Assessment of coupled 1D models for hybrid piezoelectric layered functionally graded beams

Abstract

A unified formulation is presented for coupled efficient zigzag, third order, consistent third order and first order models for hybrid piezoelectric layered FGM beams under thermoelectromechanical load. The transverse as well as inplane electric fields are considered. The potential and thermal fields are discretised sublayerwise as piecewise linear which can adequately approximate the actual distributions of these fields across the thickness. The zigzag theory accounts for the non-uniform deflection across the thickness due to the potential and thermal fields and satisfies exactly the conditions on transverse shear stress at the top, bottom and layer interfaces. The governing equilibrium equations have been derived from a variational principle. For the first time, the accuracy of the 1D models is assessed in direct comparison with the exact 2D solutions for elastic as well as piezoelectric hybrid layered FGM beams for mechanical, potential and thermal loads. The effects of the inhomogeneity parameter, span-to-thickness ratio and electric boundary conditions are investigated. It is established that the zigzag theory results are superior to those of other 1D models, even though they have the same number of displacement variables.