A quadratic piezoelectric multi-layer shell element for FE analysis of smart laminated composite plates induced by MFC actuators

Abstract

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.