Stress-strain state of a cracked elastic wedge under anti-plane deformation with mixed boundary conditions on its faces

A problem about the stress-strain state of an elastic wedge with an arbitra ry angel of opening, when on its bisector there is a system of a finite num ber collinear cracks, is studied by the means of the theory of elasticity. The anti-symmetric mixed boundary conditions given on both wedge-faces, tog ether with the forces applied to the cracks' surfaces are provoking the ant i-plane deformation of the wedge. The displacement components are given for the same group of nonintersecting intervals on each wedge-face and the str ess components are given on the rest of the faces. The problem is formulate d as a known mixed boundary problem of the theory of harmonic functions for a half-wedge because of the wedge symmetry relative to its bisector The so lution of this mixed boundary problem is derived in the closed form by usin g the Mellin integral transformation in combination with the methods of sin gular integral equations. Based on this the density of displacements' dislo cations on the cracks' surfaces, the stress intensity factors, the stresses on those intervals on the wedge-faces, where the displacements are given, and other characteristics of the investigating problem are determined by ex plicit analytical formulas. Particular cases are discussed as well.