A new modal theory for wrinkling analysis of stretched membranes

This paper presents a new modal theory for the wrinkling analysis of membranes and discusses the stretch-induced wrinkling behaviour of fixed-ended thin sheets. This modal theory corresponds to an extension of Generalised Beam Theory (GBT) to analyse the wrinkling behaviour of highly stretched sheets. The inherent GBT modal nature adopted in this investigation enables the acquisition of an in-depth knowledge (when compared with the traditional shell finite element analysis) of the behaviour underlying this peculiar buckling phenomena. In order to conduct this study, the work begins by presenting the formulation, describing its main steps and concepts involved in the determination of the “deformation modes” (cross-section analysis), followed by the description of the procedures involved in the development and implementation of the aforementioned formulation that accounts for pre-wrinkling and wrinkling analysis (member analysis). Then, an illustrative example is presented and discussed in detail, which involves the characterisation of the sheet “signature curve” (tensile critical stress vs. length), respective critical wrinkling modes, modal participation diagrams and pre-wrinkling stress distribution patterns. For comparison and validation purposes, refined ABAQUS shell finite element wrinkling results are also reported. Finally, several conclusions are drawn regarding the wrinkling behaviour of stretched sheets, mostly based on the modal nature of this formulation.