Equilibrium of elastic media with internal nonFiat cracks

Abstract

A problem on torsion of an elastic medium weakened by mathematical cut on a part of the cylindrical surface is solved by exact methods of the linear theory of elasticity. The problem is reduced to a system of dual integral equations with respect to the trigonometric functions with one unknown density. Then the Fredholm integral-differential equation is examined. The analytical expressions for the stress intensity factor, the stress components on the cylinder surface outside the cut and difference between the displacements of the cut surfaces are obtained. Data obtained are applicable to the study of material damage.