Abstract

In this article, an accurate mixed zigzag theory (HZZTM) is proposed for free vibration analysis of laminated composite and sandwich plates. In-plane displacements in the proposed zigzag theory nonlinearly distribute through the thickness and exhibit an abrupt discontinuity of slope at interfaces, which coincide with three-dimensional analysis. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT) is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stress fields, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient C⁰-type three-node triangular plate element with linear interpolation function is proposed for free vibration analysis of thick laminated composite and sandwich plates. Moreover, the accurate transverse shear stresses are introduced in the dynamic equilibrium equation by employing the Hamilton’s principle, which can actively improve the accuracy of natural frequencies of the laminated composite plates with different thickness and material properties at each ply. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model.

摘要

在本文中，提出了一种精确的混合之字形理论 (HZZTM)，用于层压复合材料和夹层板的自由振动分析。所提出的之字形理论中的面内位移非线性地分布在整个厚度上，并在界面处表现出陡峭的坡度不连续性，这与三维分析一致。为了获得准确的横向剪切应力，使用了基于三维 (3D) 平衡方程和 Reissner 混合变分定理 (RMVT) 的预处理方法。重要的是，平面内位移变量的二阶导数已从横向剪应力场中去除，从而大大简化了有限元的实现。因此，基于所提出的 zigzag 模型，计算效率高的 C ⁰提出了具有线性插值函数的-型三节点三角形板单元，用于厚层合板和夹层板的自由振动分析。此外，利用Hamilton原理在动态平衡方程中引入精确的横向剪应力，可以积极提高不同厚度和材料性能的叠层复合板各层的固有频率精度。通过与几个基准解决方案进行比较来评估所提出模型的性能。目前的结果与参考解决方案之间的一致性非常好，并且所提出的模型仅包含能够证明所提出模型的准确性和有效性的七个位移变量。