On the contact problem for an elastic strip with two semi-infinite overlays

A plane problem of the contact interaction of two symmetrically located semi-infinite overlays of small thickness with a strip is considered, when horizontal concentrated forces act on the edges of the overlays. The solution of the problem using the integral Fourier transform is reduced to solving a singular integral equation of the first kind with the Cauchy kernel with respect to the deformation of the intermediate interval between the overlays. The solution of the latter is constructed using the apparatus of Chebyshev orthogonal polynomials. After determining the deformation in a finite interval, the contact stresses on the semi-infinite intervals are determined through the found deformations in closed form.