The location of discontinuity intervals of sectionally analytic functions: Application to the interface crack problem

Abstract

Complex path-independent integrals have been extensively used in applied mathematics for the location of zeros and poles of analytic and meromorphic functions, but also in applied mechanics for the computation of stress intensity factors and the location of simple cracks and related discontinuity intervals of sectionally analytic functions, as well as for the computation of stress intensity factors. Here we generalize this approach to the problem of location of discontinuity intervals corresponding to interface cracks in plane elasticity (or to ordinary cracks, but under mixed loading conditions). The general case of this problem is also considered. The computer algebra system DERIVE was found appropriate for use in the formal (symbolic) computations of the present paper.