Experimental verification on simplified estimation method for envelope curve of wrinkled membrane surface distortions

Abstract

The effectiveness of a simplified method for estimating an envelope curve of wrinkled-membrane-surface distortion, which was recently proposed by the author, was experimentally assessed. The equation is formulated using three physical quantities regarding wrinkles: the length of the wrinkle line, the major principal strain in wrinkled regions, and the in-plane shrinkage strain appearing in the orthogonal direction of the wrinkle line. Since these three physical quantities are attributed to two-dimensional problems, the formula makes it possible to simply estimate wrinkle amplitude without a cumbersome bifurcation analysis. Applying a wrinkle strain in tension-field theory instead of the in-plane shrinkage strain in the formula, a simplified method to estimate an envelope curve of a wrinkled membrane with a low computational cost was developed using the wrinkling analysis with tension-field theory. Wrinkling phenomena appearing on two membrane models subjected to an in-plane shear and a corner-tension load were experimentally measured by photogrammetry using the direct linear-transformation method and a laser-displacement sensor. The experiment model was then subjected to a finite element analysis using tension-field theory, and an envelope curve of the wrinkled membrane was estimated using the method. The estimated envelope curves appropriately captured the actual wrinkle amplitude appearing on the membrane surface regardless of the formation process of wrinkles. From the result, the validity of the proposed estimation method was confirmed. This paper offers an effective method to predict the magnitude of the wrinkled-membrane-surface distortion with a low computational cost, and will assist the development of future gossamer space structures incorporating membranes.