The diffusion of load from a stiffener into an infinite elastic sheet

Abstract

The use of complex variable theory to express problems in generalized plane stress is well known, but methods of finding particular solutions are available for only a limited range of problems. This paper and its sequel will develop a new technique, reducing certain problems with mixed boundary conditions to second order functional differential equations, whose solutions can be found in series form. Exact solutions are given to three fundamental problems of the diffusion of load in an infinite two-dimensional elastic sheet to which a semi-infinite elastic stiffener is continuously attached throughout its length. The first problem has a load applied to the end of the stiffener, with its line of action along the stiffener and its reactions at infinity. In the other two problems the stiffener end is unloaded but a uniform tension is applied to the sheet at infinity, in one case parallel to the stiffener, in the other perpendicular to it. Expressions for the load in the stiffener and for the direct and shear stresses in the sheet are found and plotted in non-dimensional form.