Three-dimensional contact problems for a composite elastic wedge

The integral equations of new three-dimensional contact problems for a composite elastic wedge are obtained by reducing a boundary problem of the theory of elasticity to a Hilbert problem extended according to Vekua using complex Fourier and Kontorovich–Lebedev transforms. The wedge consists of two wedge-shaped layers with a common vertex and different aperture angles joined by a sliding restraint and the layer that is remote from the punch is incompressible. Three types of boundary conditions are considered on one face of the incompressible layer: when there are no stresses and when there is a sliding or rigid restraint. When the contact area is unknown, the method of non-linear boundary integral equations of the Hammerstein type is used that allows the contact area and the contact pressure to be determined simultaneously.