双材料自由边界面端部问题的数值分析

Numerical Analysis to Interface at Free-edge of Bimaterial

对各向异性双材料自由边界面端部奇异性场问题进行了研究,利用有限元分析法所得到的各向异性双材料自由边界面端部的应力奇异性指数以及角分布函数,构造了一个自由边界面端部单元,据此建立了自由边界面端部奇异性场的杂交应力模型,并结合Hellinger-Reissner变分原理导出应力杂交元方程,建立了求解平面各向异性材料裂纹尖端问题的杂交元计算模型。与四节点单元相结合,提出一种求解自由边界面端部广义应力强度因子的杂交元法。考核例结果表明:本文方法的数值解精度高,可应用于各向异性材料双材料自由边界面端部问题。

The singular field near at interface of free-edge in anisotropic bimaterial is investigated, finite element method is applied to solve the stress singularities of interface edge, and a new singular interface element is constructed. With the interface element, a hybrid-stress finite element equation is deduced following Hellinger-Reissner principle. Combining general four-node element around crack tip element, a hybrid-stress finite element model is developed, Accordingly a hybrid finite element method to for generalized stress intensity factors is introduced. To illustrate the efficiency of the suggested procedure, some numerical examples are presented to verify the higher accuracy than the exisiting solutions.