Large transformations with moderate strains of tensile membrane structures

Abstract

Using a classical non-linear theory, we analytically investigate possible ways for transforming the shape of a curved elastic membrane while keeping it tensioned and moderately strained. This is a critical issue because, as a rule, membranes must be considerably stretched in order to avoid wrinkling and slackening. If the final configuration is fixed, the membrane can be cut and formed according to the final shape, but this cannot be done if more configurations, considerably distant from one another, have to be achieved. Nevertheless, we propose large transformation movements that can be obtained starting from flat membranes while maintaining their strain as limited. We discuss in detail the paradigmatic example of the hyperbolic-paraboloid-shaped membrane. These opportunities are suitable for applications of transformable architecture because they do not require excessive tensioning, compatible with the strength of materials used for this kind of structures.

Transformable Curved Thin Glass Greenhouse

“…If the substructures is designed so as to fit with the straight edge of the HP panel, the geometry modification due to buckling generates an opening between the plate and the substructure itself. Remarkably, this change of configuration may be obtained in different ways, i.e., by prescribing in-plane displacements to the plate corners' (so to bring two extremes of one diagonal closer one to each other), or by changing the tensioning of the plate diagonals, as discussed in (Beatini and Royer-Carfagni, 2017). The buckling phenomenon, provoking the shape modification, may be also promoted by slightly "pushing" the plate at right angle to its middle plane by applying a load q.…”