Tensegrity Lattices Research Articles

Rarefaction pulses on tensegrity lattices are just $$\text {sech}^2$$-solitary (dark) waves

Rarefaction pulses on tensegrity lattices are just $$\text {sech}^2$$-solitary (dark) waves

Optimization for energy absorption of 3-dimensional tensegrity lattice with truncated octahedral units

Tensegrity structures have recently found new applications as energy absorbers in the field of aerospace engineering. In this study, we introduce an optimization method to maximize the energy absorption capability of a 3D tensegrity lattice composed of truncated octahedral units. The stored strain energy of the tensegrity lattice subjected to forced vertical displacement is maximized under constraints on the stress, structural material volume, and volume occupied by the lattice. The force density of the bar that defines the shape of each unit is regarded as a parameter, and the design variables are the cross-sectional areas of cables and bars as well as the level of prestresses on the lattice. Buckling of the bars is extensively utilized to significantly increase energy absorption. The nonlinear behavior of bars allowing buckling is modeled as a smoothed function of bi-linear elastic material, in which imperfection in the bar shape is also taken into account. Numerical examples show that tensegrity lattices, with flexibility in the vertical direction and adequate (shear) stiffness in the horizontal direction, can be obtained by solving the optimization problem. It is also shown that energy absorption by the structure scales cubically when its sizes and prestress level are uniformly scaled.

Towards Recognition of Scale Effects in a Solid Model of Lattices with Tensegrity-Inspired Microstructure

This paper is dedicated to the extended solid (continuum) model of tensegrity structures or lattices. Tensegrity is defined as a pin-joined truss structure with an infinitesimal mechanism stabilized by a set of self-equilibrated normal forces. The proposed model is inspired by the continuum model that matches the first gradient theory of elasticity. The extension leads to the second- or higher-order gradient formulation. General description is supplemented with examples in 2D and 3D spaces. A detailed form of material coefficients related to the first and second deformation gradients is presented. Substitute mechanical properties of the lattice are dependent on the cable-to-strut stiffness ratio and self-stress. Scale effect as well as coupling of the first and second gradient terms are identified. The extended solid model can be used for the evaluation of unusual mechanical properties of tensegrity lattices.

Extreme Mechanical Properties of Regular Tensegrity Unit Cells in 3D Lattice Metamaterials.

The study focuses on the identification of extreme mechanical properties of 3D lattice metamaterials based on regular tensegrity modules: 4-strut simplex, 3-strut simplex, expanded octahedron, truncated tetrahedron and X-module. The basis of the analysis is a continuum model which is used to find the equivalent elasticity matrices of the unit cells. For each examined tensegrity module a line of extreme properties is determined, which indicates the occurrence of the soft mode of deformation. Moreover, the eigenvectors corresponding to soft and stiff deformation modes are calculated and presented graphically. The obtained results are promising from the point of view of future creation of tensegrity lattices and metamaterials with extreme mechanical properties. One of the analysed materials is identified as quasi bimode, two as quasi trimodes, another one as a trimode and one more as a unimode.

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography.

A bistable response is an innate feature of tensegrity metamaterials, which is a conundrum to attain in other metamaterials, since it ushers unconventional static and dynamical mechanical behaviors. This paper investigates the design, modeling, fabrication and testing of bistable lattices with tensegrity architecture and nanoscale features. First, a method to design bistable lattices tessellating tensegrity units is formulated. The additive manufacturing of these structures is performed through multiphoton lithography, which enables the fabrication of microscale structures with nanoscale features and extremely high resolution. Different modular lattices, comprised of struts with 250 nm minimum radius, are tested under loading-unloading uniaxial compression nanoindentation tests. The compression tests confirmed the activation of the designed bistable twisting mechanism in the examined lattices, combined with a moderate viscoelastic response. The force-displacement plots of the 3D assemblies of bistable tensegrity prisms reveal a softening behavior during the loading from the primary stable configuration and a subsequent snapping event that drives the structure into a secondary stable configuration. The twisting mechanism that characterizes such a transition is preserved after unloading and during repeated loading-unloading cycles. The results of the present study elucidate that fabrication of multistable tensegrity lattices is highly feasible via multiphoton lithography and promulgates the fabrication of multi-cell tensegrity metamaterials with unprecedented static and dynamic responses.

Design of minimal mass load-bearing tensegrity lattices

Lattice metamaterials have demonstrated promising characteristics such as having tunable/unconventional properties and being lightweight. This work centers on the design of tensegrity-based lattices, known as “T-bar” structures, capable of supporting compressive loads with minimum mass. Analytical formulas for the calculation of the mass of these structures under externally applied forces and pre-stress are derived. These formulas account for local failure of the T-bar structures (material yielding and buckling of its individual members). A numerical approach is introduced to assess the global stability of the structures under external forces and pre-stress and to account for global buckling in the design process. The mass of the structure is minimized by adjusting its shape and topology while global buckling is simultaneously prevented using two different design methods: i) optimizing the pre-stress distribution in the structure, and ii) optimizing the cross-section areas of the tensegrity members. Using either method, the results show that 2D and 3D T-bars possess a global minimum mass design for a given externally applied force and length. The computed results also show that designs obtained by optimizing the cross-section areas of the members have lower mass than those obtained by optimizing the pre-stress distribution.

On the compact wave dynamics of tensegrity beams in multiple dimensions

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams reveal - for the first time - the presence of compact compression waves in two- and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices.

Analytical study of tensegrity lattices for mass-efficient mechanical energy absorption

This article studies tensegrity structures known as “D-bar” systems for applications as lightweight components for mechanical energy absorption. Aerospace structures such as planetary landers, designed to absorb energy from large impact loads while requiring minimal mass, would benefit from such components. Previous studies showed that D-bar systems support compressive loads with minimal mass compared with continuum options such as single columns. In this work, analytical equations for the mechanical (elastic) energy stored in D-bar systems of any complexity (a quantity proportional to the number of strings/bars in the system) are derived for the first time. The energy stored in D-bar systems is compared with that of bent buckled beams used in “flexible-bar tensegrity” concepts, which were proposed in the literature as energy absorption components for planetary landers. Comparisons are made between D-bar systems and bent buckled beams as isolated components subjected to a compressive load and as components of planetary landers. In all comparisons, the results show that D-bar systems of low complexity allow for higher energy storage and lower mass than bent buckled beams. Thus, it is concluded that D-bar systems can enhance the design of planetary landers and other applications that need lightweight mechanical energy absorption components.

On the Kinematics and Actuation of Dynamic Sunscreens With Tensegrity Architecture

This paper presents a mechanical study on the use of tensegrity lattices for the design of energy efficient sunscreens inspired by the dynamic solar fa\c{c}ades of the Al Bahar Towers in Abu Dhabi. The analyzed screens tassellate origami modules formed by 12-bar and 3-string tensegrity systems. The actuation of each module is controlled through the stretching of the perimeter strings, which form macro-triangles moving parallel to the building, while all the bars and the fabric mesh infills form micro-triangles that are allowed to move rigidly in space. We develop an analytic formulation of the deformation mapping associated with such an actuation motion, which gives rise to a morphing-type behavior. We also estimate the energy that is needed to activate the analyzed shading system, and establish a comparison between its weight and that of the original screens of the Al Bahar Towers. The proposed tensegrity design concept leads to realize shading screens that are markedly lightweight, work on very low energy consumption, and can be usefully employed to harvest solar and wind energies.

Soft and Stiff Simplex Tensegrity Lattices as Extreme Smart Metamaterials.

The present paper is dedicated to an evaluation of novel cellular metamaterials based on a tensegrity pattern. The materials are constructed from supercells, each of which consists of a number of simplex modules with different geometrical proportions. Mechanical properties of the metamaterial can be controlled by adjusting the level of self-equilibrated forces or by changing the properties of structural members. A continuum model based on the equivalence of strain energy of the 3D theory of elasticity with a discrete formulation is used to identify the qualitative properties of the considered metamaterials. The model allows the inclusion of nonlinearities related to the equations of equilibrium in actual configuration of the structure with self-equilibrated set of normal forces typical for tensegrities. The lattices are recognised as extreme metamaterials according to the eigensolution of the equivalent elasticity matrices of the continuum model. The six representative deformation modes are defined and discussed: stiff, soft and medium extensional modes and high (double) as well as low shear modes. The lattices are identified as unimode or nearly bimode according to the classification of extreme materials.

Towards unusual mechanical properties of tensegrity lattice metamaterial

In the present paper a novel cellular metamaterial based on a tensegrity pattern is presented. The material is constructed from supercells, each of which consists of eight 4-strutsimplexmodules. The proposed metamaterial exhibits some unusual properties. It is possible to control its mechanical characteristics by adjusting the level of self-stress or by changing the properties of structural members. A discrete model is introduced to identify the properties of the considered metamaterial and to estimate how the applied self-stress and the characteristics of cables and struts affect the whole structure. The performed analyses is an attempt to the future design of tensegrity lattices which can be recognised as a metamaterial for engineering applications.

Three-dimensional modeling of the wave dynamics of tensegrity lattices

This paper develops effective numerical models to study the wave dynamics of highly nonlinear tensegrity metamaterials. Recent studies have highlighted the geometrically nonlinear response of structural lattices based on tensegrity prisms, which may gradually change their elastic response from stiffening to softening through the modification of mechanical, geometrical, and prestress variables. We here study the nonlinear dynamics of columns of tensegrity prisms subject to impulsive compressive loading. An effective nonlinear rigid body dynamics is employed to simulate the dynamic response of such metamaterials. We illustrate how to pass from the matrix to the vector form of the equations of motions, on accounting for a rigid response of the compressive members (bars). Numerical simulations show that the wave dynamics of the examined metamaterials supports compression solitary pulses with profile dependent on the elastic properties of the tensile members (strings), the given impact velocity, and the applied prestress. We conclude that tensegrity columns can be effectively used as tunable acoustic lenses, which are able to generate acoustic solitary waves with adjustable profile in a host medium.

Mechanical response of 3-dimensional tensegrity lattices

Abstract Most available techniques for the design of tensegrity structures can be grouped in two categories. On the one hand, methods that rely on the systematic application of topological and geometric rules to regular polyhedrons have been applied to the generation of tensegrity elementary cells. On the other hand, efforts have been made to either combine elementary cells or apply rules of self-similarity in order to generate complex structures of engineering interest, for example, columns, beams, and plates. However, perhaps due to the lack of adequate symmetries on traditional tensegrity elementary cells, the design of 3-dimensional tensegrity lattices has remained an elusive goal. In this work, we first develop a method to construct 3-dimensional tensegrity lattices from truncated octahedron elementary cells. The required space-tiling translational symmetry is achieved by performing recursive reflection operations on the elementary cells. We then analyze the mechanical response of the resulting lattices in the fully nonlinear regime via two distinctive approaches: we first adopt a discrete reduced-order model that explicitly accounts for the deformation of individual tensegrity members, and we then utilize this model as the basis for the development of a continuum approximation for the tensegrity lattices. Using this homogenization method, we study tensegrity lattices under a wide range of loading conditions and prestressed configurations. We present Ashby charts for yield strength to density ratio to illustrate how our tensegrity lattices can potentially achieve superior performance when compared to other lattices available in the literature. Finally, using the discrete model, we analyze the dynamic response of a finite tensegrity lattice impacting an elastic wall, where a strong asymmetry in the dispersion of tensile and compressive stress-waves propagating through the medium is observed.

On the use of tensegrity structures for kinetic solar facades of smart buildings

We investigate the use of tensegrity structures with morphing and prestress-stability capabilities for the design of active solar façades of smart buildings. Morphing tensegrity lattices are used to design shading screens composed of umbrella-shaped ‘eyes’ that are opened and closed by adjusting the elongation in a limited number of cables. Prestressable lattices are instead employed to design superstable Venetian blinds that are composed of orientable slats. Future use of tensegrity solutions for next-generation smart buildings are outlined, with the aim of designing kinetic solar façades that combine morphing abilities with prestress-stability.

On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms

We study the geometrically nonlinear behavior of uniformly compressed tensegrity prisms through fully elastic and rigid-elastic models. The given models predict a variety of mechanical behaviors in the regime of large displacements, including an extreme stiffening-type response, already known in the literature, and a newly discovered, extreme softening behavior. The latter may lead to a snap buckling event producing an axial collapse of the structure. The switching from one mechanical regime to another depends on the aspect ratio of the structure, the magnitude of the applied prestress, and the material properties of the constituent elements. We discuss potential mechanical and acoustic applications of such behaviors, which are related to the design and manufacture of tensegrity lattices and innovative metamaterials.

Solitary waves on tensegrity lattices

We study the dynamics of lattices formed by masses connected through tensegrity prisms. By employing analytic and numerical arguments, we show that such structures support two limit dynamic regimes controlled by the prisms’ properties: (i) in the low-energy (sonic) regime the system supports the formation and propagation of solitary waves which exhibit sech2 shape and (ii) in the high-energy (ultrasonic) regime the system supports atomic-scale localization. Such peculiar features found in periodic arrays of tensegrity structures suggest their use for the creation of new composite materials (here called “tensegrity materials”) of potential interest for applications in impact absorption, energy localization and in new acoustic devices.