Andrea Micheletti

Bistable Regimes in an Elastic Tensegrity System

Tensegrity systems are prestressed frameworks composed of bars and cables. A particular elastic tensegrity system is examined. This system can be bistable in two fundamentally different ways, one depending on its geometric dimensions, and the other one depending on the initial deformation, or prestrain, of the elastic elements. A reduced-order semi-analytical model is derived, and its predictions are verified with a full-order numerical model. In particular, the critical geometry and prestrain at which the system switches from one regime to another are determined. This case study provides a benchmark and new insights on this class of structures.

On Generalized Reciprocal Diagrams for Self-Stressed Frameworks

We present the duality between edge lengths and axial forces in self-stressed frameworks, upon which are based reciprocal diagrams, introduced by Maxwell and Cremona in the nineteenth century. The main concepts and principles are simplified by using a graph theoretic approach. We describe some unusual orthogonality relations, involving lengths, axial forces and their rates of change. Reciprocal diagrams, which exist for frameworks with underlying planar graph, are extended also to the non-planar case by introducing a new criterion. When this criterion can be applied, different reciprocals can be obtained as symmetric frameworks. The same criterion can also be applied to planar cases giving new reciprocals as a result. Although reciprocal diagrams cannot be obtained for all self-stressed frameworks, the presented duality always holds and it provides useful insights for design and form-finding purposes.

Design and experimental testing of an adaptive shape-morphing tensegrity structure, with frequency self-tuning capabilities, using shape-memory alloys

The present paper explores the capabilities of a tensegrity-inspired tower with regard to frequency tuning by shape morphing. To change the configuration of the proposed structure, shape-memory-alloy (SMA) actuators are used. This actuation principle also takes advantage of the variation of the elastic modulus of SMAs associated with the martensitic transformation. The temperature modulation of the SMA wires is successfully achieved by Joule heating, through a proportional-integral-derivative controller, to change between a low-temperature shape and a high-temperature shape. The implementation of a short-time-Fourier-transform control algorithm allows for the correct identification of the dominant input frequency, associated with the dynamic excitation. This information is used to automatically change the configuration of the structure in order to shift its natural frequency away from that of the dynamic excitation. With this frequency tuning, one obtains a reduction of the accelerations throughout the structure up to about 80%. The good performance of the proposed control approach gives promising indications regarding the use of tensegrity systems, in combination with SMAs, for shape-morphing applications, and, in particular, for self-tuning structures.

An analytical benchmark and a Mathematica program for MD codes: Testing LAMMPS on the 2nd generation Brenner potential

Abstract An analytical benchmark and a simple consistent Mathematica program are proposed for graphene and carbon nanotubes, that may serve to test any molecular dynamics code implemented with REBO potentials. By exploiting the benchmark, we checked results produced by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) when adopting the second generation Brenner potential, we made evident that this code in its current implementation produces results which are offset from those of the benchmark by a significant amount, and provide evidence of the reason. Program summary Program title: MDBenchmarks Catalogue identifier: AFAS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAS_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 22854 No. of bytes in distributed program, including test data, etc.: 369171 Distribution format: tar.gz Programming language: Mathematica 9. Computer: Any PC. Operating system: Any which supports Mathematica; tested under OS Yosemite. RAM: 5 gigabytes Classification: 7.7, 16.1, 16.13. Nature of problem: Testing commercial or open-source molecular dynamics codes implementing off-the-shelf REBO potentials on an analytical benchmark. Solution method: Analytical equilibrium conditions for achiral carbon nanotubes are implemented and solved, delivering benchmark values for the corresponding natural radius and cohesive energy; material properties (Young’s modulus and Poisson coefficient) are also computed. Running time: Instantaneous, or a few seconds, depending on computer hardware

How graphene flexes and stretches under concomitant bending couples and tractions

AbstractWe propose a geometrically and materially nonlinear discrete mechanical model of graphene that assigns an energetic cost to changes in bond lengths, bond angles, and dihedral angles. We formulate a variational equilibrium problem for a rectangular graphene sheet with assigned balanced forces and couples uniformly distributed over opposite side pairs. We show that the resulting combination of stretching and bending makes achiral graphene easier to bend and harder (easier) to stretch for small (large) traction loads. Our general developments hold for a wide class of REBO potentials; we illustrate them in detail by numerical calculations performed in the case of a widely used 2nd-generation Brenner potential.

Study of various tensegrity modules as building blocks for slender booms

This study investigates the structural performance of long and slender tensegrity booms. Previous studies show that tensegrity structures are generally more flexible than conventional trusses or space frames. The aims here were (i) to quantify how much more flexible eleven different tensegrity booms are, when compared to state-of-the-art truss booms, (ii) to find a general explanation for this. The performance criterion used for the comparison was the first natural frequency of the boom. A finite element program with truss elements was used to compute the natural frequencies around the initial prestressed configurations. The results show that tensegrity booms have between one and three orders of magnitude lower natural frequencies than truss booms. It is concluded that for the best performing tensegrity booms, the bending stiffness is independent of the level of pre-stress and the number of infinitesimal mechanisms as the bending stiffness is given mainly by the material stiffness of the tension elements and not the geometric stiffness as the infinitesimal mechanisms are not activated by bending. Thus, whereas the level of pre-stress and the presence of infinitesimal mechanisms play major roles for the stiffness of some tensegrity structures, the axial stiffness and orientation of tension elements are most important for the studied slender booms.

The indeterminacy condition for tensegrity towers: A kinematic approach

ABSTRACT We propose to find the configurations of tensegrity towers by means of a kinematic method based on the indeterminacy condition. After a description of tensegrity towers, we present our method in general and then apply it to some simple cases.

A 2D microstructure with auxetic out-of-plane behavior and non-auxetic in-plane behavior

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance, two-dimensional bodies have more freedom to deform than three-dimensional ones. Here, we exploit this peculiarity and propose a two-dimensional honeycomb microstructure with out-of-plane auxetic behavior opposite to the in-plane one. With a suitable choice of the lattice constitutive parameters, in its continuum description such a structure can achieve the whole range of values for the bending Poisson coefficient, while retaining a membranal Poisson coefficient equal to 1. In particular, this structure can reach the extreme values, −1 and +1, of the bending Poisson coefficient. Analytical calculations are supported by numerical simulations, showing the accuracy of the continuum formulas in predicting the response of the discrete structure.

Structural Performances of Single-layer Tensegrity Domes

We consider here floating-compression tensegrity systems: prestressed spatial trusses, composed by cables and struts, such that struts are never connected to each other. In particular, we focus on single-layer systems: all the nodal positions are assumed to lie on a closed synclastic surface, such as a sphere or an ellipsoid. In this study we perform the form-finding and the structural design of a new tensegrity dome of small size; then we compare it to a conventional truss structure. Theoretically, floating-compression systems are not the best choice for carrying loads, a fact which is confirmed in this study. Nevertheless, our tensegrity design improves previous ones significantly. The structural performances evaluated here provide a reference point for assessing the feasibility of floating-compression systems.

Tensegrity Rings for Deployable Space Antennas: Concept, Design, Analysis, and Prototype Testing

In this paper, an extended version of Zolesi et al. (Proceedings of the 42nd ICES (AIAA 2012-3601), San Diego, CA, 2012), we describe a tensegrity ring of innovative conception for deployable space antennas. Large deployable space structures are mission-critical technologies for which deployment failure cannot be an option. The difficulty to fully reproduce and test on ground the deployment of large systems dictates the need for extremely reliable architectural concepts. In 2010, ESA promoted a study focused on the pre-development of breakthrough architectural concepts offering superior reliability. This study, which was performed as an initiative of ESA Small Medium Enterprises Office by Kayser Italia at its premises in Livorno (Italy), with Universita di Roma TorVergata (Rome, Italy) as sub-contractor and consultancy from KTH (Stockholm, Sweden), led to the identification of an innovative large deployable structure of tensegrity type, which achieves the required reliability because of a drastic reduction in the number of articulated joints in comparison with non-tensegrity architectures. The identified target application was in the field of large space antenna reflectors. The project focused on the overall architecture of a deployable system and the related design implications. With a view toward verifying experimentally the performance of the deployable structure, a reduced-scale breadboard model was designed and manufactured. A gravity off-loading system was designed and implemented, so as to check deployment functionality in a 1-g environment. Finally, a test campaign was conducted, to validate the main design assumptions as well as to ensure the concept’s suitability for the selected target application. The test activities demonstrated satisfactory stiffness, deployment repeatability, and geometric precision in the fully deployed configuration. The test data were also used to validate a finite element model, which predicts a good static and dynamic behavior of the full-scale deployable structure.