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首页> 外文期刊>International journal of structural stability and dynamics >PLATE BUCKLING ANALYSIS USING A GENERAL HIGHER-ORDER SHEAR DEFORMATION THEORY
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PLATE BUCKLING ANALYSIS USING A GENERAL HIGHER-ORDER SHEAR DEFORMATION THEORY

机译：一般高阶剪切变形理论的板屈曲分析

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摘要

The buckling of higher-order shear plates is studied in this paper with a unified formalism. It is shown that usual higher-order shear plate models can be classified as gradient elasticity Mindlin plate models, by augmenting the constitutive law with the shear strain gradient. These equivalences are useful for a hierarchical classification of usual plate theories comprising Kirchhoff plate theory, Mindlin plate theory and third-order shear plate theories. The same conclusions were derived by Challamel [Mech. Res. Commun. 38 (2011) 388] for higher-order shear beam models. A consistent variational presentation is derived for all generic plate theories, leading to meaningful buckling solutions. In particular, the variationally-based boundary conditions are obtained for general loading configurations. The buckling of the isotropic or orthotropic composite plates is then investigated analytically for simply supported plates under uniaxial or hydrostatic in-plane loading. An analytical buckling formula is derived that is common to all higher-order shear plate models. It is shown that cubic-based interpolation models for the displacement field are kinematically equivalent, and lead to the same buckling load results. This conclusion concerns for instance the plate models of Reddy [J. Appl. Mech. 51 (1984) 745] or the one of Shi [Int. J. Solids Struct. 44 (2007) 4299] even though these models are statically distinct (leading to different stress calculations along the cross-section). Finally, a numerical sensitivity study is made.
机译：本文以统一的形式主义对高阶剪力板的屈曲进行了研究。结果表明，通常的高阶剪切板模型可以通过用剪切应变梯度增加本构律来分类为梯度弹性Mindlin板模型。这些等价对于包括Kirchhoff板理论，Mindlin板理论和三阶剪切板理论在内的常规板理论的分层分类很有用。查勒梅尔[Mech。 Res。公社38（2011）388]。对所有通用板理论都得出了一致的变体表示法，从而得出了有意义的屈曲解决方案。特别地，对于一般的载荷配置获得基于变化的边界条件。然后，在单轴或静水面内载荷下，对简单支撑的板进行各向同性或正交异性复合板的屈曲分析。推导了所有高阶剪力板模型通用的分析屈曲公式。结果表明，基于三次方的位移场插值模型在运动学上是等效的，并导致相同的屈曲载荷结果。这个结论涉及例如Reddy的板模型[J.应用机甲。 51（1984）745]或Shi之一。 J.固体结构。 44（2007）4299]，尽管这些模型在静态上是不同的（导致沿横截面的应力计算不同）。最后，进行了数值敏感性研究。

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