A superconvergent piezoelectric beam finite element

Resumo

A piezoelectric beam finite element is proposed, where the displacement is assumed to vary in
accordance with the Timoshenko assumption and the electric potential has linear variation through each
piezoelectric layer thickness. The solution of the homogeneous form of the linear differential equations which
describe the behavior of the piezoelectric Timoshenko beam is used as interpolation functions to develop a 2-
node finite element for planar frames. According to the adopted procedure the element has the following
properties: (a) it has the same degrees of freedom as its purely mechanical counterpart; (b) it is free of shear
locking; (c) it is superconvergent, i.e. the computed nodal values are exact with respect to the element
formulation regardless the applied loading pattern. In the solution of the numerical examples, the efficiency of
the developed finite element is illustrated showing that few elements are adequate to precisely capture the static
response for both mechanical and electrical variables.