. The theory and finite element model was evaluated in the context of static and dynamic responses without and with actuators. In the static part, the performance of the developed finite element model is compared with that of the existing models in determining the displacement and stress fields for composite laminates and FGM plates under mechanical and/or thermal loads. In the dynamic case, coupled and uncoupled electro-thermo-mechanical analysis were performed to see the difference in the evolution of the mechanical, electrical and thermal fields with time. Finally, to test how well the developed theory and finite element model simulates the smart structural system, two different control strategies were employed: the negative velocity feedback control and the Least Quadratic Regulator (LQR) control. It is found that the refined plate theory provides results that are in good agreement with the those of the 3-D layerwise theory of Reddy. The present theory and finite element model enables one to obtain very accurate response of most composite and FGM plate structures with considerably less computational resources.