Contact problem for an orthotropic plane with a slit

An exact solution of a mixed boundary-value problem for an orthotropic plane with a slit on one of the principal directions of orthotropy is constructed in the case where an absolutely rigid stamp with a flat base is pressed into one face of the slit. Using the method of discontinuous solutions for the equations of elasticity theory, the problem stated is reduced to the Riemann problem for two functions, and a closed solution of this problem is constructed. Simple expressions for the basic mechanical characteristics, such as the opening of the slit, contact stresses under the die, and the intensity factor of breaking stresses at the end points of the slit are obtained. Solutions of similar problems for an orthotropic plane are found when the stamp reaches only one or both end points of the slit, as well as for a semi-infinite slit. A numerical analysis is carried out.