Finite element modelling to assess the effect of position and size of the piezoelectric layer of a hybrid beam

Abstract A one dimensional finite element model is presented to assess the effect of position and size of the piezoelectric layer of a hybrid beam. The efficient layerwise (zigzag) theory is used for making the finite element model. The 1D beam element has eight mechanical and a variable number of electrical degrees of freedom. The codes are developed in Matlab based on the FE formulation. The beams are also modelled in 2D planar modelling space as a deformable shell using FE package ABAQUS for comparison of results. An 8-noded piezoelectric quadrilateral element is used for piezo layers and an 8-noded quadrilateral element with reduced integration is used for the elastic layers of hybrid beams for making the finite element mesh in ABAQUS. The accuracy of the used elements are assessed for static response. Cantilever hybrid beams with a piezoelectric layer bonded on top of the elastic substrate are considered for the analysis. The beams are subjected to electromechanical loading. A detailed study is conducted to highlight the influence of positon and size of piezoelectric layer on the deflection profiles, tip deflections and through the thickness distribution of displacements and stresses of hybrid composite/sandwich beams. The shape control using various numbers of piezoelectric patches is also studied. The 1D-FE results are compared with the 2D-FE results.