A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates
A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates
复制标题
DOI：
10.1016/j.compstruct.2014.05.002
复制
发表时间：
2014-11
影响因子：
6.3
通讯作者：
R. Sahoo;B. N. Singh
中科院分区：
文献类型：
--
作者：
R. Sahoo;B. N. Singh
在这项工作中，提出了一种新的三角曲折理论来分析层合复合材料和夹层板。该理论基于假设横向剪切应力非线性分布的剪切应变形状函数。满足层界面层间应力连续性的必要条件以及板顶面和底面横向剪应力为零的条件。该理论具有与 FSDT 相同数量的未知场变量，并且未知数的数量与层无关，这使得解决方案的计算效率更高。采用 C0 连续等参意外元素来求解这两个问题中出现的离散特征值方程。因此，通过对具有不同模数比、长宽比、跨厚比、载荷和边界条件、铺层方向、铺层数、本征模态等的层合复合材料和夹层板的自由振动和稳定性分析的数值实验，证明了该理论的准确性和效率。层合复合材料和夹层板还表示了具有相应振动和屈曲模态形状的更高模式。当用相关数值例子验证该理论时，可以观察到该理论的优雅表现。
In this work, a new trigonometric zigzag theory is proposed for the analysis of laminated composite and sandwich plates. The theory is based upon shear strain shape function assuming non-linear distribution of transverse shear stresses. It satisfies the necessary conditions of inter-laminar stress continuity at the layer interfaces as well as the condition of zero transverse shear stresses at the top and bottom surfaces of the plates. The theory has the same number of unknown field variables as that of FSDT and the number of unknowns is layer independent which makes the solution computationally more efficient. A C0continuous isoparametric serendipity element is employed to solve the discrete eigenvalue equations arising in both the problems. The accuracy and the efficiency of the theory are thus demonstrated through numerical experiments on the free vibration and stability analysis of laminated composite and sandwich plates with different modular ratio, aspect ratio, span to thickness ratio, loading and boundary conditions, ply orientations, lay-up number, eigen modes, etc. Higher modes with corresponding mode shapes of vibration and buckling are also represented for laminated composite and sandwich plates. An elegant performance of the proposed theory is observed when it is validated with relevant numerical examples.