Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions

LIU You-wen; FANG Qi-hong; WANG Ming-bin

Volume 25 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(4): 417-424

LIU You-wen, FANG Qi-hong, WANG Ming-bin. Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions[J]. Applied Mathematics and Mechanics, 2004, 25(4): 417-424.

Citation:

LIU You-wen, FANG Qi-hong, WANG Ming-bin. Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions[J]. Applied Mathematics and Mechanics, 2004, 25(4): 417-424.

Citation:

LIU You-wen, FANG Qi-hong, WANG Ming-bin. Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions[J]. Applied Mathematics and Mechanics, 2004, 25(4): 417-424.

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Antiplane Problem of Circular Arc Interfacial Rigid Line Inclusions

Department of Engineering Mechanics, Hunan University, Changsha 410082, P. R. China

Received Date: 2002-02-24
Rev Recd Date: 2003-11-28
Publish Date: 2004-04-15

Abstract

Abstract

The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with.By using Riemann-Schwarz's symmetry principle integrated with the singularity analysis of complex functions,the general solution of the problem and the closed form solutions for some important practical problems were presented.The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail.The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading,but no oscillatory character. Furthermore,the stresses are found to depend on geometrical dimension,loading conditions and materials parameters.Some practical results concluded are in agreement with the previous solutions.
- rigid line inclusion,
- circular arc interface,
- antiplane problem,
- complex variable method

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References(16)

References

[1]	Wang Z Y, Zhang H T, Chou Y T. Stress singularity at the top of a rigid line inhomogeneity under antiplane shear loading [J]. ASME Journal of Applied Mechanics,1986,53：459—461. doi: 10.1115/1.3171782
[2]	Li Q Q,Ting T C T.Line inclusions in anisotropic elastic solids[J].ASME Journal of Applied Mechanics,1989,56:556—563. doi: 10.1115/1.3176127
[3]	Chueng Y C, Chen Y Z. Multiple rigid line problem in infinite plate [J].Eng Frac Mech,1989,34(2):379—391. doi: 10.1016/0013-7944(89)90151-3
[4]	Ballarini R. A rigid line inclusion at a biomaterial interface[J].Eng Frac Mech,1990,37(1):1—5. doi: 10.1016/0013-7944(90)90326-C
[5]	Jiang C P, Liu C T. Stress distribution around a rigid line in dissimilar media [J].Eng Frac Mech,1992,42(1):27—32. doi: 10.1016/0013-7944(92)90273-H
[6]	Jiang C P. The plane problem of collinear rigid lines arbitrary loads [J].Eng Frac Mech,1991,39(2):299—308. doi: 10.1016/0013-7944(91)90044-2
[7]	Hao T H, Wu Y C. Elastic plane problem of collinear periodical rigid lines[J].Eng Frac Mech,1989,33(2):979—981. doi: 10.1016/0013-7944(89)90112-4
[8]	Jiang C P, Chueng Y C. Antiplane problems of collinear rigid line inclusions in dissimilar media[J].Eng Frac Mech,1995,52(5):907—916. doi: 10.1016/0013-7944(95)00039-X
[9]	刘又文.各向异性材料界面周期性刚性线夹杂的反平面问题[J].应用数学和力学, 2001,22(10):1037—1042.
[10]	刘又文.各向异性材料界面共线刚性线夹杂的反平面问题[J]. 固体力学学报,2001,22(2):214—218.
[11]	Liu Y W, Jiang C P. Stress distribution at the rigid circular arc inclusion end[J].Eng Frac Mech,1994,47(3):431—440. doi: 10.1016/0013-7944(94)90099-X
[12]	Shen M H, Chao C K. Explicit solutions for elastic and thermoelastic fields with rigid circular arc inclusion[J].Int J Fracture,1994,65:1—18. doi: 10.1007/BF00017139
[13]	Muskhelishvili, N L.Some Basic Problems of Mathematical Theory of Elasticity[M].Leyden:Noordhoff,1975.
[14]	樊大钧.数学弹性力学[M].北京:新时代出版社，1983.
[15]	蒋持平,刘振国.纵向剪切三相共焦点椭圆模型的精确解及其应用[J].力学学报,2000,32(4):251—256.
[16]	刘又文,蒋持平.含圆形弹性夹杂的反平面问题[J].中南矿冶学院学报,1991,22(2):196—201.

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