Thermo-magneto-mechanical analysis of curved laminated structures with arbitrary variation of the material properties and novel recovery procedure

Abstract

The paper introduces a novel methodology based on a generalized formulation and higher-order-theories for the fully-coupled multifield analysis of laminated curved structures subjected to thermal, magnetic, and mechanical loads. The formulation follows the Equivalent Single Layer approach, taking into account a generalized through-the-thickness expansion of displacement field components, scalar magnetic potential, and temperature variation with respect to the reference configuration. In addition, specific thickness functions are selected according to the Equivalent Layer Wise methodology, allowing the imposition of particular values of configuration variables in specific regions of the structure. The lamination scheme includes smart materials derived from an analytical homogenization technique, with material properties varying arbitrarily along the thickness direction within each layer. The fundamental relations are derived under thermodynamic equilibrium using curvilinear principal coordinates, and a semi-analytical Navier solution is derived for specific geometric, material, and loading conditions. A recovery procedure using Generalized Differential Quadrature is presented for reconstructing three-dimensional primary and secondary variables. In addition, a novel recovery procedure is presented for the first time, based on a Generalized Integral Quadrature. The model is validated through numerical examples involving straight and curved panels with various multifield load distributions, showing consistency and the computational efficiency when compared to three-dimensional reference solutions. New coupling effects between physical problems are explored, and parametric investigations highlight the influence of key governing parameters. Unlike the existing literature, this paper presents an efficient and accurate methodology for analyzing laminated smart structures of various curvatures with multifield couplings, not usually addressed by commercial software. This theory allows for arbitrary variations in multifield properties without using three-dimensional models that can be computationally expensive. In this way, novel possible design applications of smart materials and structures are offered in many engineering fields.