A beam finite element for magneto-electro-elastic multilayered composite structures

Finite element formulation of laminated beams with capability to model the thickness expansion

“…Milazzo and Orlando [35] presented a beam finite element for the analysis of magneto-electro-elastic multilayered composite structures. Zemanová et al [36] developed a finite element approach to model laminated glass beams under finite strain.…”

Dynamics of magneto electro elastic curved beams: Quantification of parametric uncertainties

“…(12), M CI is defined in Eq. (7),P is the vector of distributed forces,F BC is a vector of prescribed forces at the ends of the element, the matrix M CF = diag(k 1 , k 2 , k 3 ) is the matrix of elastic foundation constants and D D1 is a differential operator.…”

“…The constitutive equations of a magneto-electro-elastic solid under the hypothesis of plane stress -assuming σ yy << σ xx and employing the hypothesis (d) -can be written in the following matrix form [23,11,12]:…”

“…The papers of Milazzo and coworkers [11,12,13] are, apparently, the very first in which studies about the dynamics of MEE beams (for enhanced Bernoulli-Euler and/or Timoshenko theories) have been carried out. Besides these works are quite recent.…”

A 1D model for the dynamic analysis of magneto-electro-elastic beams with curved configuration

“…According to a thorough bibliographical review, it is important to remark that there are quite few articles related to the study of MEE slender structures in the context of a beam model or theory. The papers of Milazzo and coworkers [12][13][14] are the very firsts where studies about the dynamics of MEE beams (in the context of extended Bernoulli-Euler and/or Timoshenko theories) have been carried out, and besides these works are quite recent. However to the best of authors' knowledge, articles related to static/dynamic behavior of MEE curved beams are apparently absent.…”