关于集中载荷作用下不同材料界面的共线裂纹问题

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Problems on Collinear Cracks between Bonded Dissimilar Materials under Concentrated Loads

1.
Engineering Mechanics Department, Haerbin Institute of Technology, Haerbin;
2.
Mathematics and Physics Department, Central-South University of Technology, Changsha

摘要: 本文继文[6]之后,研究在集中力和集中力偶作用下不同材料界面的共线裂纹问题.得到了几个典型的复应力函数封闭解,算出了应力强度因子.本文解答的若干特殊情形,与前人成果吻合.通过比较还发现了以往文献[3]、[4]在研究含无限长裂纹一类问题中的错误.

Abstract: Following Ref. [6], this paper deals with the problem on collinear cracks between bonded dissimilar materials under a concentrated force and moment at an arbitrary point. Several typical solutions of complex stress functions in closed form are formulated and the stress intensity factors are given. These solutions include a series of results of previous researchers, and redress some errors in the researches of problems containing semi-infinite cracks^[3][4].

[1]	樊大钧,《数学弹性力学》,新时代出版社(1983), 374.
[2]	Мусхелишвили Н.И.,《数学弹性力学的几个基不问题》,科学出版社(1958).
[3]	Erdogan, F., On the stress distribution in plates with collinear cuts under arbitrary loads, Proceedings of the 4-th U.S. National Congress of Applied Mechanics, Vol. 1 (1962).
[4]	Erdogan, F., Stress distribution in a nonhomogeneous elastic plane with cracks, J. Appl. Mech., 30 (1963), 232-236.
[5]	Loeber, J.F. and G.C. Sih, Green's function for cracks in nonhomogeneous materials, J. Appl. Mech., 34 (1967), 240-243.
[6]	刘又文、蒋持平,在集中力和集中力偶作用下不同弹性材料圆形界面的裂纹问题,应用数学和力学.8.3(1987).267-276.