Abstract

An analytical solution to the direct boundary-value problem and the two-dimensional problem concerning the stressed condition in the median surface of a step-shaped shaft is presented. In the boundary-value problem, a singular integral equation with the Cauchy kernel is used, the solution of which can be found in the form of an unlimited increase in stresses at the ends of the integration interval. The two-dimensional problem is presented in trigonometric series, where constant coefficients can be determined from the boundary conditions that have been previously expanded into a Fourier series. Comparison of the results obtained with the data taken from scientific sources and experimental studies on the stressed condition by means of a laser polariscope using flat transparent models of step-shaped parts with fillets having constant and variable curvature has confirmed the adequacy of the solution presented.

中文翻译：

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阶梯形轴圆角表面的应力集中和形状优化

摘要

提出了关于阶跃形轴中间表面受力状态的直接边值问题和二维问题的解析解。在边值问题中，使用具有柯西核的奇异积分方程，其解可以以积分区间两端的应力无限增大的形式找到。二维问题以三角级数表示，其中常数系数可以根据先前已扩展为傅立叶级数的边界条件确定。