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 Pri nciple of Virtual Displacements (PVD) to mixed theories formulated on the b asis of the Reissner Mixed Variational Theorem (RMVT) to evaluate the therm al response of orthotropic laminated plates. So-called layer-wise (LW) and equivalent-single-layer (ESL) modelings have been developed for both classi cal 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 displace ment and stress field cases have been implemented to derive thermomechanica l governing equations, consistent with the used variational statements. All the theories have been presented in a unified manner by referring to findi ngs recently presented by the author. The numerical investigation has been restricted to a simply supported plate loaded by harmonic distribution of i n-plane temperature fields. Constant and linear through-the-thickness tempe rature distributions have been considered for which exact three-dimensional solutions are available. The results of in-plane and out-of-plane displace ment and stress components are given in the form of tables and diagrams. Th e superiority of the mixed approach to the PVD formulation has been confirm ed. Higher order, layer-wise expansions for the unknown variables are requi red for an accurate description of the thermomechanical response of thick m ultilayered plates. It has been found that the thickness temperature distri butions T(z) have a significant influence on the accuracy of the considered theories.