Complex variable formulations for usual and hypersingular integral equations for potential problems — with applications to corners and cracks

摘要

This paper first presents an unified discussion of real and complex boundary integral equations (BIEs) for two-dimensional potential problems. Relationships between real and complex formulations, for both usual and hypersingular BIEs, are discussed. Potential problems in bounded as well as in unbounded domains are of concern in this work. Quantities of particular interest are derivatives of the primary field that exhibit discontinuities across corners, as well as stress intensity factors at the tips of mode III cracks. The latter problem in an application of a recent generalization of the well-known Plemelj-Sokhotsky formulae. Numerical implementations and results for interior problems in bounded domains, as well as for crack problems in unbounded domains, are presented and discussed.