Weakly singular, singular and hypersingular integrals in 3-D elasticity and fracture mechanics

This article considers weakly singular, singular and hypersingular integral s which arise when the boundary integral equations (BIE) are used to solve problems in the theory of elasticity and fracture mechanics. For their regu larization, an approach based on the application of the Gauss-Ostrogradskii and the Green theorems has been used. The expressions, which allow an easy calculation of the weakly singular; singular and hypersingular integrals f or any convex polygon, have been constructed. Such an approach may be gener alized easily and applied for the calculation of multidimensional integrals with various singularities.