Contact problem for an elastic half-plane with heterogeneous (piecewise-homogeneous) elastic overlay in the presence of shear interlayer

The contact problem for an elastic half-plane strengthened at its boundary by heterogeneous (piecewise-homogeneous) elastic overlay consisting of two semiinfinite pieces and one finite piece having different elastic characteristics has been considered. It was supposed that the contact interaction between the deformable foundation and an overlay was realized through a shear interlayer having different physico-mechanical properties and geometric configuration. The contact triple (overlay, interlayer, half-plane) was assumed to be deformed under the action of horizontal forces applied to the overlay. Using generalized Fourier transform the determinational problem of unknown contact stresses are reduced to the systems of Fredholm’s second kind integral eqations with two unknown functions within the different intervals, which in the region in the large change values of ratio of the problem characteristic parameters in the $B$ Banach space may be solved by the method of successive approximations. Possible particular cases have been observed and the character of change contact stresses is illustrated in different contact parts.