An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates

This article compares theories formulated on the basis of the classical Principle of Virtual Displacements (PVD) to mixed theories formulated on the basis of the Reissner Mixed Variational Theorem (RMVT) to evaluate the thermal response of orthotropic laminated plates. So-called layer-wise (LW) and equivalent-single-layer (ESL) modelings have been developed for both classical and mixed approaches (each layer is considered as a single plate for LW analysis, while the unknown variables are independent of the number of the constitutive layers for the ESL cases). Linear up-to fourth-order displacement and stress field cases have been implemented to derive thermomechanical governing equations, consistent with the used variational statements. All the theories have been presented in a unified manner by referring to findings recently presented by the author. The numerical investigation has been restricted to a simply supported plate loaded by harmonic distribution of in-plane temperature fields. Constant and linear through-the-thickness temperature distributions have been considered for which exact three-dimensional solutions are available. The results of in-plane and out-of-plane displacement and stress components are given in the form of tables and diagrams. The superiority of the mixed approach to the PVD formulation has been confirmed. Higher order, layer-wise expansions for the unknown variables are required for an accurate description of the thermomechanical response of thick multilayered plates. It has been found that the thickness temperature distributions T(z) have a significant influence on the accuracy of the considered theories.