Static shape control of smart functionally graded beams using an efficient finite element model

In this work, finite element model based on third-order efficient layer-wise theory for smart functionally graded material (FGM) beams equipped with distributed piezoelectric active layers has been presented. The properties in the FGM substrate are assumed to vary along transverse direction according to the power law distribution. The effective properties at any point in the thickness direction are estimated using Mori-Tanaka method. Variational principle has been used to derive governing equations. Electric potential is assumed to vary quadratically across the thickness of PZT layers. A novel concept of electric node is used to model the equipotential condition of electroded piezoelectric surfaces. Deflection, stresses under mechanical pressure load and uniform electric potential are presented. Effect of multiple actuation on the performance of shape control smart FGM beams using piezoelectric actuators under static loading for simply supported and cantilever boundary conditions have been discussed.