在面斜对称载荷下无限各向异性介质内的周期裂纹
The Periodic Cracks of an Infinite Anisotropic Media for Plane Skew-Symmetric Loadings
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摘要: 本文试图藉助复变函数方法求解在面斜对称载荷下无限各向异性弹性介质的周期裂纹问题.这问题将化为欲确定满足某种边值条件的两个复变函数.文中假定应力、位移与边值条件是周期的,而且假定应力在无穷远处有界.这里的解答已表示为封闭形式.Abstract: This paper attempts to solve the periodic crack problems of infinitive anisotropic media for plane skew-symmetric loadings by means of the method of complex function. The problems are now reduced to the determination of two complex functions that must satisfy certain boundary conditions. In this paper, the stresses, the displacements and the boundary conditions are assumed to be periodic, md further, the stresses are assumed to be bounded at infinity. The solutions are expressed in closed forms.
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[1] Мусхелишвили Н.И.,.《数学弹性力学中的几个基本问题》,科学出版社(1958). [2] Лехницкий С.Г,《各向异性板》,科学出版社(1955). [3] Равии Г.Н.,《孔附近的应力集中》,科学出版社(1958). [4] Sih,G,C,and H .Liebowitz,Mathematical theories of brittle fracture,in Fracture H,Liebowitz ed.,Academic Press,2(1968). [5] 路见可.关于周期应力平面弹性基本问题,力学学报.7,4(1964),316-327. [6] 蔡海涛,平面弹性理论的周期接触问题.应用数学学报,2,2(1979),181 -195. [7] 路见可.周期Riemann边值问题及其在弹性力学中的应用,数学学报.13,3(1963). -
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