A SINGULAR INTEGRAL-EQUATION SOLUTION FOR THE LINEAR ELASTIC CRACK OPENING DISPLACEMENT OF AN ARBITRARILY-SHAPED PLANE CRACK .1. FINITE-PART INTEGRAL SOLUTIONS

The aim of the paper is to compute the local crack face displacements of a linear elastic body containing an arbitrarily shaped plane crack. From the crack face displacements the local stress intensity factors can be derived. The boundary value problem for a plane crack of arbitr ary shape, embedded in a linear elastic medium, has been treated by se veral authors by the singular integral equation (SIE) approach. Their computations lead to a set of hyper-singular integral equations for th e Cartesian components of the unknown crack face displacements. To sol ve these equations the authors present a discretization procedure base d on six-node triangular finite elements. A total set of 24 finite-par t integrals defined over a triangular area can be developed. These 2D- finite-part integrals can be split into both a 1D-regular and a 1D-fin ite-part-integral by means of the polar coordinates so that they can b e solved in closed form. Finally, the investigation of the SIEs is red uced to a discrete set of linear algebraic equations for the unknown n odal point values. The necessary steps will be demonstrated in detail. The derived closed-form solutions will be offered in the text and in the appendices.