Performance of consistent through-thickness electric potential distribution for Euler-Bernoulli piezoelectric beam finite elements

Abstract

An accurate piezoelectric beam finite element analysis essentially requires appropriate assumptions of the field variables involved in the formulation. The conventional Euler-Bernoulli piezoelectric beam finite elements assume an independent linear through-thickness distribution of electric potential in a physical piezoelectric layer which is actually nonlinear due to induced potential effects. Here, a consistent through-thickness potential distribution in a physical piezoelectric layer derived from the electrostatic equilibrium equation is tested for its accuracy against the linear assumption. This consistent potential field contains, in addition to the conventional linear terms, a higher order term coupled with bending strain. Thus, this finite element, though employing higher order potential, does not increase the number of nodal electrical degrees of freedom. It is shown that the performance of the present formulation with consistent through-thickness potential is insensitive to the geometric configuration and material properties of the beam cross-section, unlike the conventional formulations.