The three-dimensional problem of a thin inclusion in a composite elastic wedge

The three-dimensional problem of a thin rigid elliptic inclusion in the middle of a composite elastic wedge is investigated. The wedge consists of three connected wedge-shaped layers connected by a sliding clamp, in which the layer containing the inclusion is incompressible. The outer faces of the composite wedge are also under sliding-clamp conditions. The inclusion is completely bonded to the elastic medium in the contact region. Using Fourier and Kontorovich–Lebedev transformations, a system of integral equations of the problems are derived for the shear contact stresses. A regular asymptotic method is used to solve this system. Calculations are carried out. The results can be used for calculations on the strength of rubber-metal articles and structures having a corner line.