Closed-form solutions to assess multilayered-plate theories for various thermal stress problems

TLDR: In this paper, the Fourier expansion was used to solve problems related to uniform, triangular, bitriangular (tent-like), and localized in-plane distribution of temperature.

Abstract: This paper represents a further development of the first author’s works on twodimensional modeling for thermal stress analysis of multilayered composite plates. The governing equations are written by referring to the unified compact formulation. These equations have been obtained in a form that is not affected by the order of the expansion in the thickness plate direction z or by variable descriptions (layer-wise models and equivalent single layers models). Classical theories based on the principle of virtual displacements and advanced mixed theories based on the Reissner mixed variational theorem are both considered. As a result, a large variety of theories are derived and compared. The temperature profile TP in the direction z is calculated by solving the heat conduction problem and it is compared to the case in which TP is assumed linear in z. Exact closed-form solutions have been derived for the case of the in-plane harmonic distribution of displacements, transverse stress variables, and temperature fields. The Fourier expansion was then used to solve problems related to uniform, triangular, bitriangular (tentlike), and localized in-plane distribution of temperature. In some cases more than 25 theories were compared. The effect of transverse shear deformation, the zig-zag form of displacement fields, and interlaminar continuity of transverse stresses (both shear and normal components) have been evaluated in the framework of both classical and mixed theories.