Contact problem for an infinite composite elastic (piecewise-homogeneous) plate with an infinite elastic stringer glued to the plate surface

The contact problem has been considered for an infinite composite elastic (piecewise homogeneous) plate consisting of two semi-infinite plates having different elastic characteristics, that are linked to each other along the common straight border. It was assumed that an infinite elastic stringer (IES) is glued over its full length and width to the upper surface of an infinite composite elastic plate parallel to the line of heterogeneity of the mentioned two semi-infinite plates that have different elastic properties, the layer of glue being in the state of pure shear. The contacting triple (plate–glue–stringer) is simultaneously deformed by a concentrated force applied to IES and by uniformly distributed horizontal tension stresses of constant rate that act at infinity on the infinite composite elastic plate. The solution of contact problem under consideration is reduced under certain condition to the solution of functional equation in the Fourier transform of required function. The closed-form solution of the contact problem at issue is constructed in the integral form. The tangential contact and normal stresses arising in IES have been determined. Asymptotic formulae describing the behavior of stresses both near and far from the origin of force have been obtained.