Contact problem for a stamp in the form of a plane without an acute-angled sector

For the first time, an accurate solution of the contact problem of the action of a rigid wedgeshaped die having a solution in the range of 270-360° is constructed. The stamp acts on a layer of composite material having an arbitrary anisotropy. A homeomorphic mapping of the topological space of the bearer of this stamp onto the topological space of the first quadrant is used, followed by the construction of a fractal and the application of an exact solution of the two-dimensional Wiener-Hopf integral equation for a wedgeshaped stamp with a right angle. In comparison with strip stamps, the solution contains an additively additional term describing the concentration of contact stresses at the angular point of the stamp. The calculation of the characteristic of the contact stress concentration at this point is close to the values obtained by approximate numerical methods in a number of studies. In the area considered away from the top of the stamp, the exact solution becomes the solution for the case of a semi-infinite stamp. The developed method is applicable to composites of arbitrary anisotropies occurring in linearly elastic materials and crystals of any cross-section. It can be useful in engineering practice when assessing the concentrations of contact stresses in the zones of the comer points of stamps having similar angles. In seismology, this approach is applicable for estimating stress concentrations in lithospheric plates in the zones of transition of a mountain ridge to a plain in the presence of angular zones of the specified range.