Exploiting active-bending for double curved structures

Research in self-supporting double-curved structures composed of elastically deformed planar elements

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This thesis aims to exploit active bending as an approach to create complex curved geometries, which are structurally self-supporting systems. The simplicity of creating complex curved geometries from initially planar elements is the leading motivator for this research. The central research question is: ‘How can double curvature be exploited in a structural system composed of elastically deformed planar elements’’? This research answers questions like what double curvature is and how it can be measured and controlled. What is the relationship between an elastically deformed double-curved geometry and the structural characteristics of active bending structures? The literature review is composed of part A: research into double-curvature, and part B: the structural behaviour of active bending structure.

For the question to what extent planar elements can deform, the measure of Gaussian curvature has been used. The Gaussian measure provides the relationship between bending and torsional curvatures. Bending moments relate to these curvatures. However, the Gaussian curvature is a purely geometrical measure without incorporation of material properties. The problem is that deformation of planar elements results in double curved geometries rather than, according to the Gaussian measure, in single curved geometries.

The inclusion of material properties such as Poisson’s ratio and bending rigidity in the Gaussian measure allows for prediction of curvature and the related bending moments. The basic geometry of a rectangular plate has been used to do physical tests, followed by computational test and FEA analysis. It has been proved that the stiffness of an elastically bend plate increases for a large Poisson’s ratio. This makes the Poisson’s ratio an essential parameter for active bending plate structures.

Further stiffness can be achieved through torsion. Torsional displacement of a clamped planar plate leads to increased tension, which leads to increased stiffness. The combination of bending and twisting a planar plate leads to a structurally stiff arch, which is both a structural element and an architectural design component.

Suitable materials for active bending plates structures are composites. They offer a relatively high Poisson’s ratio and a high strength to flexibility ratio.

For a planar plate of epoxy glass fibre composite of fifteen by one meter, only 20 mm thickness is required to make it structurally sufficient.

The feasibility and application of an active bending arch plate depend on the building method. The building method aims to keep the bending process and building sequence simple and modular. The erection process of the arch will be performed through the motion of the ends of the plate in a single direction over a modular gliding rail system, which allows for a simple assembly process.

The double curvature, the structural performance and the aligned building method prove the feasibility of active bending plate structures. Active bending does not have to be considered just a formation process, but a structural system itself. The exploitation of active bending is found in the nuance of double curvature as a result of the material dependent Poisson’s ratio. The simplicity of deforming planar elements, which is feasible with the developed building method results in an active bending arch system which can be used as a cantilever, bridge support, or cladding system.