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

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Problem on Circular-Arc Cracks between Bonded Dissimilar Materials under Concentrated Force and Moment

1.
Mathematics and Physics Department, Central-South University of Technology, Changsha;
2.
Hunan University, Changsha

摘要: 运用推广的Schwarz延拓原理结合对复应力函数的奇性主部分析,求解一类有集中荷载的平面弹性问题,十分有效。文[1]用此方法研究了同种材料的弹性问题。本文把它推广于在集中力和集中力偶作用下不同弹性材料的圆形界面上有多条裂纹的情形,求出了几种典型情况复应力函数的封闭解,算出了应力强度因子,并由此导出一系列特殊解答,其中两个在文[1]、[6]中找到一致结果。

Abstract: The method is very efficient by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions to solve some plane-elastic problems under concentrated loads, in Ref.[1], this method is used to deal with the elastic problems of homogeneous plane. In this paper, it is extended to the case of dissimilar materials with co-circular cracks under concentrated force and moment. For several typical cases the solutions of complex stress function in closed form are built up and the stress intensity factors are given. From these solutions, we provide a series of particular results, in which two of them coincide with those in Refs. [1] and [6].

[1]	樊大钧,《数学弹性力学》,新时代出版社(1983), 373
[2]	Мусхелищвили Н.И.,《数学弹性力学的几个基本问题》,科学出版社(1965).
[3]	Cook, T.S.and F.Erdogan, Stresses in bonded materials with a crack perpendicular to the interface, Int.J Eng.Sci., 10 (1972), 677-697.
[4]	Erdogan, F.and O.Aksogan, Bonded half planes containing an arbitrary oriented crack, Int.J.Solids Structures, 10 (1974), 569-585.
[5]	路见可,有一条裂纹的圆形焊接问题,应用数学和力学,4, 5 (1983),679
[6]	Locber, J.F.and G.C.Sih, Green's functions for cracks in nonhomogeneous materials, J.Appl.Mech., 34 (1967), 240-243.
[7]	Sih, G.C., Handbook of Stress Intensity Factors for Reserchers and Engineers (1974).
[8]	Sih, G.C.and E.P.Chen, Cracks in Composite Materials Martinus Nijoff, The Hague/Boston/London (1981), 172.
[9]	Sih, G.C., et al., Crack-tip stress-intensity factors for plane extension and plate bending problems, J.Appl.Mech., 29, (1962), 306．