About a class of contact problems for the elastic half-plane and the infinite plate which are strengthened by partially glued heterogeneous elastic stringers

This work observes a class of contact problems for elastic half-plane and the infinite plate which along the length of the line $y=0$ in the plane $x0y$ (for the plate $x0y$ its average plane) is strengthened by heterogeneous elastic stringers (overlays) which consist of two semi-infinite pieces and one separated finite piece with other elastic characteristics. It is supposed that contact interaction in semiinfinite parts is realized by a thin layer of glue (other physicomechanical characteristics) and stringers are deformed under the action of horizontal forces. Using generalized Fourier transforms the determinational problem of contact stresses is reduced to the system of singular integral equations within the finite intervals with certain boundary conditions. Its solution is constructed using Chebishev polynomials unknown coefficents of which are received from the quasiperfectly regular infinite systems of the linear algebraic equations. Particular cases are obsereved and the character of the change contact stresses are illustrated in different contact parts. Particulary solutions by homogeneous elastic stringers are obtained.