Contact problems for the elastic half-plane and the infinite plate which are strengthened to partially glued stringers

This work considers contact problems for elastic half-plane and the infinite plate the boundary of which $y=0$ (in plane $xoy$) is strengthened by elastic stringers (overlays) which consist of two semi infinite parts and one separate finite part. It is supposed that contact interaction in finite part is realized by a thin layer of glue (another physicomechanical characteristic) and stringers are deformed under the action of horizontal forces. Using generalized Fourier transforms the determinational problem of unknown contact stresses is reduced to the system of singular integrodifferential equations with Cauchy’s Kernel within the finite intervals. The solution is constructed using Chebishev polynomials. The particular cases are considered and the character of the change contact stresses are illustrated in different contact parts.