基于扩展有限元法的裂尖场精度研究

扩展有限元方法基于单元分解的基本思想,通过引入位移加强函数来表征裂纹的不连续性和裂尖的奇异性。在裂尖加强单元与常规单元之间有一层混合单元,当对裂尖特定区域进行加强时,混合单元个数相应增加,混合单元个数与计算精度存在一定联系。本文提出一种正方形裂尖加强区域的选择方式,可得到较单个加强和圆形加强精度更高、更稳定的计算结果。对于不同长度的裂纹,表征裂尖场奇异性所需的裂尖加强范围存在较大差异,以正方形裂尖加强方式进行计算,得到了不同裂纹长度下最优的加强尺寸。

Numerical study on the accuracy of crack tip field by extended finite element method

Based on concept of partition of unity method, the discontinuity of crack line and the singularity of the crack tip are represented by enrichment functions in extended finite element method.In the middle of crack tip enriched elements and traditional elements, there is a layer of blending elements.When enrich the region of area around the crack tip, the number and the mix ability of blending elements would be enlarged, and the accuracy would be affected.The squared region of crack tip enrichment is proposed in this paper.The results show the stability and higher accuracy than that of single and circle enrichments.For different crack lengths, to represent the singularity of the crack tip, the region of enrichment is different.The optimized sizes are obtained with squared enrichment region in different crack lengths.