The Wrinkling of Rectangular Webs Under Nonlinearly Distributed Edge Loading

Abstract

Nonlinearly distributed in-plane tension at the edges of a thin, flat, rectangular material with small flexural stiffness, called a web, can cause it to wrinkle. Airy stress functions are determined in closed form for webs under arbitrarily prescribed, in-plane edge loading. The loading at impending wrinkling, and the corresponding wrinkling shape in the web, are predicted by the solution of an eigenvalue problem. This analysis is illustrated through two examples: (I) wrinkling of a web induced by nearly uniform normal edge tension; (II) wrinkling of a web induced by uniform normal tension distributed over a section of the edge. Predictions of wrinkling using membrane theory are compared to those obtained with the current web theory. The contribution of small flexural stiffness to the prediction of the condition of wrinkling is shown to be substantial.