一种计算复合材料层合板面外应力的新型线性分析方法

复合材料层合板壳结构的面外应力对于层间分层的起始和扩展具有重要意义。首先简要地给出了经典的非协调位移有限元列式,然后基于修正的H-R变分原理导出了单元面外应力变量与位移变量的关系。面外应力的有限元线性系统为面外应力边界条件的引入提供了方便。同时,通过该线性系统可直接获得节点上唯一且连续的面外应力结果。与非协调位移有限元的结果比较,本文的方法可明显地提高数值结果的精度,且计算效率及资源要求均优于非协调辛元法和非协调广义混合元法。

A New Linear Analysis Method for Calculating Out-of-Plane Stress of Composite Laminates

The out-of-plane stress of composite laminated plates and shells is of great significance to the initiation and expansion of interlaminar delamination. Firstly, the formulation of classical non-compatible displacement finite element is given out briefly. And then, based on the modified Hellinger-Reissner (H-R) principle, the relationship between out-of-plane stress variables and displacement variables is derived. The finite element linear system of out-of-plane stress provides convenience for the introduction of out-of-plane stress boundary conditions. At the same time, the uniqueness and continuity of the out-of-plane stress at the node can be obtained directly by the finite element linear system. Compared with the results of non-compatible displacement finite element method, the proposed method can improve the accuracy of numerical results obviously, and the computational efficiency and resource requirements are superior to the non-compatible symplectic element method and the non-compatible generalized mixed element method.