A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates

Abstract

A comprehensive analysis of available models and techniques to evaluate transverse shear and normal stresses in multilayered orthotropic plates is given in this paper. Transverse stresses evaluated a posteriori by integration of the 3D indefinite equilibrium equations and from Hooke's law are compared to those given a priori by an assumed stress model (if implemented). Classical theories formulated on the basis of assumed through-the-thickness displacement fields as well as mixed modelings originated by a Reissner's mixed variational theorem are considered. Both cases of Equivalent Single Layer Models (ESLMs) and Layer Wise Models (LWMs) have been investigated. Linear up to fourth N-order expansions, in the thickness layer/plate direction, have been implemented for the introduced displacement and stress fields. As a result, theories describing so-called zigzag effects and accounting for interlaminar continuous transverse stresses are compared to simplified cases which neglect zigzag and violate interlaminar equilibrium. A numerical investigation has been restricted to bending of simply supported, orthotropic plates. It is mainly concluded that: (1) N-order increasing, layer-wise analysis could furnish excellent a priori as well as a posteriori description of transverse stresses of laminate thick and thin plates; ESLM accuracy remains subordinate to laminate lay-out, to plate thickness and to two-dimensional modelings (mixed results are much more accurate than classical ones). (2) The discrepancy among the three manners of evaluating transverse shear stresses is scarcely dependent on plate thickness ratio. (3) In most of the considered cases, the best description of transverse stresses has been obtained by layer-wise mixed analysis upon integration of the 3D indefinite equilibrium equations.