Investigation of the stress state of the elastic semi-strip with a transverse crack

Abstract

The stress state of the semi-strip with a transverse crack is investigated. The mechanical load is applied to the semi-strip’s short edge. The initial problem is reduced to the one-dimensional vector boundary-value problem with the help of the semi-infinite Fourier transformation applied by the generalized scheme. The vector boundary-value problem is solved with the help of the matrix differential calculation apparatus and Green’s matrix-function apparatus. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). First singular equation contains two fixed singularities, so the special method is used for the SSIE’s solving. Stress intensity factors (SIF) are calculated for the different crack’s length.