A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups

XU Hua; XU De-feng; YANG Lü-feng

doi:10.21656/1000-0887.370050

Volume 37 Issue 10

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(10): 1039-1049

XU Hua, XU De-feng, YANG Lü-feng. A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups[J]. Applied Mathematics and Mechanics, 2016, 37(10): 1039-1049. doi: 10.21656/1000-0887.370050

Citation:

PDF( 953 KB)

A Finite Element Method With Generalized DOFs for Stress Intensity Factors of Crack Groups

doi: 10.21656/1000-0887.370050

¹Guangxi Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education; Guangxi Key Laboratory of Disaster Prevention and Sturctural Safety; Gollege of Civil Engineering and Architecture, Guangxi University, Nanning 530004, P.R.China;²Department of Housing and UrbanRural Development, Guangxi Zhuang Autonomous Region, Nanning 530028, P.R.China

Funds: The National Natural Science Foundation of China(51268003；51478125)

Received Date: 2016-02-16
Rev Recd Date: 2016-09-11
Publish Date: 2016-10-15

Abstract

Abstract

Stress intensity factors (SIFs) at crack tips of crack groups were solved by means of the finite element method with generalized DOFs. Firstly, based on the improved Williams series, the typical Williams elements in the singular region around the crack tip were set up. Then the global governing equations were formulated through intergration of the block matrices. Finally, with the undetermined parameters of the Williams series, SIFs at all the crack tips could be directly obtained. The influences of the parameters such as the distance between the centers of 2 adjacent cracks, and angle γ between the oblique crack and axis X on the calculation results were further analyzed through several examples. The results show that the proposed method can effectively overcome the defects of traditional finite element methods and it has higher accuracy and efficiency. Moreover, as for an infinite plate with multiple collinear horizontal cracks, when the ratio of the distance between the centers of 2 adjacent cracks to the half crack length is bigger than 9, the interaction among cracks can be ignored, so multiple cracks can be regarded as a single crack for calculation. For an infinite plate with an even number of axisymmetric oblique cracks, as angle γ increases, K_Ⅰ decreases, but K_Ⅱ first increases and then decreases.
- generalized DOF,
- stress intensity factor,
- crack group,
- Williams element,
- singular region size

FullText(HTML)

References(15)

References

[1]	马文涛, 许艳, 马海龙. 修正的内部基扩充无网格法求解多裂纹应力强度因子[J]. 工程力学, 2015,32(10): 18-24.(MA Wen-tao, XU Yan, MA Hai-long. Solving stress intensity factors of multiple cracks by using a modified intrinsic basis enriched meshless method[J]. Engineering Mechanics,2015,32(10): 18-24.(in Chinese））
[2]	Muskhelishvili N I. Some Basic Problems of the Mathematical Theory of Elasticity [M]. Holland: Noordhoff Press, 1953: 1-768.
[3]	Wang Y H, Tham L G, Lee P K K, Tsui Y. A boundary collocation method for cracked plates[J]. Computers & Structures,2003,81(28): 2621-2630.
[4]	李爱民, 崔海涛, 温卫东. I-II复合型多裂纹板的应力强度因子分析[J]. 机械科学与技术, 2015,34(5): 803-807.(LI Ai-min, CUI Hai-tao, WEN Wei-dong. Analyzing stress intensity factors of a plate with multiple mixed-mode cracks[J]. Mechanical Science and Technology for Aerospace Engineering,2015,34(5): 803-807.(in Chinese））
[5]	Chen W H, Chang C S. Analysis of two dimensional fracture problems with multiple cracks under mixed boundary conditions[J]. Engineering Fracture Mechanics,1989,34(4): 921-934.
[6]	刘钧玉, 林皋, 胡志强. 裂纹面荷载作用下多裂纹应力强度因子计算[J]. 工程力学, 2011,28(4): 7-12.(LIU Jun-yu, LIN Gao, HU Zhi-qiang. The calculation of stress intensity factors of multiple cracks under surface tractions[J]. Engineering Mechanics,2011,28(4): 7-12.(in Chinese））
[7]	Cartwright D J, Rooke D P. Approximate stress intensity factors compounded from known solutions[J]. Engineering Fracture Mechanics,1974,6(3): 563-571.
[8]	陈莉, 王志智, 聂学州. 一种多裂纹应力强度因子计算的新方法[J]. 结构强度, 2004,26(S): 210-212.(CHEN Li, WANG Zhi-zhi, NIE Xue-zhou. New approach for stress intensity factor calculation of multiple site cracks[J]. Journal of Mechanical Strength,2004,26(S): 210-212.（in Chinese））
[9]	Guo Z, Liu Y J, Ma H, Huang S. A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements[J]. Engineering Analysis With Boundary Elements,2014,47: 1-9.
[10]	Singh I V, Mishra B K, Pant M. A modified intrinsic enriched element free Galerkin method for multiple cracks simulation[J]. Materials and Design,2010,31(1): 628-632.
[11]	陈军斌, 魏波, 谢青, 王汉青, 李涛涛, 王浩. 基于扩展有限元的页岩水平井多裂缝模拟研究[J]. 应用数学和力学, 2016,37(1): 73-83.(CHEN Jun-bin, WEI Bo, XIE Qing, WANG Han-Qing, LI Tao-tao, WANG Hao. Simulation of multi-hydrofracture horizontal wells in shale based on the extended finite element method[J]. Applied Mathematics and Mechanics, 2016,37(1): 73-83.（in Chinese））
[12]	杨绿峰, 徐华, 彭俚, 李冉. 断裂问题分析的Williams广义参数单元[J]. 计算力学学报, 2009,26(1): 33-39.(YANG Lü-feng, XU Hua, PENG Li, LI Ran. Analysis of crack problems by Williams generalized parametric element[J]. Chinese Journal of Computational Mechanics,2009,26(1): 33-39.(in Chinese））
[13]	杨绿峰, 徐华, 李冉, 彭俚. 广义参数有限元法计算应力强度因子[J]. 工程力学, 2009,26(3): 48-54.(YANG Lü-feng, XU Hua, LI Ran, PENG Li. The finite element with generalized coefficients for stress intensity factor[J]. Engineering Mechanics,2009,26(3): 48-54.(in Chinese））
[14]	徐华, 杨绿峰, 佘振平. Ⅲ型应力强度因子分析的Williams单元[J]. 中南大学学报(自然科学版), 2012,43（8）: 3237-3243.(XU Hua, YANG Lü-feng, SHE Zhen-pin. Williams element for mode-Ⅲ stress intensity factor[J]. Journal of Central South University(Science and Technology), 2012,43(8): 3237-3243.(in Chinese））
[15]	中国航空研究院. 应力强度因子手册（增订版）[M]. 北京: 科学出版社, 1993: 75-76, 110-113.（China Aviation Institute. The Stress Intensity Factor Handbook(Updated Version) [M]. Beijing: Science Press, 1993: 75-76， 110-113.（in Chinese））