On a novel approach to the problem of the concentration of elastic stresses near a crack (Q1190081)

The modified form of the Trefftz solution is used to represent displacements and stresses in three-dimensional elasticity. The linear boundary value problem for a planar crack in an elastic space has been reduced to a system of two-dimensional integral equations over the domain occupied by the crack. It is shown on an example, related to a circular crack, that the class of integrable functions is not sufficient for the solution of the problem. Finite-part integrals, defined in the sense of generalized functions, are used to obtain the solution. Finally, the example of the stress-intensity factor calculation for a circular crack in an unbounded elastic space with a concentrated force is considered.