Wrinkle generation in shear-enforced rectangular membrane

Abstract

The objective of this study is to clarify the wrinkle behavior of a flat rectangular membrane undergoing shear displacement. To achieve this goal, an equilibrium path tracking method using a finite element method is developed. This method includes a bifurcation path tracking analysis that searches for bifurcation solutions. This method establishes an image of the membrane behavior by calculating a series of successive equilibrium states before and after bifurcation buckling. Generally in experiments, flat rectangular membranes have shear displacement imposed on top or bottom edges, while the left and right sides have free boundaries. At large values of shear displacement, the wrinkles cover the entire membrane, but the free boundaries result in uneven shapes and distributions. Further increase in shear results in small wrinkles, referred to as collapsed sections, generated on existing wrinkles. As collapsed sections grow, new wrinkles are generated. However, the universality of this wrinkle generation mechanism may be affected by the free boundaries. By applying cyclic boundary conditions, effects of free boundaries, which include uneven wrinkle shape and distribution, can be eliminated. In addition, by changing the membrane aspect ratio, the effects of geometry are also evaluated. For all membranes, the wrinkle generation from collapsed sections is observed and its independence from free boundaries and aspect ratio is shown. By analyzing stress and displacement fields, the formation of collapsed sections is explained. In addition, for the cyclic boundary conditions, the change in aspect ratio results in almost the same bifurcation structure. Therefore, the wrinkle behavior evaluation in this study can be useful in predicting wrinkle behavior.

Numerical analysis of dynamic properties of wrinkled thin membranes

“…The present literature, however, was mainly concerned about the static behavior of a membrane, e.g. wrinkling patterns (Miyamura, 2000; Wong and Pellegrino, 2006a, 2006b, 2006c; Lecieux and Bouzidi, 2010; Atai and Steigmann, 2012, 2014; Taylor et al , 2014; Lan et al , 2014; Patil et al , 2015), wrinkling evolution (Wong and Pellegrino, 2006a, 2006b, 2006c; Wang et al , 2012, 2013a, 2013b) or transition (Davidovitch et al , 2011; Taylor et al , 2015), wrinkling location (Atai and Steigmann, 2012, 2014; Wang et al , 2014), stress distribution (Li et al , 2012; Huang et al , 2015; Senda et al , 2015), wrinkling critical load (Li, 2008; Wang et al , 2013b), post-wrinkling bearing capacity (Deng and Pellegrino, 2012; Hong et al , 2017), optimum design to eliminate wrinkles (Li et al , 2017; Liu et al , 2017; Luo et al , 2017), etc. A limited number of documents investigated the dynamic properties or dynamic responses of a membrane when its constitutive relationship was elastic (Hasheminejad et al , 2011; DasGupta and Tamadapu, 2013), orthotropic (Liu et al , 2013a, 2013b, 2016), hyperelastic (Soares and Gonçalves, 2012; Chaudhuri and DasGupta, 2014) or viscoelastic (Katsikadelis, 2012), or when it was subjected to impact loads (Liu et al , 2016), axial movement (Shin et al , 2005, 2006) or dynamic extension (Tuzela and Erbay, 2004).…”