An accurate modeling of piezoelectric smart beams with first-order shear deformation theory

Abstract

A finite element model for piezoelectric smart beam in extension mode based on First-order Shear Deformation Theory (FSDT) with an appropriate through-thickness distribution of electric potential is presented. Accuracy of piezoelectric finite element formulations depends on the selection of assumed mechanical and electrical fields. Most of the conventional FSDT-based piezoelectric beam formulations available in the literature use linear through-thickness distribution of electric potential which is actually nonlinear. Here, a novel quadratic profile of the through-thickness electric potential is proposed to include the nonlinear effects. The results obtained show that the accuracy of conventional formulations with linear through-thickness potential approximation is affected by the material configuration, especially when the piezoelectric material dominates the beam cross section. It is shown that the present formulation gives the same level of accuracy for all regimes of material configurations in the beam cross section. Also, a modified form of the FSDT displacements is employed, which utilizes the shear angle as a degree of freedom instead of section rotation. Such a FSDT displacement field shows improved performance compared to the conventional field. The present formulation is validated by comparing the results with ANSYS 2D simulation. The comparison of results proves the improved efficiency and accuracy of the present formulation over the conventional formulations.