Analysis of a Single Stiffener on an Infinite Sheet

Abstract

Abstract The use of stiffened-sheet construction in aircraft design has brought about the study of many problems in mechanics in which concentrated loads are introduced into stiffeners and transferred to the sheet. In the present paper a basic problem of this type is considered. A single stiffener of finite length is assumed to be attached to a sheet of infinite extent. A concentrated force is applied to the stiffener at each end. Any given problem may be divided into symmetrical and antisymmetrical parts. The physical condition that governs the problem is that the axial strain in the stiffener must be equal to the normal strain in the sheet at all points along the stiffener. In order to formulate the solution, it is necessary to employ an influence function for the strain in the sheet. This function is known from the classical theory of elasticity. The solution is found to be governed by an integral equation which has the same form as the equation which governs spanwise air-load distribution on an airplane wing. Hence a number of mathematical methods are known for solving the equation. A numerical example is presented.