MATHEMATICAL MODELING OF A SYMMETRIC BOUNDARY-VALUE PROBLEM FOR A LAYER WEAKENED BY A THROUGH HOLE WITH THE ENDS COVERED WITH A DIAPHRAGM

Abstract

The paper presents a new mathematical model for the solution of a static symmetric boundary-value problem for a layer weakened by a through hole with ends covered with a diaphragm. A new method based on a system of three singular integral equations has been developed and tested numerically. As a result of a high-precision numerical study, it was found that with an increase in the thickness of the layer, an increase in the relative circumferential stress occurs. With a decrease in one of the radii of the elliptical hole, an increase in the relative circumferential stress is also observed. The paper presents the respective dependency graphs. Keywords: three-dimensional boundary-value problems, singular integral equations, numerical experiment, static stretching–compression, a through hole.