FINITE-PART INTEGRALS IN PROBLEMS OF THE THREE-DIMENSIONAL CRACKS.

An effective method is proposed for solving the boundary integral equation (BIE) for the problem of a crack along a curvilinear surface in an elastic space on the basis of the transformation of the initial integrodifferential equation into an equation without derivatives. This is achieved by using the concept of the finite-part integral (FPI). Quadrature formulas are presented for such integrals over arbitrary convex polygons by approximating displacement discontinuities on the boundary by polynomials.