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.
Similar content being viewed by others
References
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.
Li Q Q, Ting T C T. Line inclusions in anisotropic elastic solids[J].ASME Journal of Applied Mechanics, 1989,56:556–563.
Chueng Y C, Chen Y Z. Multiple rigid line problem in infinite plate[J].Eng Frac Mech, 1989,34 (2):379–391.
Ballarini R. A rigid line inclusion at a biomaterial interface[J].Eng Frac Mech, 1990,37(1): 1–5.
Jiang C P, Liu C T. Stress distribution around a rigid line in dissimilar media[J].Eng Frac Mech, 1992,42(1):27–32.
Jiang C P. The plane problem of collinear rigid lines arbitrary loads[J].Eng Frac Mech, 1991,39 (2):299–308.
Hao T H, Wu Y C. Elastic plane problem of collinear periodical rigid lines[J].Eng Frac Mech, 1989,33(2):979–981.
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.
LIU You-wen. Antiplane problems of periodical rigid line inclusions between dissimilar anisotropic materials[J].Applied Mathematics and Mechanics (English Edition), 2001,22(10):1149–1154.
LIU You-wen. Antiplane problems of collinear rigid line inclusions between dissimilar anisotropic materials[J].Acta Mechanica Solida Sinica, 2001,22(2):214–218. (in Chinese)
Liu Y W, Jiang C P. Stress distribution at the rigid circular arc inclusion end[J].Eng Frac Mech, 1994,47(3):431–440.
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.
Muskhelishvili, N L.Some Basic Problems of Mathematical Theory of Elasticity[M]. Leyden: Noordhoff, 1975.
FAN Da-jun.Mathematical Theory of Elasticity [M]. Beijing: New Times Press, 1983. (in Chinese)
JIANG Chi-ping, LIU Zhen-guo. A closed solution and its applications for the 3-phase confocal ellipse model under longitudinal shear[J].Acta mechanica Sinica, 2000,32(4):251–256. (in Chinese)
LIU You-wen, JIANG Chi-ping. Antiplane problem of circular elastic inclusion[J].J Cent South Inst Min Metall, 1991,22(2):196–201. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by FAN Da-jun, Original Member of Editorial Committee, AMM
Foundation item: the Natural Science Foundation of Human Province (02JJY2014)
Biography: LIU You-wen (1948≈), Professor, Master
Rights and permissions
About this article
Cite this article
You-wen, L., Qi-hong, F. & Ming-bin, W. Antiplane problem of circular ARC interfacial rigid line inclusions. Appl Math Mech 25, 458–466 (2004). https://doi.org/10.1007/BF02437530
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437530