夹杂尖端奇异性场的新型杂交元分析

Analysis of Singular Stress Field Around the Inclusion Corner Tip Based on A Novel Hybrid Finite Element Method

提出了一种夹杂尖端邻域杂交元模型,与全域杂交应力元结合,求解夹杂尖端的奇性应力场的数值解.利用高次内插有限元法求解特征问题,得到反映夹杂尖端场奇异性状况的特征值和特征角分布函数;利用Hellinger-Reissner变分原理以及特征问题的解,推导夹杂尖端邻域的单元矩阵.模型只考虑夹杂尖端邻域的边界,避免了在夹杂尖端划分高密度网格.采用正方形夹杂作为算例,数值结果显示了良好的精确性.

A new super corner-tip hybrid element model is proposed to solve the singular stress fields near the corner tip of inclusion together with an assumed hybrid stress finite element model. The establishment of the super corner tip element model consists of two steps： （1） an ad doe finite element method is developed to determine the characteristic problems; （2） results of step 1 are substituted into Hellinger-Reissner variational principle, through which element matrix of the super corner tip element is deduced. This new model only considers the boundary of corner tip domain, thus can effectively avoid high dense meshes near the corner tip. The model is verified by a benchmark example, and the numerical results of singular stress fields exhibit good accuracy.