A SINGULAR INTEGRAL-EQUATION SOLUTION FOR THE LINEAR ELASTIC CRACK OPENING DISPLACEMENT OF AN ARBITRARILY-SHAPED PLANE CRACK .2. REGULAR INTEGRAL SOLUTIONS

The boundary value problem for an arbitrarily shaped plane crack embed ded in a 3D linear elastic solid can be reduced to a governing hyper-s ingular integral equation. A discretizing procedure based on a triangu lation of the crack area has been offered in Part I of this work. The main goal of Part I is to introduce the analytical results for the 18 resulting finite-part integrals defined over a triangular mesh area. T he finite-part integrals occur in those triangles where the source poi nt coincides with one of the element nodes. Mostly the source point li es outside of the considered triangle. In these cases the occurring ar ea integrals are regular. The aim of Part II is, therefore, the deriva tion of the closed form expressions for the relevant 18 regular area i ntegrals. The resulting relations are of algebraic form which can easi ly be coded in compact form. Their numerical proof by two different me thods shows the highest accuracy and, therefore, the correctness of th e final solutions. The relevant numerical results are offered in Appen dix I. With the formulae provided in Part I and Part II of the paper t he determination of the coefficient matrix, necessary for the calculat ion of COD values from a linear equation system, is precise and needs only minimum computer time.