De-wrinkling of pre-tensioned membranes

Abstract

Thin membranes are used in the spacecraft industry as extremely lightweight structural components.They need to be stiffened, usually by applying discrete forces, and this increases their susceptibility to wrinkling in regions where high tensile stresses develop. We consider a regular polygonal membrane uniformly loaded at its corners by equal forces and we prevent wrinkle formation by trimming the edges of the polygon into very gentle curves. We confirm this performance through simple physical experiments using Kapton, a typical membrane material and, using computational analysis, we show how the distribution of compressive stresses, responsible for causing wrinkles, dissipates following trimming.Finally, we accurately predict the required level of trimming for any number of sides of polygon using a simple, linear model, which invokes a plate-bending analogy.

Analysis of wrinkled membrane structures based on a wrinkle-wave model

“…This is because in the FEA model, at least eight elements per wrinkling half-wavelength are needed to capture the rapidly varying displacement. 16 Otherwise, the initial imperfections added to the membrane must be large enough to ensure that wrinkling occurs. Initial imperfections and the low number of elements lead to inexact or divergent wrinkling half-wavelengths.…”

Wrinkling reduction of membrane structure by trimming edges

“…Figure 8 shows the variation of the optimal trimming level, δ/L (×100%), with the number of sides, n. By Comparing with the results in reference (Bonin and Seffen 2014), 12 it can be seen that there exist a notable divergence when the number of sides, n, is larger than six. Then, in-plane stress analysis was done for an arc-edge octagon structure.…”

“…It is difficult to determine the optimal trimming level. While Bonin 12 has been able to predict the optimal trimming level by changing the tensile model into a bending analogy model, and the displaced shape is considered under edge-wise rotations, this method is not intuitive, besides, deformation gradients and any intrinsic length changes between a straight-edge model and an arc-edge model are neglected, which may lead to inaccurate results. In this paper, the assumption of the in-plane stress field is introduced in order to generalize the results obtained for a square structure as proposed by Wong and Pellegrino, 13,14 and the stress field can be derived for n-sided regular polygonal structures that are subjected to equal radial forces.…”

Wrinkling of cylindrical membranes with non-uniform thickness

“…This breaks the convexity condition of the strain energy density function of the membrane (Pipkin, 1986;Steigmann, 1990), so standard strain energy function can not be used in the wrinkled regions. Several theories regarding the wrinkling phenomenon are available in the literature (Wagner, 1929;Reissner, 1938;Wu and Canfield, 1981;Pipkin, 1986Pipkin, , 1993Pipkin, , 1994Steigmann, 1990;Mansfield, 1970), and detailed investigations on wrinkling phenomena can be found in Li and Steigmann (1994a, b); Roxburgh (1994); Haseganu and Steigmann (1994); Massabo and Gambarotta (2007); Bonin and Seffen (2014).…”

“…As the applications of membranes vary from space technologies through diverse engineering applications to biological sciences, the wrinkling instability is an unwelcome phenomenon which can be detrimental to the overall performance of membranes (Haughton and Mckay, 1997;Massabo and Gambarotta, 2007;Lu et al, 2001;Bonin and Seffen, 2014). The computational prediction of wrinkling does not always match accurately with experiments, due to many reasons like the idealization of the membrane with a specific material model, the idealization of loading and boundary conditions, a non-uniform thickness and others.…”