Wrinkle Generation Without Bifurcation in a Shear-Enforced Rectangular Membrane with Free Boundaries

Abstract

The object of this study is to clarify wrinkling behavior of a shear-enforced flat rectangular membrane with free boundaries. For this purpose, an equilibrium path tracking method using a finite element method is developed. This method includes bifurcation path tracking analysis that searches for bifurcation solutions. This method establishes an image of membrane behavior by calculating a series of successive equilibrium states before and after bifurcation buckling. Through detailed analysis of stress, displacement fields, and wrinkle interaction over a load parameter range, the analysis shows how existing wrinkles affect each other and the generation of new wrinkles. As a result, there is wrinkle generation with bifurcation and without bifurcation. The wrinkle generation mechanism without bifurcation is analyzed in detail. Wrinkle generation caused by bifurcations could potentially result in a large number of equilibrium paths. Each equilibrium path represents a specific wrinkle pattern. However, the analyzed results show that significantly fewer equilibrium paths are obtained than expected. These are due to wrinkle generation without bifurcations and to deformation symmetry.