Magneto-Electro-Elastic Analysis of Doubly-Curved Shells: Higher-Order Equivalent Layer-Wise Formulation
Francesco Tornabene*, Matteo Viscoti, Rossana Dimitri
Department of Innovation Engineering, University of Salento, Lecce, 73100, Italy
* Corresponding Author: Francesco Tornabene. Email: francesco.tornabene@unisalento.it
(This article belongs to the Special Issue: Theoretical and Computational Modeling of Advanced Materials and Structures-II)
Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2024.058842
Received 22 September 2024; Accepted 27 November 2024; Published online 25 December 2024
Abstract
Recent engineering applications increasingly adopt smart materials, whose mechanical responses are sensitive to
magnetic and electric fields. In this context, new and computationally efficient modeling strategies are essential to
predict the multiphysic behavior of advanced structures accurately. Therefore, the manuscript presents a higherorder formulation for the static analysis of laminated anisotropic magneto-electro-elastic doubly-curved shell
structures. The fundamental relations account for the full coupling between the electric field, magnetic field, and
mechanical elasticity. The configuration variables are expanded along the thickness direction using a generalized
formulation based on the Equivalent Layer-Wise approach. Higher-order polynomials are selected, allowing for
the assessment of prescribed values of the configuration variables at the top and bottom sides of solids. In
addition, an effective strategy is provided for modeling general surface distributions of mechanical pressures
and electromagnetic external fluxes. The model is based on a continuum-based formulation which employs an
analytical homogenization of the multifield material properties, based on Mori & Tanaka approach, of a magnetoelectro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase, with coupled magnetoelectro-elastic effects. A semi-analytical Navier solution is applied to the fundamental equations, and an efficient
post-processing equilibrium-based procedure is here used, based on the numerical assessment with the Generalized
Differential Quadrature (GDQ) method, to recover the response of three-dimensional shells. The formulation is
validated through various examples, investigating the multifield response of panels of different curvatures and
lamination schemes. An efficient homogenization procedure, based on the Mori & Tanaka approach, is employed
to obtain the three-dimensional constitutive relation of magneto-electro-elastic materials. Each model is validated
against three-dimensional finite-element simulations, as developed in commercial codes. Furthermore, the full
coupling effect between the electric and magnetic response is evaluated via a parametric investigation, with useful
insights for design purposes of many engineering applications. The paper, thus, provides a formulation for the
magneto-electro-elastic analysis of laminated structures, with a high computational efficiency, since it provides
results with three-dimensional capabilities with a two-dimensional formulation. The adoption of higher-order
theories, indeed, allows us to efficiently predict not only the mechanical response of the structure as happens in
existing literature, but also the through-the-thickness distribution of electric and magnetic variables.
Keywords
Magneto-electro-elastic materials; equivalent layer-wise; generalized differential quadrature; higher-order theories; navier solution; recovery procedure; smart structures
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