NUMERICAL TREATMENT OF FINITE-PART INTEGRALS IN 2-D BOUNDARY-ELEMENT ANALYSIS WITH APPLICATION IN FRACTURE-MECHANICS

For the solution of problems in fracture mechanics by the boundary ele ment method usually the subregion technique is employed to decouple th e crack surfaces. In this paper a different procedure is presented. By using the displacement boundary integral equation on one side of the crack surface and the hypersingular traction boundary integral equatio n on the opposite side, one can renounce the subregion technique. An e ssential point when applying the traction boundary integral equation i s the treatment of the thus arising hypersingular integrals, Two metho ds for their numerical computation are presented, both based on the fi nite part concept. One may either scale the integrals properly and use a specific quadrature rule, or one may apply the definition formula f or finite part integrals and transform the resulting regular integrals into the usual element coordinate system afterwards. While the former method is restricted to linear or circular approximations of the boun dary geometry, the latter one allows for arbitrary curved (e.g. isopar ametric) elements. Two numerical examples are enclosed to demonstrate the accuracy of the two boundary integral equations technique compared with the subregion technique.