A spatial problem for an elastic wedge with a strip cut (Q1369946)

The paper deals with the stress distribution in a spatial wedge which is weakened by a planar strip cut located in the medium half-plane of the wedge. Three problems are studied when the faces of the wedge are either free from stresses, or rigidly clamped; or there is no friction between the rigid base and the wedge. In the case when the cut reaches the edge of the wedge, the solution is obtained by reducing the problem to a Fredholm integral equation of the second kind with symmetrical kernels. To solve this equation, the author uses harmonic functions in the Papkovich-Neuber representation in the form of Fourier-Kontorovich-Lebedev integrals in the complex plane. The possibility of the cleavage of the wedge along an edge is shown. A simple expression for normal stress intensity factor at one end of the cut has been obtained. For various wedge apertures, numerical values of the stress intensity factor can be obtained by using this formula.