A MIXED PROBLEM FOR AN ELASTIC WEDGE WEAKENED BY A CRACK

The basic results obtained for different classes of mixed and contact problems of the theory of elasticity for wedge-like solids are summarized in [1]. Related studies were reported in [2, 3]. In the present paper, the stress state of a homogeneous elastic wedge weakened by a crack on a segment of its middle line is considered: the displacements are prescribed at one face of the crack and the stresses at the other. In the general case, the problem is formulated mathematically as a system of two singular integral equations of the second kind and solved by the method of Jacobi orthogonal polynomials. It is shown also that in the particular case where the wedge angle is equal to 2(pi) a closed-form solution of the problem stated can be obtained.