In this paper, a linear smoothing scheme over eight-node Reissner-Mindlin plate element under the framework of the CS-FEM is employed to buckling analysis of laminated composite plates based on the first-order shear deformation theory. The modified stain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor's expansion. Isoparametric mapping and the computation of interior derivatives of shape function is not required in the proposed method, furthermore, all the computation are based on the global Cartesian coordinates. Some numerical examples are given at the end to demonstrate that the present method has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes.

中文翻译：

---

用于层合复合板屈曲分析的线性平滑二次有限元

本文采用CS-FEM框架下八节点Reissner-Mindlin板单元的线性平滑方案，基于一阶剪切变形理论对层合复合材料板进行屈曲分析。修改后的染色矩阵是使用泰勒展开通过节点形状函数及其导数之间的散度定理计算的。该方法不需要等参映射和形函数内导数的计算，而且所有计算都基于全局笛卡尔坐标。最后给出了一些数值例子，表明该方法具有良好的性能，可以缓解剪切锁定现象并提高扭曲网格解的质量。