Three-Dimensional Analysis of Some Symmetric Hybrid Piezoelectric Laminates

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

“…[11]). In our opinion, it should be also the assumption made in [6,5] to get the electrically induced tip deflection of cantilevered bimorph and sandwich beams (so explaining the high discrepancy they found with respect to the Wang and Cross model [21], which is in plane-stress).…”

“…For this reason, the errors between three-dimensional numerical results and estimates from simple beam models were often entirely imputed to neglecting the quadratic contribution of the electric potential [5,6]. A first discussion of this point can be found in [26], where the effect of the transverse bending is investigated by FE numerical simulations.…”

“…The FE results show that the actual capacitance, being always comprised between these two values, can significantly differ from both. 5 These errors are explained by keeping in mind that the equivalent capacitance of a piezoelectric sheet depends on the conditions on mechanical stresses and strains. The standard models associate to piezoelectric layers either the value obtained under the condition of null transverse strain or null transverse stress.…”

“…For this reason, a great number of research works dealing with structural modelling of piezoelectric composites can be found (see [2,3] for reviews on the subjects). They can be classified in those attempting to solve exact 3D electromechanical problems [4][5][6], those concentrating on the derivation of plate models [3] and those reducing to the solution of one-dimensional beam problems. In early works actuating [7] and sensing [8] functions of piezoelectric materials have been studied separately.…”

“…Simple electromechanical models for their constitutive behavior are given in [19][20][21][22], under the standard Euler-Bernoulli hypotheses. More recently, He [5] and Lim and He [6] propose a threedimensional approach to two-layer bimorphs and threelayer sandwiches. They combine state form formulation of 3D piezoelectricity with asymptotic methods to get an analytical solution for the thickness distribution of the electromechanical fields as a function of the midplane motion.…”