非均匀双周期裂纹场的反平面问题
The Antiplane Problem of Double Period Non-Uniform Distribution Crack Field
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摘要: 本文从虎克定律与平衡方程出发,利用复变函数映象的理论.将裂纹发生的矩形区域保角变换到ζ平面的上半平面去.再根据H.И.穆斯黑里什维利[1]的理论,对非均匀双周期裂纹场的反平面问题,我们求得闭合解,并推出了应力强度因子.Abstract: Originating from Robert Hooke's law and equilibrious equations, and using the theory of the complex variable function, this paper transfers the rectaugle region in which the cracks emerge into upper-half part of ζplane by means of conformal mapping. Then according to the theory of ref.[1]. We find the solution in closed form, there by the stress intensity factors are derived.
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[1] Н.И.穆斯黑里什维利,《数学弹性力学的几个基本问题》,赵惠元译,科学出版社(1965). [2] Lawn, B. R., and T. R. Wilshaw, Fracture of Brittle Solids, Cambridge University Press. (1975). [3] D. I. NAVS. and Lott, Fracture toughness of portland cement concrectes,J.Amer.Conr.Inst..66 (1969),481. [4] Shie,J.,Quantum reaction in solids,thesis, Dept. of Materials Science,State University of New York at Stony Brook,(1977). [5] Панасюк В.В.et al.,Pacnepeбeieнuе Нanряженuя Окоiо Трещuн б Пласmuнах u Обoioчках,Кивв《Наукова Думаа》,Акад.Наук УССР Физ-Механ.ИН-Т(1976). 443. [6] 郝天护,双周期裂缝反平面问题的一个闭合解,清华大学学报,19.3 (1979). [7] 钱伟长、叶开沅,《弹性力学》,科学出版社(1956),165-172. [8] Ganesh,Prasad.,An introduction to the theory of elliptic functions and higher transcendentals, University of Calcutta.(1948). [9] Wiederhorn,S. M., and H. Johnson, Effect of electrolyte PH on crack propagation in glass J.Am. Ceram.Soc. 56, (1973) 192. -
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