A refined two-dimensional formulation is presented for the multifield analysis of laminated doubly-curved shells with full coupling between mechanical elasticity, electricity, magnetism, and hygro-thermal effects, under thermodynamic equilibrium conditions. The unknown variables are expanded along the thickness direction using higher-order theories and a unified formulation, following the Equivalent Layer-Wise (ELW) approach. This framework enables the structure to accommodate arbitrary values of multifield variables at the top and bottom surfaces, as well as general distributions of multifield surface loads. The fundamental equations are derived from the Hamiltonian principle in curvilinear principal coordinates, considering generally anisotropic layers obtained through analytical homogenization. Moreover, an arbitrary smooth through-thickness variation of the material properties is introduced within each layer. A semi-analytical Navier solution is developed for simply-supported shells. In the post processing stage, an innovative procedure based on Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) is employed to reconstruct the multifield response of the doubly-curved solid by solving the three-dimensional balance equations along the thickness direction. The model is validated through representative examples, with numerical predictions compared against 3D finite element solutions obtained from commercial software. Further analyses are carried out to explore additional coupling effects, examining the influence of multifield interactions on both the mechanical and multifield response of the structure, as well as the impact of material gradation. Overall, the proposed model provides an efficient tool for investigating the response of laminated structural components with multifield properties, while capturing coupling phenomena that cannot be addressed with conventional commercial software.
Tornabene et al. (Wed,) studied this question.