A Three-Dimensional Layer-Wise Formulation for the Coupled Thermo-Magneto-Elastic Analysis of Multilayered Composite Flat and Curved Panels

A fully coupled three-dimensional (3D) thermo-magneto-elastic layer-wise formulation is developed for the analysis of multilayered flat and curved panels used in aerospace and aeronautical applications. The model relies on a system of coupled second-order differential equations along the thickness coordinate z, formulated in a mixed orthogonal curvilinear reference system. The governing equations combine the three-dimensional equilibrium equations with the magnetic induction divergence equation and the heat conduction equation, providing a unified multifield framework for thermo-magneto-elastic analyses. Through a suitable definition of the curvature parameters, the same formulation can be directly applied to plates, cylinders, cylindrical panels, and shells with constant radii of curvature. The governing equations are analytically solved by adopting harmonic expansions in the in-plane directions together with the exponential matrix method along the thickness coordinate. The harmonic representation naturally satisfies simply-supported boundary conditions along the panel edges. The multilayered structure is modeled according to a layer-wise strategy, where the continuity of the selected mechanical, magnetic, and thermal variables is enforced across the interfaces between adjacent layers. Different loading boundary conditions can be assigned at the external surfaces by prescribing pressure loads, magnetic potential, transverse magnetic induction, and over-temperature. The numerical investigation is divided into two stages. First, the accuracy of the proposed formulation is verified through comparisons with thermo-magneto-elastic solutions available in the literature. Then, a comprehensive set of new benchmark results is presented by considering different geometries, thickness ratios, and loading boundary conditions. Both tabulated values and through-the-thickness distributions are reported for the most significant field variables. These benchmark results provide useful reference data for the assessment and validation of future two-dimensional and three-dimensional analytical and numerical formulations devoted to coupled thermo-magneto-elastic problems.