A Layer-Wise Coupled Thermo-Elastic Shell Model for Three-Dimensional Stress Analysis of Functionally Graded Material Structures

Abstract

In this work, a coupled 3D thermo-elastic shell model is presented. The primary variables are the scalar sovra-temperature and the displacement vector. This model allows for the thermal stress analysis of one-layered and sandwich plates and shells embedding Functionally Graded Material (FGM) layers. The 3D equilibrium equations and the 3D Fourier heat conduction equation for spherical shells are put together into a set of four coupled equations. They automatically degenerate in those for simpler geometries thanks to proper considerations about the radii of curvature and the use of orthogonal mixed curvilinear coordinates α, β, and z. The obtained partial differential governing the equations along the thickness direction are solved using the exponential matrix method. The closed form solution is possible assuming simply supported boundary conditions and proper harmonic forms for all the unknowns. The sovra-temperature amplitudes are directly imposed at the outer surfaces for each geometry in steady-state conditions. The effects of the thermal environment are related to the sovra-temperature profiles through the thickness. The static responses are evaluated in terms of displacements and stresses. After a proper and global preliminary validation, new cases are presented for different thickness ratios, geometries, and temperature values at the external surfaces. The considered FGM is metallic at the bottom and ceramic at the top. This FGM layer can be embedded in a sandwich configuration or in a one-layered configuration. This new fully coupled thermo-elastic model provides results that are coincident with the results proposed by the uncoupled thermo-elastic model that separately solves the 3D Fourier heat conduction equation. The differences are always less than 0.5% for each investigated displacement, temperature, and stress component. The differences between the present 3D full coupled model and the the advantages of this new model are clearly shown. Both the thickness layer and material layer effects are directly included in all the conducted coupled thermal stress analyses.