THE STRESS STATE OF A HOMOGENEOUS ELASTIC PLANE WITH A STAR-SHAPED CRACK UNDER MIXED BOUNDARY CONDITIONS ON THE CRACK FACES

The stress state of an elastic plane with cracks was studied in a large number of publications. The results of these investigations are summarized in [1]. The problem related to one considered here was studied in [2]. As to similar problems with the mixed boundary conditions on the crack faces, these have been studied only in several publications, the most important of which are [3,4]. In the present paper, we study the stress state of a homogeneous elastic plane with a star-shaped crack formed by four identical cracks. Some faces of these cracks are subject to given displacements, while the other faces are subjected to prescribed stresses. The mathematical formulation of the problem leads to a system of two singular integral equations of the second kind. The system is solved by using the method of Jacobi orthogonal polynomials.