A load transfer from an elastic infinite stringer to an elastic semi-infinite plate

A contact problem for a solid isotropic homogeneous elastic semi-infinite plate, strengthened by a solid homogeneous infinite elastic stringer (IES), has been investigated under assumption that the homogeneous IES is welded (glued) to the semi-infinite plate parallel to its boundary and is at a finite distance from that boundary. The contact pair (plate–stringer) was simultaneously deformed by uniformly distributed horizontal tensile stresses of constant intensity acting on the infinity of the plate, and by a concentrated force applied to the stringer and directed along the axis of stringer. The problem was formulated as a singular integral equation with kernel consisting of singular and regular parts. Then for solution of this equation the generalized Fourier integral transform was used, by means of which this integral equation was reduced to a functional equation with respect to the Fourier transform of unknown function. The closed solution of the contact problem was constructed in an integral form. The tangential contact forces and normal stresses arising in the IES were determined. Asymptotic formulas describing the behavior of stresses both near and far from the application point of concentrated force were obtained.