Abstract The paper presents a locking-free four-node element for laminated composite and sandwich plates based on Refined Zigzag Theory (RZT). Initially, two RZT-based plate elements are derived using four-node and eight-node configurations, achieved by way of standard C0 isoparametric shape functions. In addition, with a view on improving the modelling of extremely thin plates, an anisoparametric four-node element is developed in which the transverse deflection variable is interpolated using quadratic polynomial shape functions, whereas the remaining kinematic variables are bilinear. A straightforward transverse-shear edge-constraint procedure gives rise to a four-node anisoparametric element. A further enhancement is achieved using an Element Shear Correction (ESC) factor that is derived from a strain-energy matching procedure. The resulting four-node element (ZQ4c) uses full Gauss quadrature, consistent load vector, and mass matrix. Furthermore, the ZQ4c stiffness matrix has no spurious zero-energy modes, and the element is extremely robust when modelling ultra-thin plates. Several numerical studies are carried out to demonstrate the predictive capabilities of the four elements examined in this investigation. It is concluded ZQ4c is a highly accurate element over a wide range of material systems and span-to-thickness ratios, and is the best performing element of the four elements examined in this study.

中文翻译：

---

基于 Refined Zigzag 理论的用于层压复合板和夹层板的稳健四节点四边形单元

摘要 本文基于细化之字形理论（RZT）提出了一种用于层压复合板和夹层板的无锁定四节点单元。最初，使用四节点和八节点配置导出两个基于 RZT 的板单元，通过标准 C0 等参形状函数实现。此外，为了改进极薄板的建模，开发了一种非等参四节点单元，其中使用二次多项式形状函数对横向偏转变量进行插值，而其余运动学变量是双线性的。一个简单的横向剪切边缘约束程序产生了一个四节点的各参数单元。使用源自应变能量匹配程序的单元剪切校正 (ESC) 因子可实现进一步增强。生成的四节点元素 (ZQ4c) 使用完全高斯正交、一致载荷向量和质量矩阵。此外，ZQ4c 刚度矩阵没有虚假零能量模式，并且该单元在建模超薄板时非常稳健。进行了几项数值研究，以证明本调查中检查的四个元素的预测能力。得出的结论是，ZQ4c 是适用于各种材料系统和跨厚比的高精度元件，并且是本研究中检查的四种元件中性能最佳的元件。进行了几项数值研究，以证明本调查中检查的四个元素的预测能力。得出的结论是，ZQ4c 是适用于各种材料系统和跨厚比的高精度元件，并且是本研究中检查的四种元件中性能最佳的元件。进行了几项数值研究，以证明本调查中检查的四个元素的预测能力。得出的结论是，ZQ4c 是适用于各种材料系统和跨厚比的高精度元件，并且是本研究中检查的四种元件中性能最佳的元件。