On the Diffusion of Load From a Transverse Tension Bar Into a Semi-Infinite Elastic Sheet

Abstract

This paper deals with the load diffusion from a tension bar of finite length and uniform cross section into a semi-infinite sheet, the axis of the bar being perpendicular to the edge of the sheet. The bar is regarded as a one-dimensional elastic continuum, whereas the elastic sheet is treated within the two-dimensional theory of generalized plane stress. Three alternative models for the stringer-attachment are considered: (a) line-contact, (b) area-contact based on matching the axial stringer-strain and the corresponding average sheet-strain across the width of the strip of adhesion, and (c) area-contact based on matching the stringer strain and the corresponding sheet-strain along the center line of the strip of adhesion. It is shown that the line-contact model, in contrast to both area-contact models, does not admit the transmission of portions of the applied load through forces concentrated at the ends of the adhering bar segment. Further, asymptotic estimates are deduced for the end slopes of the load-diffusion curves appropriate to the three models under consideration. The integro-differential equation for the stringer-force in Case (b) and Case (c) is reduced to a standard Fredholm integral equation, which is solved numerically. The results thus obtained are compared with available experimental findings.