The Extension and Application of the Hierarchical Beam Theory to Piezoelectrically Actuated Beams

Abstract

An accurate, internally consistent modelling process is needed in order to realize the full compatibility of advanced composite and sandwich structures. The recently proposed unified hierarchical theory for layered beams which uses the moments of displacements, stress and strains without a priori assumptions on the form of the displacement field variables is one such effort. The theory relies on the concept of fundamental states and assumes that all load states can be decomposed as supposition of fundamental load states. The extension of this theory to include piezoelectric actuation is object of this paper. The through-the-thickness stress and strain distributions, and the displacement moments are calculated and observed to be comparable to the corresponding values obtained from two-dimensional finite element analyses with the commercial finite element software ANSYS.