Non-linear analysis of smart annular plates using cylindrically orthotropic piezoelectric fiber-reinforced composite

This article deals with geometrically non-linear finite element analysis of substrate annular plates integrated with the annular patches of the piezoelectric fiber reinforced composite (PFRC) material. The PFRC material is a cylindrically orthotropic smart composite material in which the piezoelectric fibers are circumferentially reinforced in the epoxy matrix material. The annular PFRC patches are activated by the externally applied voltage across their thickness and act as the distributed actuators for controlling the non-linear deformations of the substrate annular plates. Based on the first-order shear deformation theory and the von Karman non-linear strain–displacement relations, the non-linear governing finite element equations of equilibrium of this electro-elastic coupled problem are derived employing the principle of minimum potential energy. The governing non-linear finite element equations are then solved using direct iteration method. The numerical illustrations reveal the significant control authority of the cylindrically orthotropic annular PFRC patches in counteracting the non-linear deformations of the substrate annular plates. The numerical illustrations also reveal that for the constant circumferential stretch of the annular PFRC patches, if their radial span is less than that of the substrate annular plate, then the radial location of the annular patches attached to the top surface of the substrate plate plays an important role for their effective control authority. Along with this location, the minimum radial length of the annular PFRC patches is also assessed without affecting the performance of the overall smart plate significantly.