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A family of higher-order single layer plate models meeting C_z~0-requirements for arbitrary laminates

机译：一个高阶单层板型号会满足C_Z〜0 - 任意层压板的要求

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摘要

In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic...) to a multilayer C-z(0) higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C-z(1) function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are considered. The coefficients of these four warping functions are determined in such a manner that the interlaminar continuity as well as the homogeneity conditions at the plate's top and bottom surfaces are a priori exactly verified by the transverse shear stress field. These C-z(0) ESL models all have the same number of DOF as the original basis HSDT. Numerical assessments are presented by referring to a strong-form Navier-type solution for laminates with arbitrary stacking sequences as well for a sandwich plate. In all practically relevant configurations for which laminated plate models are usually applied, the results obtained in terms of deflection, fundamental frequency and local stress response show that the proposed zig-zag models give better results than the basis models they are issued from.
机译：在基于位移的等效单层（ESL）平板理论的框架中，本文介绍了一种通用和自动方法，以将基础剪切变形理论（多项式，三角，双曲线......）延伸到多层CZ （0）高阶剪切变形理论。关键的想法是提高横截面翘曲的描述：基础模型的奇数高阶CZ（1）函数被一个奇数和一个甚至高阶函数所取代，包括特征Zag行为分段线性函数的方法。为了考虑任意层压方案，考虑四个这样的分段连续功能。以这样的方式确定这四个翘曲功能的系数，使得板式顶部和底表面处的均匀性条件是由横向剪切应力场精确验证的先验。这些C-Z（0）ESL模型都具有与原始基础HSDT相同的DOF。通过参考具有任意堆叠序列的层压板的强型Navier型解决方案来提出数值评估，以及用于三明治板的层压板。在通常应用层压板模型的所有实际相关配置中，在偏转，基本频率和局部应力响应方面获得的结果表明，所提出的Zig-ZAG模型提供了比它们发布的基础模型更好的结果。

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