Coupled Efficient Zigzag Finite Element Analysis of Piezoelectric Hybrid Beams under Thermal Loads

Abstract

A new one-dimensional beam finite element is developed for hybrid piezoelectric beams under thermal load, using a coupled efficient layerwise (zigzag) theory developed recently by the authors. The theory accounts for the layerwise variations of the axial and the transverse displacements while keeping the number of displacement variables independent of the number layers. The beam element has two nodes with four mechanical and a variable number of electric potential degrees of freedom at each node. In the thickness direction, the thermal and the electric fields are approximated as piecewise linear across an arbitrary number of sublayers in a layer. Cubic Hermite interpolation is used for the deflection and electric potentials at the sublayers and linear interpolation is used for the axial displacement and the shear rotation. The thermal field is computed using a consistent six-noded thermal finite element with a quadratic interpolation along longitudinal direction and a linear interpolation along thickness direction. The formulation is validated by comparing the results with the Navier-type solution of the zigzag theory for simply-supported hybrid beams. The element is free from shear locking. The accuracy of the zigzag theory is established by comparing the results of hybrid composite and sandwich beams with the two-dimensional finite element results using ABAQUS for cantilever and clamped-clamped end conditions under different thermal loads. The control of thermal deflection by the application of actuation potential is illustrated. The effects of electric boundary conditions and the pyroelectric effect on the response are discussed.