Inflationary routes to Gaussian curved topography

Abstract

Gaussian-curved shapes are obtained by inflating initially flat systems made of two superimposed strong and light thermoplastic impregnated fabric sheets heat-sealed together along a specific network of lines. The resulting inflated structures are light and very strong because they (largely) resist deformation by the intercession of stretch. Programmed patterns of channels vary either discretely through boundaries, or continuously. The former give rise to facetted structures that are in effect non-isometric origami and which cannot unfold as in conventional folded structures, since they present localized angle deficit or surplus. Continuous variation of channel direction in the form of spirals is examined, giving rise to curved shells. We solve the inverse problem consisting in finding a network of seam lines leading to a target axisymmetric shape on inflation. They too have strength from the metric changes that have been pneumatically driven, resistance to change being met with stretch and hence high forces like typical shells .

arXiv comment17 pages, 12 figures

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Cited by in corpus (6)

• Programming stiff inflatable shells from planar patterned fabrics
• Defective nematogenesis: Gauss curvature in programmable shape-responsive sheets with topological defects
• Multi-valued inverse design: multiple surface geometries from one flat sheet
• Large deformation analysis of spontaneous twist and contraction in nematic elastomer fibres with helical director
• Interfacial metric mechanics: stitching patterns of shape change in active sheets
• Metric mechanics with non-trivial topology: actuating irises, cylinders and evertors