Solution by quadratures of the problem of a cylindrical crack by the method of matrix factorization

In this paper the axisymmetric problem on a semi-infinite cylindrical crack is considered. On the surfaces of the crack, the normal and tangential com ponents of the traction are prescribed whereas the displacement vector comp onents are unknown and supposed to be discontinuous. The problem is reduced to a 2 x 2 matrix Wiener-Hopf factorization. The solution is found by quad ratures, Thus, this is the first example of successful closed-form matrix f actorization arisen in the theory of mixed boundary-value problems for elas tic bodies with curvilinear spatial defects. In addition, the weight functi ons for the stress-intensity factors are constructed. Numerical results for the stress-intensity factors for two types of loading: (i) the exponential functions and (ii) a point force acting along the axis of symmetry, are re ported.