Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion

LIU You-wen; FANG Qi-hong

Volume 26 Issue 12

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(12): 1436-1444

LIU You-wen, FANG Qi-hong. Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1436-1444.

Citation:

LIU You-wen, FANG Qi-hong. Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1436-1444.

Citation:

LIU You-wen, FANG Qi-hong. Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1436-1444.

PDF( 375 KB)

Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion

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

Received Date: 2004-03-03
Rev Recd Date: 2005-08-02
Publish Date: 2005-12-15

Abstract

Abstract

The plane elastic problem of circular-arcrigid line inclusions is considered.The model is subjected to remote general loads and concentrated force which is applied at an arbitrary point inside either the matrix or the circular inclusion.Based on complex variable method,the general solutions of the problem were derived.The closed form expressions of the sectionally holomorphic complex potentials and the stress fields were derived for the case of the interface with a single rigid line.The exact expressions of the singular stress fields at the rigid line tips were calculated which show that they possess a pronounced oscillatory character similar to that for the corresponding crack problem under plane loads.The influence of the rigid line geometry,loading conditions and material mismatch on the stress singularity coefficients is evaluated and discussed for the case of remote uniform load.
- complex variable method,
- circular inclusion,
- interfacial rigid line,
- concentrated force

FullText(HTML)

References(12)

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(3):459—461. doi: 10.1115/1.3171782
[2]	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
[3]	JIANG Chi-ping,LIU Chun-tu.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
[4]	JIANG Chi-ping.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
[5]	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
[6]	JIANG Chi-ping,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
[7]	Markenscoff X, Ni L Q, Dundurs J. Interface anticrack and Green's functions for interacting anticracks and cracks/anticracks[J].ASME Journal of Applied Mechanics,1994,61(4):797—802. doi: 10.1115/1.2901559
[8]	LIU You-wen,JIANG Chi-ping. 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
[9]	Shen M H,Chao C K.Explicit solutions for elastic and thermo-elastic fields with rigid circular arc inclusion[J].Internat J Fracture,1995,65(1):1—18.
[10]	CHEN Yi-zhou.Circular arc rigid line problem with loading on-line[J].ASME Journal of Applied Mechanics,1998,65(4):776—778. doi: 10.1115/1.2789126
[11]	刘又文，方棋洪.圆形界面刚性线夹杂的反平面问题[J].应用数学和力学,2004,25(4):417—424.
[12]	Muskhelishvili N L.Some Basic Problems of Mathematical Theory of Elasticity[M].Leyden:Noordhoff,1975.

Relative Articles

[1]	LU Shaonan, ZHAO Xuefen, MA Yuanyuan. Research on Interfacial Collinear Cracks Between 1D Hexagonal Piezoelectric Quasicrystal Bimaterials[J]. Applied Mathematics and Mechanics, 2023, 44(7): 809-824. doi: 10.21656/1000-0887.430111
[2]	ZHANG Bingcai, DING Shenghu, ZHANG Laiping. The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials[J]. Applied Mathematics and Mechanics, 2022, 43(6): 639-647. doi: 10.21656/1000-0887.420202
[3]	WANG Shaojie, ZENG Xiangtai, Lü Aizhong. Analytical Analysis of Non-Circular Hydraulic Lined Tunnels Under Smooth Contact With Transversely Isotropic Rock Mass[J]. Applied Mathematics and Mechanics, 2021, 42(4): 342-353. doi: 10.21656/1000-0887.410182
[4]	ZHANG Jun, JIN Ying, XIONG Tao. Fracture Analysis on Multiferroic Composite Plates Under Concentrated Forces[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1390-1399. doi: 10.21656/1000-0887.390013
[5]	GUO Jun-hong, LIU Ping, LU Zi-xing, QIN Tai-yan. Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip[J]. Applied Mathematics and Mechanics, 2011, 32(1): 72-78. doi: 10.3879/j.issn.1000-0887.2011.01.008
[6]	XIAO Wan-shen, XIE Chao, LIU You-wen. Interaction Between a Heat Dipole and a Circular Interfacial Crack[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1143-1152. doi: 10.3879/j.issn.1000-0887.2009.10.002
[7]	JIN Cong-rui. Large Deflection of Circular Membrane Under Concentrated Force[J]. Applied Mathematics and Mechanics, 2008, 29(7): 806-812.
[8]	LIU You-wen, LI Bo, FANG Qi-hong. Moving Screw Dislocation Near Interfacial Rigid Lines in Two Dissimilar Anisotropic Media[J]. Applied Mathematics and Mechanics, 2008, 29(5): 564-574.
[9]	FANG Qi-hong, LIU You-wen. Elastic Interaction Between a Wedge Disclination Dipole and an Internal Crack[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1084-1092.
[10]	HAO Ji-ping, YAN Xin-li. Exact Solution of Large Deformation Basic Equations of Circular Membrane Under Central Force[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1169-1172.
[11]	ZHENG Jian-long, FANG Qi-hong, LIU You-wen. Analysis of a Screw Dislocation Inside a Circular Inclusion With Interfacial Cracks in Piezoelectric Composites[J]. Applied Mathematics and Mechanics, 2005, 26(8): 957-964.
[12]	DING Bo-yang, DING Cui-hong, CHEN Yu, TAO Hai-bing. Green Function on Two-Phase Saturated Medium by Concentrated Force in Two-Dimensional Displacement Field[J]. Applied Mathematics and Mechanics, 2004, 25(8): 869-874.
[13]	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.
[14]	CHEN Shan-lin, ZHENG Zhou-lian. Large Deformation of Circular Membrane Under the Concentrated Force[J]. Applied Mathematics and Mechanics, 2003, 24(1): 25-28.
[15]	JIANG Chi-ping, LIU You-wen, XU Yao-ling. Interaction of a Screw Dislocation in the Interphase Layer With the Inclusion and Matrix[J]. Applied Mathematics and Mechanics, 2003, 24(8): 865-873.
[16]	Liu Diankui, Hu Chao. The General Solution for the Stress Problem of Circular Cylindrical Shells with an Arbitrary Cutout[J]. Applied Mathematics and Mechanics, 1997, 18(7): 585-602.
[17]	Wu Chengping, Wang Cheng. Near Crack Line Elastic-Plastic Analysis for a Crack Loaded by Antiplane Point Forces[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1059-1064.
[18]	Wang Quan, Wang Da-jun. Singularity under a Concentrated Force in Elasticity[J]. Applied Mathematics and Mechanics, 1993, 14(8): 679-677.
[19]	Yang Wei-yang, Zhang Shao-qin, Jia Yuan-duo. On J-lntegrals in the Plane Fracture of Composite Materials[J]. Applied Mathematics and Mechanics, 1992, 13(3): 263-269.
[20]	Liu You-wen, Jiang Chi-ping. Problem on Circular-Arc Cracks between Bonded Dissimilar Materials under Concentrated Force and Moment[J]. Applied Mathematics and Mechanics, 1987, 8(3): 267-276.