Thermo-elastic analysis of multilayered plates and shells based on 1D and 3D heat conduction problems

The present work shows a generic 3D exact shell solution for the thermo-mechanical analysis of a heterogeneous group of one- and multi-layered isotropic, composite and sandwich structures. Plates, cylinders, cylindrical and spherical shells can be investigated using orthogonal mixed curvilinear coordinates. The 3D equilibrium equations for spherical shells automatically degenerate in those for simpler geometries. The elastic part of the proposed 3D model is based on a consolidated layer-wise exact solution which uses the exponential matrix method to solve the equilibrium differential equations through the thickness direction. The closed-form solution is obtained assuming simply-supported boundary conditions and harmonic forms for displacement and temperature fields. The temperature amplitudes are imposed at the top and bottom external surfaces in steady-state conditions. Therefore, the temperature profile can be evaluated through the thickness direction in three different ways: – calculation of the temperature profile via the steady-state 3D Fourier heat conduction equation; – evaluation of the temperature profile using the steady-state simplified 1D version of the Fourier heat conduction equation; – a priori assumed linear temperature profile through the entire thickness direction ranging from the bottom temperature value to the top temperature value. Once the temperature profile is defined at each thickness coordinate, it is considered as a known term in the 3D differential equilibrium equations. The obtained system consists in a set of non-homogeneous second order differential equilibrium equations which can be solved introducing appropriate mathematical layers. After a reduction to a first order differential equation system, the exponential matrix method is used to calculate both the general and the particular solutions. The effects of the temperature field on the static response of plates and shells are evaluated in terms of displacements and stresses. The proposed solution will be validated using reference results available in the literature. Then, new analyses will be presented for different thickness ratios, geometries, lamination schemes, materials and temperature values at the external surfaces. Results will demonstrate the importance in the 3D shell model of both the correct definition of the elastic part and the appropriate evaluation of the temperature profile through the thickness of the structure..