各向异性材料中共线刚性线夹杂的纵向剪切问题
Longituanal Shear Problems of Collinear Rigid Line Inclusions in Anisotropic Materials
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摘要: 本文研究各向异性材料中共线刚性线夹杂,(有时称作“硬裂纹”或“反裂纹”问题)的纵向剪切问题。利用复变函数方法,提出了一般问题的公式和某些实际重要问题的封闭形式解,考察了刚性线端点附近的应力分布。从本文解答的特殊情形,可以直接导出各向同性材料相应问题的公式和结果,包括某些已有的结果[7].Abstract: Longitudinal shear problems of collinear rigid line inclusions (sometimes called hard crack or inverse crack problems) in anisotropic materials are dealt with. By usingthe conplex variable method, we present the formulation of the general problem and the closed form solutions to some problems of practical importance, The atress distribution in the immediate vicinity of the rigid line end is examined. The corresponding formulation and solutions for isotropic materials can be arrived at from the special cases of those in the present paper, some of which are in agreement with the existing results[1].
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Key words:
- longitudinal shear /
- rigid line inclusion /
- fracture /
- stressconcentration /
- anisotropy
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[1] Jiang Chi-ping,Zou Zhen-zhu, Wang Duo and Liu You-wen.A discussion about a class of stress intensity factors and its verification,Inf,J.F rocture,48(1991),141-157. [2] Lt,Q.Q, and T, C, T, Ting, Line inclusions in anisotropic elastic solids, J.Appl. Mech.,56 (1989), 556-563. [3] Hao, T.H, and Y.C.Wu,Elastic plane problem of collinear periodical rigid lines, Engng, Fracture Mech,33 (1989), 979-981. [4] Markenscoff, X, and J. Dundurs, Weight functions for rigid line inclusions,Proc, 7th Int. Conf, on Fracture, Houston, TX,(1989), 37-39. [5] Jiang Chi-ping and Liu Chun-tu, Stress distribution around a rigid line in dissimilar media, Engng, Fracture Mech.,42 (1992), 27-32. [6] Jiang C hi-ping, The plane problem of collinear rigid lines under arbitrary loads, Engng. Fracture Mech.,39(1991), 299-308. [7] Wang, Z.Y.,H, T, Zhang and Y, T.Chou, Stress singularity at the tip ofa rigid line inhomogeneity under antiplane shear loading, J.Appl. Mech.,53 (1986), 450-461. [8] Sih, G, C, and H, Liebowitz.Mathem atical theories of brittle fracture, Fracture, Vol.Ⅱ Ed, by H, Liebowitz, Academic Press, New York(1968). [9] 樊大钧,《数学弹性力学》.新时代出版社(1983). [10] Мусхелишвили Н.И,《数学弹性理论的几个基本问题》,赵惠元译,科学出版社(1958).
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