基于扩展有限元的应力强度因子计算精度研究

doi:10.13232/j.cnki.jnju.2019.03.003

南京大学学报(自然科学版) ›› 2019, Vol. 55 ›› Issue (3): 361–369.doi: 10.13232/j.cnki.jnju.2019.03.003

所属专题：测试专题

基于扩展有限元的应力强度因子计算精度研究

王哲成¹，张　云¹*，于　军²，龚绪龙²

1.南京大学地球科学与工程学院，南京，210023； 2.江苏省地质调查研究院，南京，210008

收稿日期:2019-02-25 出版日期:2019-06-01 发布日期:2019-05-31
通讯作者: 张　云 E-mail:zhangyun@nju.edu.cn
基金资助:
国家自然科学基金(41572250)，国土资源部地裂缝地质灾害重点实验室开放课题

Calculation of stress intensity factor based on the extended finite element method

Wang Zhecheng¹，Zhang Yun¹*，Yu Jun²，Gong Xulong²

1.School of Earth Sciences and Engineering，Nanjing University，Nanjing，210023，China； 2.Institute of Geological Survey of Jiangsu Province，Nanjing，210008，China;

Received:2019-02-25 Online:2019-06-01 Published:2019-05-31
Contact: Zhang Yun E-mail:zhangyun@nju.edu.cn

摘要/Abstract

摘要： 应力强度因子(Stress intensity factor，SIF)是判断已有裂缝是否扩展的物理量，其计算精度对地裂缝扩展模拟具有重要影响. 基于扩展有限元的互作用积分法是一种常用的计算开裂问题应力强度因子的方法，其数值积分中的权函数通常为平台型或金字塔型，但目前对权函数的选取以及权函数对应力强度因子计算的影响研究得很少. 针对不同形式的权函数提出了统一的计算公式，并引入权函数因子来进一步控制权函数的具体形式；提出了非平台型的权函数的修正方法，以提高应力强度因子的计算精度；讨论了权函数因子以及积分区域因子对应力强度因子计算精度的影响，并通过算例进行了计算. 结果表明，当积分区域因子为3～5，采用修正的权函数且权函数因子取1～3时，应力强度因子的计算精度最高．

关键词: 扩展有限元, 互作用积分, 应力强度因子, 权函数, 权函数因子, 积分区域因子

Abstract: Stress intensity factor(SIF) is usually used in fracture simulation to determine the propagation of fissures. Its accuracy is vital to fracture simulation such as earth fissure. SIF is usually obtained by interaction integral method for its convenience and high accuracy. The weight function in the integration，namely q－function，is usually chosen as a plateau function or a ramp function. However，few attentions have been paid on the impact of different q－function shape type on the SIF. This paper presented a united formula for calculating different q－function types at nodes. A new weight function factor has been introduced to control the actual form of q－function. A modification has been made to improve the accuracy of SIF when a non－plateau q－function is used. Additionally，the effect of different q－function forms on the accuracy of SIF has been discussed，and the results show that the best integral domain factor is 3～5 and weight function factor is 1～3 with the modified weight function.

Key words: extended finite element method, interaction integral method, stress intensity factor, weight function, weight function factor, integral domain factor

中图分类号:

TU44

王哲成，张　云，于　军，龚绪龙. 基于扩展有限元的应力强度因子计算精度研究[J]. 南京大学学报(自然科学版), 2019, 55(3): 361–369.

Wang Zhecheng，Zhang Yun，Yu Jun，Gong Xulong. Calculation of stress intensity factor based on the extended finite element method[J]. Journal of Nanjing University(Natural Sciences), 2019, 55(3): 361–369.

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基于扩展有限元的应力强度因子计算精度研究

Calculation of stress intensity factor based on the extended finite element method

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