Elsevier

Composite Structures

Volume 117, November 2014, Pages 234-243
Composite Structures

Experimental investigation of the softening–stiffening response of tensegrity prisms under compressive loading

https://doi.org/10.1016/j.compstruct.2014.06.022Get rights and content

Abstract

The present paper is concerned with the formulation of new assembly methods of bi-material tensegrity prisms, and the experimental characterization of the compressive response of such structures. The presented assembly techniques are easy to implement, including a string-first approach in the case of ordinary tensegrity prisms, and a base-first approach in the case of systems equipped with rigid bases. The experimental section shows that the compressive response of tensegrity prisms switches from stiffening to softening under large displacements, in dependence on the current values of suitable geometric and prestress variables. Future research lines regarding the mechanical modeling of tensegrity prisms and their use as building blocks of nonlinear periodic lattices and acoustic metamaterials are discussed.

Introduction

The construction and testing of physical tensegrity models is a topic of particular interest for a broad audience of researchers and engineers, due to the large use of tensegrity concepts in engineering and the physical sciences, and the lack of standardized assembly methods for such structures (refer, e.g., to Skelton and de Oliveira [26], Fest et al. [11], Motro [21], Burkhardt [3]). A rich variety of small- and full-scale tensegrity structures is presented in [26], including a nickel-titanium controllable tensegrity column, which is a small-scale model of a tall adaptive building (cf. Fig. 1.28 of [26]); a full-scale model of a deployable tensegrity wing (Fig. 1.28); a marine tensegrity structure easily dropped into the sea to serve for weather forecasting or ocean studies (Figs. 1.34–1.37); and a vibration control device consisting of a tensegrity column with 9 bars, three actuators, and three sensors (Fig. 1.40), just to name a few examples. Due to their lightness and deployability, it is well known that tensegrity structures are well suited for space applications (cf., e.g., [26], [10]). An interesting model of a deployable reflector structure serving a small satellite is presented in [27]. Such authors make use of a tensegrity system with 6 telescopic bars and 18 strings to build a deployable ring element of the reflector structure. The adopted cables consist of 1.0 mm Kevlar cords connected to the bars through Al alloy cylindrical joint fittings, with length 30 mm and 15 mm diameter. The foldability and deployability of a model is demonstrated through laboratory tests.

For what concerns the experimental response of full-scale models, an interesting system composed of three repetitive modules is analyzed in [11]. Such a system is equipped with sensors and actuators to control its shape and response. Each unit is formed by 6 telescopic bars made up of fiberglass-reinforced polyester tubes with a cross-sectional area of 703 mm2, and 24 stainless steel cables of 6 mm diameter. The nodes of the different units are equipped with ball bearings preventing the transmission of bending moments, and the units are connected with each other through special connection joints. The structure is prestressed by elongating the bars through nut/threaded rod systems, and the cable tension is measured with an interferometric laser system [6]. Symmetric and asymmetric loading tests allow the authors to detect geometrical and mechanical nonlinearities of the overall response. An experimental study of the nonlinear mechanical response of tensegrity prisms equipped with semi-spherical joints is performed in [5], by employing a cable-shortening method and considering different prestress levels. A tensegrity prism controlled by a pneumatic bar has been constructed in the Structural Systems and Control Laboratory of the University of California, San Diego, employing pneumatic cylinders to realize the compressive members, and replacing the top and bottom cables with rigid aluminum plates (http://maeresearch.ucsd.edu/skelton/laboratory/tensegrity_platform.htm).

The issue of the effective measurement of the self-stress state of a tensegrity structure is treated by Dubé et al. [9], using direct and indirect measurement methods. The monitored structure consists of a tensegrity minigrid featuring 24 struts and 57 cables. The nodes have a cylindrical shape and host the cables and the pointed extremities of the bars. Direct measurements of the stresses running along the cables and struts are performed by equipping such elements with strain gauges, while indirect estimates of the cable tensions are obtained through the vibrating wire method [1]. Panigrahi et al. [24] present experimental and numerical analyses of tensegrity prototypes made through two different (strut based and cable based) techniques. The strut based method changes the length of a suitable telescopic bar to apply the desired prestress. The cable based method instead makes use of a turnbuckle placed on a selected string. A tension meter is used in [25] to measure the tension in the cables of an adaptive tensegrity grid. The cables are tensioned by screwing their adjustable ends, and the tension meter is employed to reach the desired prestress through iterative steps.

The present paper is concerned with the formulation and the practical implementation of original assembly methods of bi-material tensegrity prisms, and the laboratory testing of uniformly compressed prisms with different aspect ratios and boundary conditions. We begin by describing the materials used for the construction of the physical tensegrity models, which consist of threaded steel bars for the compressed members, and Spectra® fibers for the tensile elements. Additional aluminum plates are used in the case of special systems equipped with rigid bases (Section 2). Next, we accurately illustrate the assembly methods proposed in the present study, which include a string-first approach in the case of ordinary prisms, and a base-first approach in the case of systems with rigid bases (Section 3). We then pass to describing the quasi-static testing used to characterize the response in compression of the examined prism models, with the aim of identifying the nature of those responses in the large displacement regime (Section 4). We observe a marked variability of the mechanical response of a tensegrity prism under uniform axial loading: it ranges from stiffening to softening depending on the aspect ratio of the structure, the magnitude of the applied state of prestress, and the rigidity of the terminal bases. We end in Section 5 by drawing the main conclusions of the present study and outlining avenues for future research.

Section snippets

Materials

The present section illustrates the materials used to construct the physical tensegrity prism models analyzed in the present paper, and the experimental measurements that were conducted in order to identify the Young’s moduli of the component materials. We analyze ordinary minimal regular tensegrity prisms [26], which are composed of three struts (or ‘bars’), three cross-strings, and six horizontal strings (‘db’ systems, cf. Fig. 1). In addition, we examine a special tensegrity prism which is

Assembling methods

We now describe the assembly methods used to manufacture the physical prisms models. These methods are based on a string-first approach in the case of ‘db’ prisms, and a base-first approach in the case of the ‘rb’ system.

Quasi-static compression tests

This section presents the results of quasi-static compression tests on the ‘db’ and ‘rb’ systems, showing different aspect ratios and states of prestress. We performed compression tests through a Matest® electromechanical testing system equipped with 50 kN (thick prisms) or 200 kN (slender prisms) load cells, employing displacement control loading with a loading rate of 3 mm/min (Fig. 14). In order to facilitate the twisting of the terminal bases and to minimize frictional effects, we carefully

Concluding remarks

We have presented new assembly methods for tensegrity prisms, which include a string-first approach in the case of ordinary prisms, and a base-first approach in the case of prisms endowed with rigid bases. The proposed methods are easy to manage, and require common hardware materials, especially in the case of prisms with deformable bases (cf. Section 3.1). We have also presented the results of quasi-static compression tests on tensegrity prism models, with the aim of characterizing the

Acknowledgements

Support for this work was received from the Italian Ministry of Foreign Affairs, Grant No. 00173/2014, Italy–USA Scientific and Technological Cooperation 2014–2015 (‘Lavoro realizzato con il contributo del Ministero degli Affari Esteri, Direzione Generale per la Promozione del Sistema Paese’). The authors wish to thank Saverio Spadea and Cristian Santomauro (Department of Civil Engineering, University of Salerno), Vittorio Vecchiarelli (Sporting Tennis Team, Mercogliano, Avellino, Italy), and

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