The article is dedicated to the investigation of the stress state of a semi‐strip weakened by a longitudinal crack. Two statements of the problem are considered. The integral Fourier transform is applied directly to the initial problem. The discontinuous boundary problem which is formulated in vector form is solved with the help of the matrix differential calculation and the Green's matrix‐function's discontinuous properties. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). This system is solved by two methods regarding to the conditions at the semi‐strip's short edge. The orthogonal polynomials method is used when the semi‐strip is loaded at the center of its short edge, and the special generalized scheme, which allows consideration of fixed singularities, this is applied when the whole semi‐strip's short edge is loaded. The stress intensity factors (SIF) are investigated for the two cases.

中文翻译：

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带有纵向裂纹的半钢带应力状态研究

该文章致力于研究纵向裂纹削弱的半钢带的应力状态。考虑该问题的两个陈述。积分傅立叶变换直接应用于初始问题。通过矩阵微分计算和格林矩阵函数的不连续性，可以解决以向量形式表示的不连续边界问题。问题的求解被简化为三个奇异积分方程（SSIE）系统的求解。该系统可以通过两种方法解决半带钢短边的情况。当半带钢在其短边的中心加载时，将使用正交多项式方法，并且采用特殊的通用方案，该方案可以考虑固定的奇点，当整个半条的短边加载时，将应用此功能。研究了两种情况下的应力强度因子（SIF）。