DYNAMIC CONTACT PROBLEMS FOR A HALF-STRIP STAMP ON AN ANISOTROPIC COMPOSITE

Abstract

For the first time, the exact solution of the dynamic contact problem of the frictionless action of a rigid die in the form of a half-strip on an anisotropic multilayer composite base is constructed by the block element method. It is assumed that the stamp is subjected to a harmonic effect in time, causing a wave process outside the contact zone. Thus, for the first time, the two-dimensional Wiener – Hopf integral equation with a difference kernel in the region representing the half-band is precisely solved. Using known numerical methods, it is possible to describe the behavior of the concentration of contact stresses at the stamp boundary in cases of isotropic materials. However, it was not possible to construct an accurate solution for the distribution of contact stresses in the anisotropic case under a half-strip stamp, together with features at the boundary. For the first time, a solution was constructed reflecting the real distribution of contact stresses and their concentrations under the stamp. The solution obtained in the work tends to the solutions obtained for a strip or a quarter of the plane when the half-strip degenerates into these areas. To ensure the correct formulation of the problem, the principle of Mandelstam's marginal absorption is applied. The block element method, factorization methods, and the Newton – Kantorovich method are used in the research process. The constructed exact solution of the contact problem makes it possible to distinguish functions describing the concentration of contact stresses at the boundaries of the stamp, including at the corner points of the half-strip stamp. The constructed indicators of the concentration of contact stresses in the angular zones of the half-strip stamp are close to the values constructed earlier in publications by approximate methods. The result of this work can be useful in engineering practice, seismology, as well as in other fields.