To make use of the merit of designability, each lamina in layered structures may possess diverse materials and geometry to realize specific application. For the hybridized structures, geometry and material properties relative to the middle surface are generally unsymmetrical, which have a significant impact on stability. Some models might lose capability to deal with such issues, so that these issues are less reported. Within the developed models, Reddy’s model possesses merit of simplicity and efficiency, so a Reddy-type higher-order zig-zag model is constructed by utilizing the proposed zig-zag function (ZZF). Instead of the standard finite element formulation using the principle of minimum potential energy, the three-field Hu–Washizu (HW) mixed variational principle is employed to acquire the finite element formulation which can meet the harmonious conditions of transverse shear stress at the interface of adjacent layers. By investigating buckling behaviors of hybridized structures, performance of the proposed finite element formulation is appraised by comparing with the results obtained from the three-dimensional (3D) model as well as other models. Effect of boundary conditions (BCs), material properties, and span-to-thickness ratio on the buckling loads is also studied in detail. Numerical results show that buckling loads of hybridized structures are significantly impacted by the chosen parameters. The results acquired from proposed model are in very good agreement with those obtained from the layerwise (LW) model and the 3D finite element results.

中文翻译：

---

用Reddy型高阶有限元公式研究具有杂化构型的层状结构的稳定性

为了利用可设计性的优点，分层结构中的每个薄片可以具有不同的材料和几何形状以实现特定的应用。对于杂化结构，相对于中间表面的几何形状和材料性质通常是不对称的，这对稳定性有很大影响。某些模型可能会失去处理此类问题的能力，因此这些问题的报道较少。在所开发的模型中，Reddy 模型具有简单和高效的优点，因此利用所提出的之字形函数（ZZF）构建了一个 Reddy 型高阶之字形模型。代替使用最小势能原理的标准有限元公式，采用三场胡-和士祖（HW）混合变分原理，获得了满足相邻层界面横向剪应力协调条件的有限元公式。通过研究混合结构的屈曲行为，通过与从三维 (3D) 模型以及其他模型获得的结果进行比较，评估了所提出的有限元公式的性能。还详细研究了边界条件 (BC)、材料特性和跨厚比对屈曲载荷的影响。数值结果表明，混合结构的屈曲载荷受所选参数的显着影响。从提出的模型获得的结果与从分层（LW）模型和3D有限元结果获得的结果非常一致。