Theoretical basis of regularized integral equations for elastostatic crack problems

Abstract

Integral equations derived by means of the potential theory for statical crack problems are singular in the sense of the principal value. In the present paper, these integrals are transformed into weakly singular ones and the so-called regularized integral equation is thus obtained. The conditions which permit the transformation are discussed and the weak singularity is proved. The kernel of the regularized equation is written in terms of the density, equal to the displacement discontinuity on the crack surface, in such a way that no extension of this density is involved. The results obtained hold for either embedded or surface crack problems.