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

机译：正交各向异性多层板中横向应力的先验与后验评估

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摘要

A comprehensive analysis of available models and techniques to evaluate transverse shear and normal stresses in multlayered orthotropic plates is given in this paper. Transverse stresses evaluated a posteriori by integration of the 3D indefinite equilibrium equations and from Hook's law are compared to those given a priori by an assumed stress mode (if implemented). Classic theories formulated on the basis of assumed through-the-thickness displacement fields as well as mixed modeling originated by a Resister's mixed variation 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 interlamianr 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.
机译：本文对评估多层正交异性板中的横向剪切力和法向应力的可用模型和技术进行了综合分析。通过3D不定平衡方程的积分并根据Hook定律评估后验的横向应力与假定应力模式（如果已实现）先验给出的横向应力进行比较。考虑了基于假设的整个厚度位移场以及由Resister的混合变异定理产生的混合建模而建立的经典理论。研究了等效单层模型（ESLM）和明智层模型（LWM）的两种情况。对于引入的位移场和应力场，已经实现了在厚度层/板方向上线性的至多四次N阶展开。结果，将描述所谓的之字形效应并解释层间连续横向应力的理论与忽略了之字形并违反层间平衡的简化情况进行了比较。数值研究仅限于简单支撑的正交异性板的弯曲。

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