GAUGE CONDITIONS AND THE ANALYSIS OF SINGULAR FIELDS WITH BOUNDARY INTEGRAL-EQUATIONS

The analysis of singular and near-singular integrals by the continuati on approach leads to a unified treatment of Cauchy and hypersingular i ntegrals, and results in numerical procedures for integral evaluation which are simple and robust. Perhaps as important is the insight, prov ided by the approach, into the conditions which guarantee the existenc e of singular integrals. The 'gauge conditions', arising during the co ntinuation analysis of singular integrals, provide a new perspective o n some very important issues relevant to the BEM. In the present paper , it is shown how the gauge conditions provide the additional inter-el ement continuity relationships, and constraints on solution functional ity, which must be satisfied at geometric discontinuities, in order to obtain correct solutions. As examples, the problems of a line crack a nd a free surface corner in two-dimensional, plane strain elasticity a re analyzed using the indirect, double layer BEM formulation. Valuable mathematical and physical insights result for the latter problem. It is demonstrated that, for both re-entrant and non-re-entrant corners, the double layer density functionality must not contain a linear term, but should contain three fractional power terms. The neglect of this proper functionality leads to ill-behaved solutions in the vicinity of even non-re-entrant corners. Copyright (C) 1996 Elsevier Science Ltd.