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Magneto-Electro-Elastic Analysis of Doubly-Curved Shells: Higher-Order Equivalent Layer-Wise Formulation

by Francesco Tornabene*, Matteo Viscoti, Rossana Dimitri

Department of Innovation Engineering, University of Salento, Lecce, 73100, Italy

* Corresponding Author: Francesco Tornabene. Email: email

(This article belongs to the Special Issue: Theoretical and Computational Modeling of Advanced Materials and Structures-II)

Computer Modeling in Engineering & Sciences 2025, 142(2), 1767-1838. https://doi.org/10.32604/cmes.2024.058842

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 higher-order 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 magneto-electro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase, with coupled magneto-electro-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.

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APA Style
Tornabene, F., Viscoti, M., Dimitri, R. (2025). Magneto-electro-elastic analysis of doubly-curved shells: higher-order equivalent layer-wise formulation. Computer Modeling in Engineering & Sciences, 142(2), 1767–1838. https://doi.org/10.32604/cmes.2024.058842
Vancouver Style
Tornabene F, Viscoti M, Dimitri R. Magneto-electro-elastic analysis of doubly-curved shells: higher-order equivalent layer-wise formulation. Comput Model Eng Sci. 2025;142(2):1767–1838. https://doi.org/10.32604/cmes.2024.058842
IEEE Style
F. Tornabene, M. Viscoti, and R. Dimitri, “Magneto-Electro-Elastic Analysis of Doubly-Curved Shells: Higher-Order Equivalent Layer-Wise Formulation,” Comput. Model. Eng. Sci., vol. 142, no. 2, pp. 1767–1838, 2025. https://doi.org/10.32604/cmes.2024.058842



cc Copyright © 2025 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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