An Asymptotic Method for Solving Contact Problems on the Effect of a Half-Strip Stamp on an Anisotropic Composite

For the first time, an asymptotic solution has been constructed for the contact problem of friction of a rigid half-strip stamp of an anisotropic multilayer composite material. The relative width of the half-strip is assumed to be a large parameter that determines the asymptotic expansion. The method is based on generalizing the approach to constructing asymptotic solutions for simpler contact problems. Previously, the asymptotic method has been developed to solve the contact problem in case of a strip-stamp with a large relative width. The method proved to be effective because it provided a satisfactory agreement with the solution constructed by the counter asymptotic expansion for the stamps in the form of a strip of a small relative width. In this paper, it is applied in a much more complex and previously unsolved contact problem for a stamp in the form of a semi-infinite strip. The complexity of this problem lies in the fact that in order to apply the asymptotic approach, it is necessary to develop a method for solving two-dimensional Wiener-Hopf equations, which has already been done by the authors and it is already used in this work. Similar problems occur in engineering practice and construction when creating various objects, when developing an electronic element base, in seismology, when assessing the state of seismicity in the transition zone of a mountain range into a plain. By using the existing numerical methods, it is possible to describe the behavior of the concentration of contact stresses at the stamp boundary, and especially at the corner points of the boundary, where the most vulnerable parts of the structure are located. However, it is not possible to construct a complete solution of the distribution of contact stresses under the half-strip stamp together with the features at the boundary, due to the area infiniteness. In this paper, a solution is constructed that correctly reflects the real distribution of the contact stresses under the stamp and aims at an accurate solution with an increasing strip width parameter.