Topology, stability and robustness of tensegrity structures
Creators: name: Dong, Wenru
Publisher: name: Imperial College London
Year: 2017

description: Tensegrity structures are pin-jointed frameworks that need prestresses to be equilibrated. They are candidates for lightweight roof structures, deployable structures, footbridges, soft robots, and can even be found in biological field, such as DNA nanostructures. However, the number of actual projects are limited. One of the reasons may be the lack of understanding of the structural form and hence design guidance is needed. To address this issue, several aspects related to designing tensegrity structure topology, the stability and robustness of tensegrities are considered so that designing them can become more approachable with designers being more confident. The shape of a tensegrity and its topology are related in a highly nonlinear way. Often designing starts from a known topology and search for a shape. Such a task is referred to as form-finding. However, it is more common for an architect to outline a concept of how a structure will look once constructed. The challenge is to work backwards from this final position to determine what initial properties a tensegrity must have. This process is termed inverse form-finding, and is seldom studied due to the nonlinearity and the combinatorial nature in the problem. A new approach is presented in the thesis to tackle this challenge, so that the final structure can be specified as stable. Given some target shape the method allows the designer to consider many/all possible tensegrities that satisfy the constraints and to choose the most aesthetically pleasing option (or apply some other criteria to rank the possible options). Compared with other alternative approaches, this method currently is the only one that can incorporate the stability of the structure into the designing process. It is not known how much construction imperfection can be tolerated for a tensegrity so that the constructed structure is stable. A radius of the stability region on the rank-deficiency manifold is derived, and can be used for an index measuring how robust to construction imperfections a tensegrity is. This robustness measure is suitable for comparing design proposals, and saving cost by relaxing unnecessary precision requirements. Regarding the reliability analysis of tensegrities, two methods are developed to overcome the convergence issue that may be encountered by using traditional FORM-based approaches. The first method is based upon SOS programming and can be shown to produce correct answers where the traditional FORM method fails. The second method is analytical, and it is possible for us to derive expressions showing how prestress, cross-sectional area and structural geometry may affect the reliability index. The used limit state function for member failure can also be used for any axially-loaded components. Numerical simulations are performed to study the structural responses of an icosahedron tensegrity structure subjected to sudden breakage of cables at different positions. Newton’s method is used for identifying cables whose failure is not critical in the sense that the structure will quickly find a new equilibrium position and will therefore not activate a mode of progressive collapse. The method successfully reduces the number of members that need checking using full nonlinear dynamic analysis, thus has the potential of saving time especially when the structure at hand is very complicated.