Geometric Effects on the Accuracy of Euler-Bernoulli Piezoelectric Smart Beam Finite Elements

Abstract

Numerical analysis of piezoelectric smart beams plays an important role in the design of smart beam based control systems. In general, smart beams are thin and Euler-Bernoulli piezoelectric beam element is widely used for their structural analysis. Accuracy of Euler-Bernoulli piezoelectric beam element depends on the appropriate assumptions for electric potential involved in the formulation. Most of the Euler-Bernoulli piezoelectric beam finite elements available in the literature assume linear through-thickness potential distribution. It is shown that the accuracy of these conventional formulations varies with relative proportion of piezoelectric material in the total beam cross-section. This is attributed to the effect of the induced potential due to electromechanical coupling. The use of a number of sublayers in the mathematical modeling of each piezoelectric physical layer is shown to improve accuracy, at the cost of additional computational effort due to increased number of nodal electrical degrees of freedom. A more efficient way to handle the effects of induced potential is to use a consistent through-thickness electric potential derived from the electrostatic equilibrium equation. In addition to the conventional linear terms, this field consists of a higher order coupled term which effectively takes care of the geometric effects and produce accurate results, without the use of sublayers in modeling.