Stress Concentration and Shape Optimization for a Fillet Surface of a Step-Shaped Shaft

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.