Static and dynamic analyses of tensegrity structures

Tensegrity structures are a class of truss structures consisting of a continuous set of tension members (cables) and a discrete set of compression members (bars). Since tensegrity structures are light weight and can be compactly stowed and deployed, cylindrical tensegrity modules have been proposed for space structures. From a view point of structural dynamics, tensegrity structures pose a new set of problems, i.e., initial shape finding. Initial configurations of tensegrity structures must be computed by imposing a pre-stressability condition to initial equilibrium equations. There are ample qualitative statements regarding the initial geometry of cylindrical and spherical tensegrity modules. Quantitative initial shape anlyses have only been performed on one-stage and two-stage cylindrical modules. However, analytical expressions for important geometrical parameters such as twist angles and overlap ratios lack the definition of the initial shape of both cylindrical and spherical tensegrity modules. In response to the above needs, a set of static and dynamic characterization procedures for tensegrity modules was first developed. The procedures were subsequently applied to Buckminster Fuller's spherical tensegrity modules. Both the initial shape and the corresponding pre-stress mode were analytically obtained by using the graphs of the tetrahedral, octahedral (cubic), and icosahedral (dodecahedral) groups. For pre-stressed configurations, modal analyses were conducted to classify a large number of infinitesimal mechanism modes. The procedures also applied tocyclic cylindrical tensegrity modules with an arbitrary number of stages. It was found that both the Maxwell number and the number of infinitesimal mechanism modes are independent of the number of stages in the axial direction. A reduced set of equilibrium equations was derived by incorporating cyclic symmetry and the flip, or quasi-flip, symmetry of the cylindrical modules. For multi-stage modules with more than four stages, the necessary conditions for axial assembly of one-stage interior modules with the same internal element-forces were investigated. By utilizing the uniform interior element-force mode, analytical expressions for initial configurations and associated pre-stress modes were presented. Finally, a virtual reality-based computer-aided-design (CAD) system for tensegrity structures was presented.