Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

In this paper a coupled Euler–Bernoulli model of laminated piezoelectric beams is proposed. It is characterized by accounting for the influence of 3D distribution of mechanical stresses and strains through corrected electromechanical constitutive equations. In particular, the hypothesis of vanishing transverse (width direction) normal stress typical of standard beam models is weakened by imposing vanishing stress resultants. This integral condition is enforced by adopting a mixed variational principle and Lagrange multiplier method. Explicit expressions for the beam constitutive coefficients are given and the sandwich and bimorph piezoelectric benders are studied in details. The model is assessed through comparisons with standard models and 3D finite element results, showing an important enhancement of standard beam theories.