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首页> 外文期刊>Composite Structures >∞~6 Mixed Plate Theories Based On The Generalized Unified Formulation. Part V: Results
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∞~6 Mixed Plate Theories Based On The Generalized Unified Formulation. Part V: Results

机译：基于广义统一公式的∞〜6混合板理论。第五部分：结果

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Parts Ⅰ,Ⅱ, Ⅲ and Ⅳ presented the Generalized Unified Formulation in the framework of Reissner's Mixed Variational Theorem. Layerwise theories, mixed higher order shear deformation theories and zig-zag models were introduced. In all these types of theories the displacement variables and out-of-plane stresses are independently treated and different orders of expansion for the different unknowns can be chosen. All the possible ∞~6 theories are generated by expanding 13 invariant fundamental nuclei. The relative orders used for the expansion of the stresses and displacements are important and can be the source of numerical instabilities. How the instabilities are eliminated is discussed. In the case of layerwise theories and the examined problems, it is shown that there is no numerical instability if the qrder of displacement u_z is the same as the order of stress σ_(zz). New light is also shed on the mixed equivalent single layer theories. It is shown that the poor representation of the a priori calculated transverse stresses is due to the above mentioned numerical instabilities and not only to the insufficient representation of the effects of σ_(zz). Finally, for the mixed case, it is demonstrated that the addition of Murakami'z zig-zag function (MZZF) is convenient but this is not a general property, as was believed in the literature before this work. The convenience of the addition of MZZF is linked to the relative orders of the starting theory that is being improved with the zig-zag term. Several new layerwise and equivalent single layer theories are introduced for the first time in the literature and an assessment is given with new cases compared against the elasticity solution.
机译：Ⅰ，Ⅱ，Ⅲ和Ⅳ部分在Reissner混合变分定理的框架内给出了广义统一公式。介绍了分层理论，混合高阶剪切变形理论和之字形模型。在所有这些类型的理论中，位移变量和面外应力均得到独立处理，并且可以为不同的未知数选择不同的扩展阶数。所有可能的∞〜6理论都是通过扩展13个不变基核生成的。用于应力和位移扩展的相对阶数很重要，并且可能是数值不稳定性的根源。讨论了如何消除不稳定性。在分层理论和所研究的问题的情况下，表明如果位移u_z的qrder与应力σ_（zz）的阶数相同，则不存在数值不稳定性。混合等效单层理论也有新发现。结果表明，先验计算的横向应力的较差表示是由于上述数值不稳定性，而不仅仅是由于σ_（zz）效应的不足表示。最后，对于混合情况，证明了增加村上的Z字形函数（MZZF）是方便的，但这不是一般特性，正如该工作之前的文献所认为的那样。添加MZZF的便利性与使用zig-zag项进行改进的起始理论的相对顺序有关。文献中首次引入了几种新的分层理论和等效的单层理论，并给出了与弹性解相比的新案例的评估。

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