Three-dimensional thermal stress analysis of multilayered piezoelectric curved panels

In the present work, the thermal stress analysis of curved multilayered piezoelectric structures is presented. The proposed analytical formulation directly models, in a three-dimensional (3D) form, displacements, electric potential, and temperature. The 3D equilibrium equations, the 3D divergence equation for the electric displacement, and the 3D Fourier heat conduction equation constitute the 3D governing equations for the thermal stress analysis of spherical shells involving the thermo-electro-elastic (TEE) coupling. The 3D governing equations are written for spherical shells via an orthogonal mixed curvilinear reference system ( α , β , z). Degeneration into cylindrical panels, cylinders, and plates is possible by properly considering appropriate values for radii of curvature R α and R β . Navier harmonic forms in the two in-plane directions and the exponential matrix method in the thickness direction are adopted, and simply-supported constraints are imposed. Several load boundary conditions can be considered in terms of temperature, electric potential, pressure load, and heat flux at the outer surfaces. The adopted layer-wise approach considers the interlaminar continuity conditions of elastic displacement, electric potential, temperature, transverse shear and transverse normal stresses, transverse normal electric displacement, and transverse normal heat flux. In the validation cases subsection, the present 3D model is compared with other 3D analytical models for piezoelectric multilayered structures. In the new cases subsection, several geometries and load boundary conditions are proposed for different thickness ratios and lamination schemes. Therefore, TEE coupling, material layer, thickness layer and curvature effects, are clearly shown in tabular and graphical forms. The main novelty is that the equations are general, as they are applicable to different geometries, such as plates, cylindrical shells, and spherical shells, allowing the study of the full coupling among elastic, thermal, and electrical fields without increasing computational costs, despite a 3D, layer-wise approach.