APPLICATIONS OF INTEGRAL EQUATIONS WITH STRONG SINGULARITIES IN FRACTURE MECHANICS (FINITE-PART, THREE-DIMENSIONAL, CRACK)

The main objective of this study is to investigate certain types of singular integrals which arise in the formulation of two-dimensional and three-dimensional crack problems. Although these integrals do not exist in the classical sense, they can be reinterpreted and evaluated using Hadamard's concept of "finite-part" integrals. Taking this as the starting point the thesis has been divided into two parts.;In the second part, a chronological review of the literature on the three-dimensional crack problems is given and different solution methods are summarized. Papkovitch-Neuber potentials are used to formulate the problem of a plane crack in a half-space and in an infinite strip. The two-dimensional singular integrals are evaluated by reducing them to finite-part integrals. Special cases where the crack occupies a circular or an elliptical region are discussed.;In the first part, various methods for the numerical evaluation of finite-part integrals with 1/(t-x)('2) singularities and the approximate solution techniques for the related integral equations are explained. Using integral transforms some two-dimensional crack problems are formulated in terms of singular integral equations which are then solved by applying the Galerkin or the collocation methods.