Contact problems with a stamp in the form of an acute-angled wedge acting on an anisotropic composite layer

In this paper, for the first time, the block element method provides an exact solution to the contact problem of the action of a rigid wedge-shaped stamp with an acute angle on a layer of composite material having arbitrary anisotropy. The research is based on the application of the block element method. In comparison with strip stamps, it contains an additively additional term describing the concentration of contact stresses at the angular point, that is, at the top of the stamp. The calculation of the indicator of the peculiarity of the concentration of contact stresses at this point is close to the values performed by numerical methods in a number of works. In the zone considered away from the top of the stamp, the exact solution turns into a solution for the case of a semi-infinite stamp. The developed method is applicable to composites of arbitrary anisotropies arising in linearly elastic materials and crystals of any cross sections that allow the construction of the Green function, and hence the two-dimensional Wiener-Hopf integral equations. The exact solution of two-dimensional Wiener-Hopf integral equations has made it possible, thanks to fractality, homeomorphism of stamp carriers and solution functions, to construct exact solutions to contact problems for wedge-shaped, sharply angled stamps.