Modeling and analysis of loaded multilayered magnetoelectroelastic structures composite materials: Applications

Abstract

The aim of this study is to develop a two-scale tool allowing the detailed analysis of the behavior of fiber-reinforced magneto-electro-elastic composite plates. The work is divided into two major sections. The first one deals with the homogenization of the properties of each layer based on the Mori-Tanaka mean field approach where all needed effective coefficients of each layer are determined. In the second one and in order to perform the analysis of the behavior of the obtained magneto-electro-elastic multilayered plate, the Stroh formalism is used. It allows to predict the effective behavior of such plates and the spatial distribution of the local fields along the layers.

Dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials

“…For the case where the vector a(t) is constant (a(t) = a = cte), their time derivatives vanish and the second part of equation (7a) becomes zero. This case corresponds to the static response of the multilayered plate studied by Ajdour and Azrar (2013), Ajdour et al (2016), Pan (2001Pan ( , 2003 Pan and Han (2005), and Pan and Heyliger (2003). In the case where this vector takes the form a(t) = aexp(ivt) (a and v being constants), we have the free vibration of the plate studied by Pan and Heyliger (2002).…”

“…Thus, the parameters s and j are respectively in this particular case the eigenvalues and the eigenvectors of Stroh matrix (see Ajdour and Azrar, 2013;Ajdour et al, 2016;Pan, 2001Pan, , 2003Pan and Han, 2005;Pan and Heyliger, 2003).…”

“…By the pseudo-Stroh formalism, Ajdour and Azrar (2013) carried out the static behavior of multifunctional and multilayered plates with piezoelectric layers and resting on the simply supported edges boundary conditions. Based on the same methodological approach and using the Mori-Tanaka homogenization, Ajdour et al (2016) analyzed the static response of simply supported multilayered plates reinforced with magnetoelectroelastic fibers. Coupling the state-space approach and the Laplace transform, Zaki et al (2014) treated the dynamic and static behaviors of multilayered elastic plates, with different orthotropic angles of fibers, with viscoelastic interfaces and resting on the Winkler-Pasternak foundation.…”

Prediction of the macroscopic behavior of multi-layered elastic composites

“…The Mori-Tanaka method is very popular among the existing micromechanics methods due to its effectiveness: it is easy to implement, there is no need to iterative procedures, and is known to give good estimation of effective properties of the considered composites (see references [4][5][6][7] for more readings). The Mori-Tanaka is used here to predict the behavior of reinforced layers.…”

Modeling and numerical simulation of the dynamic behavior of magneto-electro-elastic multilayer plates based on a Winkler-Pasternak elastic foundation

“…We presented in three conferences (Hamidi et al, 2019a(Hamidi et al, , 2019b(Hamidi et al, , 2019c the results of the 3D modeling of the static and dynamic behavior for multilayered MEE plate with viscoelastic interfaces based on a Winkler-Pasternak elastic support using space state method. Manyo Manyo et al (2019) treated a 3D-dynamic modeling of cross-ply MEE laminates based on the pseudo-Stroh formalism, Ewolo Ngak et al (2018Ngak et al ( , 2019 studied a dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials (Ewolo Ngak et al, 2019) and using state space approach and the Lagrange polynomial interpolation (Ewolo Ngak et al, 2018), Aljinaidi et al (2016) developed a visco-MEE effective properties' modeling for multi-phase and multi-coated magnetoelectroelastic, Ajdour et al (2016) analyzed a loaded multilayered MEE using Mori-Tanaka approach and pseudo-Stroh formalism. Zaki et al (2014Zaki et al ( , 2018 treated the static and dynamic behavior of multilayered elastic plates with interface effect and different orthotropic angles of fibers, resting on the Winkler-Pasternak elastic foundation.…”