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

Abstract

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.

Transient analysis of a three-layer microbeam subjected to electric potential

“…They laminates and a plastic foam core. Structural analysis of Euler-Bernoulli laminated piezoelectric beam subjected to three-dimensional distributions of mechanical stresses and strains has been performed by Maurini et al [4] based on mixed variational principle and Lagrange multiplier method. They evaluated efficiency of the present method by comparison with three-dimensional finite element approach.…”

A damage constitutive model for sliding friction coupled to wear

“…All these assumptions are similar to those formulated in [42]. Additional hypotheses are introduced for the interface body: (c) the absolute temperature ϑ is constant along z, that is, θ = θ(x, y), but it differs from the temperatures at the bases S + c and S − c , equal to θ + = θ + (x, y) and θ − = θ − (x, y), respectively; (d) the heat flow across the mantle of the cylinder is negligible.…”

Identification of higher-order elastic constants for grain assemblies based upon granular micromechanics

“…The micromorphic behavior of granular materials indicates the possibility of realizing materials with alternate synthesis pathways which show specific wave propagation behaviors that can be used for vibration control as an alternative to piezoelectric materials [Maurini et al 2004;2006;Porfiri et al 2005;Vidoli and dell'Isola 2001;dell'Isola and Vidoli 1998;Greco et al 2014] or for damage identification [Ferretti et al 2014;Andreaus and Baragatti 2011;. Alternatively, such materials can be applied to help optimize control procedures or for optimal biomaterial design in bone mechanics [Andreaus et al 2015b].…”