Temperature Profile Influence on Layered Plates Response Considering Classical and Advanced Theories

Abstract

A study on the influence of the through-the-thickness temperature profile T(z) on the thermomechanical response of multilayered anisotropic thick and thin plates has been conducted. The heat conduction problem is solved, and the temperature variation T c (z) is then calculated. The governing thermomechanical equations of multilayered plates are written considering a large variety of classical and advanced or zigzag theories into account. The principle of virtual displacement and the Reissner mixed variational theorem are employed. Linear, up to fourth-order expansions in z are retained for the assumed transverse stress and displacement fields. As a result, more than 20 plate theories are compared. The numerical investigation is restricted to orthotropic layered plates with harmonic in-plane distribution of both thermal loadings and unknown variables. Four sample plate problems are treated that are related to plates made of isotropic and/or orthotropic layers that are loaded by different top-bottom plate surface temperature conditions. Comparison is made to results related to a linear profile T a (z), which is usually assumed in open literature. The following is concluded: Thick plates could exhibit a layerwise form temperature profile T c (z). T a (z) case is approached for thin plate geometries. The use of linear temperature profile leads to large errors in tracing the response of thick plate geometries. The accuracy of plate theories is affected to great extent by the form of temperature variation T(z). Refinements of classical plate theories can be meaningless unless the calculated T c (z) is introduced. The layerwise form of T c (z) would require layerwise assumptions for stresses and/or displacements. Plate theories that neglect transverse normal strains lead to very inaccurate results in both thick and thin plates analysis. At least a parabolic expansion for transverse displacement is required to capture transverse normal thermal strains that vary linearly along the plate thickness.