A study on the 'skew angle' of prismatic tensegrity structures

Abstract

Tensegrity structures are self-stressed equilibrated spatial systems that exist in a self-equilibrated mechanical state as a result of the internal force interaction between the tension cables and the compression struts and their respective force distribution. Despite of the minimal use of rigid elements, such structures are remarkably stable due to the structural components’ equilibrium state as a result of the application of pre-stress. This study focused on a specific tensegrity configuration, known as prismatic tensegrity structures, consisting of two regular parallel polygonal planes interconnected by cables and triangulated by struts. For such a structure to maintain equilibrium, a required rotation of one of the polygonal faces is required. Such a rotation is referred to as the skew angle ∝, where such a value is unique for each configuration. This study is based on two studies conducted by H.Kenner (1976) and I. P. Stern (1999). The former defined the equivalence between the equilibrium and the geometrical approach for several n-strut prismatic tensegrity configurations, whilst the latter sheds light on a set of equilibrium equations and defines the interdependence of the degree of skew angle and its resultant distribution of internal forces. To elaborate more on the aforementioned relationship, this study was conducted to address a gap in the available literature regarding the skew angle of such structures and the influence that such a translation has on the force distribution of the internal components and vice versa. In order to analyse and observe such changes in geometrical and structural parameters, the utilisation of finite element software was required. Such software provided an intuitive understanding of the structural behaviour and identification of the internal force values and paths for each individual structural member inside the tensegrity structure. The study is divided into two segments, with the latter being based on the results obtained in the former. The former consists of a successful calibration test conducted using a parametric approach, where the optimal structural and geometrical properties of the model were obtained by replicating and comparing the force distribution values calculated using an analytical approach for a given set of equilibrium prismatic configurations derived by H. Kenner. The latter consisted of a parametric analysis that focused on the influence that external forces (in the form of both pre-stress by means of pre-tension and external load) have on the final geometry configuration and their respective force distribution of the tensegrity configuration obtained in the first segment. The analysis conducted in the second segment following the calibration test, showed that the aforementioned external forces resulted in significant changes of the geometrical parameters of the selected configurations. Such changes were evident upon loading of the equilibrium configurations where significant displacements were observed. Such displacements resulted in additional pre-stress of the overall system, characterised by a significant increase in internal forces of the upper and lower cables, as well as the diagonal struts. Conversely, it was noted that a stiffening to softening mechanical response occurred for the vertical cables for higher loads. The configuration’s stability and self-equilibrating state, which was disrupted by the aforementioned excessive vertical loading, was re-established by introducing appropriate pre-stress levels, given that the vertical cables and diagonal struts do not lose their tension and compression capabilities, respectively, prior to such application.