一种XFEM断裂分析的裂尖单元新型改进函数

江守燕; 杜成斌

doi:10.6052/0459-1879-12-144

一种XFEM断裂分析的裂尖单元新型改进函数

doi: 10.6052/0459-1879-12-144

江守燕,
杜成斌^,

河海大学工程力学系, 南京210098

基金项目: 国家自然科学基金(11132003, 50779011) 和江苏省研究生创新工程(CX10B 202Z) 资助项目.

详细信息

通讯作者:
杜成斌

中图分类号: TB115
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出版历程
- 收稿日期: 2012-05-17
- 修回日期: 2012-08-31
- 刊出日期: 2013-01-18

A NOVEL ENRICHED FUNCTION OF ELEMENTS CONTAINING CRACK TIP FOR FRACTURE ANALYSIS IN XFEM

Jiang Shouyan,
Du Chengbin^,

Dept. of Engineering Mechanics, Hohai University, Nanjing 210098, China

Funds: The project was supported by the National Natural Science Foundation of China (11132003, 50779011) and the Innovative Project for Graduate Students of Jiangsu Province (CX10B_202Z).

摘要

摘要: 提出了一种适用于裂尖改进单元的新型改进函数, 基于三角变换的方法, 保留裂纹尖端场的应力奇异性和裂纹上、下表面的位移不连续性, 将常规扩展有限元法裂尖改进单元的4 项改进函数缩减为2 项, 裂尖改进单元的结点由常规的8 个改进自由度减少为4 个. 采用2 个正交的水平集函数表征材料内部裂纹面, 详细阐述了改进单元类型的判别方法, 给出一种改进单元的分区域积分方案. 最后, 若干断裂力学问题经典算例的数值计算结果表明:建议的裂尖改进函数具有较高的数值精度, 该方法是十分有效的.
- 扩展有限元法 /
- 裂尖改进函数 /
- 水平集法 /
- 裂纹 /
- 断裂分析 /
- 应力强度因子
Abstract: In the paper, a novel enriched function for those elements containing crack tip is proposed. By the method of trigonometric transform, the four crack tip enriched functions in the standard extended finite element methods (XFEM) are reduced to the two ones. The reduced enriched functions still keep the two properties, such as the stress singular at the crack tip and the discontinuities of crack surfaces. The enriched degrees of freedom for those nodes of element containing crack tip is thereby reduced from 8 to 4. The two orthogonal level set functions are used to represent the existing crack in materials. The method for identifying the enriched type of elements is described in details. An integration schemes for enriched elements are given. Finally, several classic fracture problems are given to verify the numerical precision of the proposed crack tip enriched functions. The results show the effectiveness of the proposed method.
- extended finite element methods /
- crack tip enriched function /
- level set method /
- crack /
- fracture analysis /
- stress intensity factors

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参考文献(8)

1 夏晓舟, 章青. 含两类附加函数的扩展等参有限元法. 计算力学学报, 2008, 25(1): 41-47 (Xia Xiaozhou, Zhang Qing. Extended isoparametric finite element method including two class of enrichment functions. Chinese Journal of Computational Mechanics,2008, 25(1): 41-47 (in Chinese))

2 Fries T. A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 2008, 75(5): 503-532

3 Mohammadi S. Extended Finite Element Mmethod. UK: Blackwell Publishing Ltd, 2008

4 应宗权. 非均质材料(混凝土) 细观力学及断裂的扩展有限元研究. [博士论文]. 南京:河海大学, 2008. 102-103 (Ying Zongquan. Mesomechanics of heterogeneous material (concrete) and application of extended finite element method to its fracture. [PhD Thesis]. Nanjing: Hohai University, 2008. 102-103 (in Chinese))

5 江守燕,杜成斌. 弱不连续问题扩展有限元法的数值精度研究. 力学学报, 2012, 44(6): 1005-1015 (Jiang Shouyan, Du Chengbin. Study on numerical precision of extended finite element method for modeling weak discontinuities. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 1005-1015 (in Chinese))

6 余天堂. 含裂纹体的数值模拟. 岩石力学与工程学报, 2005,24(24): 4434-4438 (Yu Tiantang. Numerical simulation of a body with cracks. Chinese Journal of Rock Mechanics and Engineering,2005, 24(24): 4434-4438 (in Chinese))

7 Zamani A, Gracie R, Eslami MR. Cohesive and non-cohesive fracture by higher-order enrichment of XFEM. International Journal for Numerical Methods in Engineering, 2012, 90: 452-483

8 Stazi FL, Budyn E, Chessa J, et al. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics, 2003, 31: 38-48

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