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

A comprehensive analysis of available models and techniques to evaluate tra nsverse shear and normal stresses in multilayered orthotropic plates is giv en in this paper. Transverse stresses evaluated a posteriori by integration of the 3D indefinite equilibrium equations and from Hooke's law are compar ed to those given a priori by an assumed stress model (if implemented). Cla ssical theories formulated on the basis of assumed through-the-thickness di splacement fields as well as mixed modelings originated by a Reissner's mix ed variational theorem are considered. Both cases of Equivalent Single Laye r Models (ESLMs) and Layer Wise Models (LWMs) have been investigated. Linea r 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 case s which neglect zigzag and violate interlaminar equilibrium. A numerical in vestigation has been restricted to bending of simply supported, orthotropic plates. It is mainly concluded that: (1) N-order increasing, layer-wise an alysis could furnish excellent a priori as well as a posteriori description of transverse stresses of laminate thick and thin plates; ESLM accuracy re mains subordinate to laminate lay-out, to plate thickness and to two-dimens ional 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 th e considered cases: the best description of transverse stresses has been ob tained by layer-wise mixed analysis upon integration of the 3D indefinite e quilibrium equations. (C) 2000 Elsevier Science Ltd. All rights reserved.