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

机译：满足C_z〜0要求的任意层压板的一系列高阶单层板模型

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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：在基于位移的层压板等效单层（ESL）板理论的框架中，本文提出了一种通用的自动方法，将基础高阶剪切变形理论（多项式，三角函数，双曲线...）扩展到多层Cz （0）高阶剪切变形理论。关键思想是增强对横截面翘曲的描述：将基础模型的奇高阶Cz（1）函数替换为一个奇偶高阶函数，并通过分段线性函数的平均值。为了考虑任意的​​层叠方案，考虑了四个这样的分段连续函数。确定这四个翘曲函数的系数的方式是，通过横向剪切应力场先验准确地验证了层间连续性以及板顶面和底面的均匀性条件。这些C-z（0）ESL模型都具有与原始基础HSDT相同的DOF数。通过参考具有任意堆叠顺序的层压板以及夹心板的强形式Navier型解决方案，可以进行数值评估。在通常应用层压板模型的所有实际相关配置中，在挠度，基频和局部应力响应方面获得的结果表明，所提出的之字形模型比其基础模型产生的结果更好。

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