Contact problem for a piecewise-homogeneous infinite plate with stacked elastic piecewise-homogeneous infinite stringer

The contact problem has been considered for elastic composite (piecewisehomogeneous) infinite plate consisting of two semi-infinite plates interlinked along the common straight border. Parallel to this line of heterogeneity of these semi-infinite plates with different elastic properties, an elastic piecewise-homogeneous infinite stringer is continuously glued over its full length and width on the upper semi-infinite plate, the layer of glue during the deformation being in the state of pure shear. The contacting triple (plate–glue–stringer) is simultaneously deformed by codirectional concentrated forces applied to the stringer and uniformly distributed horizontal tensile stresses of piecewise–constant intensity acting at infinity on the plate. According to the generalized Fourier integral transform, under certain conditions the solution of contact problem under consideration reduces to a solution of functional equation in the Fourier transforms of an unknown function on the real axis. A closed form solution of the contact problem in question is given in an integral form. As a result of investigations it was shown that due to the presence of the layer of glue the tangential contact forces have no singularities in the points of application of forces and in sections of semi-infinite stringer attachment.