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The torsional resistance of the beam-like tensegrity structure is an essential mechanical property, but there is currently no systematic approach to applying torque to the structure using external force. This article presents a novel torque application strategy to analyze beam-like tensegrity structures. First, the torque that needs to be applied and the initial self-stable configuration are given. Second, the number of iteration steps is set, and the torque is gradually increased by using an arithmetic sequence, and the torque of each step is evenly distributed to the nodes of the acting surface. Third, the current external forces can be calculated by the nodal coordinates and torque, and the stable configuration under the obtained external force will be found based on the form-finding method. This process will be cycled until the specified torque is achieved. Finally, the equilibrium configuration under the set torque will be obtained, and the deformation analysis of the configuration will be carried out to study its mechanical properties. The elastic potential energy errors of the three-bar tensegrity prism unit and the class 2 tensegrity tower are corrected by 2.8198% and 66.9135%, respectively. This method has been proven to improve calculation precision. [ABSTRACT FROM AUTHOR]

AbstractThe regular tensegrity prisms are a kind of fundamental unit, which can be formed into different configurations by different splicing approaches to achieve specific structural functions. Taking regular prisms as the research object, this article presents an analytical method for structural deformations under compressive loading. The structural parameters after loading can be obtained directly by solving the nonlinear force density equation, which simplifies the form-finding process. This article also studies the structural stiffness under different connection modes. By defining the twist angle change rate and internal force utilization rate, we can compare the relative deformation of different tensegrity prisms. The results show that the relative deformation of the three-bar prism is minimal, and it has the best stiffness. [ABSTRACT FROM AUTHOR]

Tensegrity structures are prestressed structures consisting of compressed members connected by prestressed tensioned members. Due to their properties, such as flexibility and lightness, mobile robots based on these structures are an attractive subject of research and are suitable for space applications. In this work, a mobile robot based on a tensegrity structure with two curved members connected by eight tensioned strings is analyzed in terms of deformation in the curved members. Further, the difference in locomotion trajectory between the undeformed and deformed structure after the prestress is analyzed. For that, the theory of large deflections of rod-like structures is used. To determine the relationship between acting forces and the deformation, the structure is optimized using minimization algorithms in Python. The results are validated by parameter studies in FEM. The analysis shows that the distance between the two curved members significantly influences the structure's locomotion. It can be said that the deformation of the components significantly influences the locomotion of tensegrity structures and should be considered when analyzing highly compliant structures. [ABSTRACT FROM AUTHOR]

This paper provides a specific analysis strategy for tensegrity prism units with different complexities and connectivity. Through the nodal coordinate matrix and connectivity matrix, we can establish the equilibrium equation of the structure in the self-equilibrium state, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can find the self-equilibrium configuration. The torsional angle formula between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the self-equilibrium configuration, we carry out the mechanical analysis of the single node, and the force density relationship between elements is gained. As one of the standards, the mass is used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. A six-bar tensegrity prism unit is investigated in this paper, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units. [ABSTRACT FROM AUTHOR]

The quality of being adaptable/deployable of tensegrity structures provides intriguing challenges for researchers and designers. In this work, the shape-change capabilities of a V-Expander tensegrity column are analyzed: a numerical investigation is carried out for the study of the cable-actuation process for a column composed of elementary V-Expander tensegrity cells sharing horizontal cables. The actuation is performed by considering suitable sets of active and passive cables among the whole set of cables of the column. The attention is focused on the following kinds of shape-changes: stretching/shrinking, flexure, shear and torsion. Moreover, a strategy for predicting the nonlinear response of the tensegrity column in the cable-actuation process is proposed. This strategy allows for estimating quickly, among all the possible choices of active and passive cable sets, those leading to maximum displacements or rotations and to the minimum ratio between the normalized work of active cables and the deformation of the column. Further numerical analyses are performed by varying the aspect ratio of the V-Expander cell, to evaluate the effects of changes in the geometrical parameters on the nonlinear actuation process of the column. Tensegrity structures have inspired artists, biologists, engineers, and architects. Many studies have been conducted in recent years, especially related to geometry, form finding, static analysis, and dynamic response. Their use is very encouraging in projects requiring adaptable and/or deployable structures. Indeed, a tensegrity system can provide the minimal mass structure required to sustain a given external load, an intriguing feature for uses as lightweight deployable systems, such as satellites, antennas, or robots. Tensegrity systems are reticulated structures composed of bars in compression maintained in equilibrium by a network of cables in tension. This work focuses on the shape-change capabilities of V-Expander tensegrity columns, a promising type of tensegrity system in this context. Shape change can be obtained by shortening some cables using actuators, while other cables lengthen elastically keeping the system in equilibrium during the process. A fast linear prediction strategy is proposed for evaluating the efficiency of any choice of actuated elements. This strategy allows to prefigure the choices of lengthening and shortening cables which lead to the most efficient shape-change processes of V-Expander columns, here presented for the first time. Such a strategy can be applied with minor adjustments to the other types of tensegrity systems. [ABSTRACT FROM AUTHOR]

A recent study has presented a Maxwell mass–spring model for a chain formed by two different types of tensegrity prisms alternating with lumped masses. Such a model shows tensegrity theta prisms arranged in parallel with minimal regular prisms acting as resonant substructures. It features a tunable frequency bandgap response, due to the possibility of adjusting the width of the bandgap regions by playing with internal resonance effects in addition to mass and spring contrasts. This paper expands such research by presenting a continuum modeling of the tensegrity Maxwell chain, which is useful to conduct analytic studies and to develop finite element models of the plane wave dynamics of the investigated system. In correspondence to the high wave-length limit, i.e., in the low wave number regime, it is shown that the dispersion relations of the discrete and continuum models provide similar results. Analytic solutions to the wave dynamics of physical systems are presented, which validate the predictions of the bandgap response offered by the dispersion relation of the continuum model. [ABSTRACT FROM AUTHOR]

Deployable aerodynamic decelerators are more suitable for planetary exploration missions than rigid aerodynamic decelerators. Their sizes are less limited by the launch vehicle shroud, allowing heavier payloads to be delivered to the surfaces of planets. Aiming at the problem of lightweight designs in deployable aerodynamic decelerators, a deployable tensegrity structure composed of two frustum tensegrity units and a prism tensegrity unit is proposed. To design the deployable tensegrity structure, a self-equilibrium model that is especially suitable for the structure with rotational symmetry is established according to prestressability conditions and force equilibrium equations. Based on the deployable tensegrity structure, the deployment mechanism, with the action of drive units, is designed to realize the transformation from the stowed state to the deployed state of the decelerator. The tensegrity structure always has rotational symmetry to make the deployment process highly synchronized due to the fact that drive units can work simultaneously. During the deployment process, the transverse distance and longitudinal distance are used to measure the deployment degree of the tensegrity structure. The types of axial forces for members are used to determine whether the tensegrity structure is stable. The result shows that the deployment process has continuity and that the tensegrity structure always stays stable. • A deployable tensegrity structure composed of two frustum tensegrity units and a prism tensegrity unit is proposed. • A self-equilibrium model that is especially suitable for the tensegrity structure with rotational symmetry is established. • A deployable aerodynamic decelerator, with the advantage of lightweight, is designed based on the tensegrity structure. • The effect of the declination on the transverse distance, the longitudinal distance, and the values of forces are given. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work studies the mechanics of novel origami solar modules with tensegrity architecture for integration in the dynamic solar façades of energy-efficient buildings. The analyzed modules are deployed by adjusting the rest lengths of cables attached to given nodes, so as to form a tensegrity origami. Their stiffness is tuned by adjusting the pretension of the actuation cables, when the deployment motion is locked. The insertion of solar thermal or photovoltaic panels into the rigid elements of the module makes it possible to form positive-energy solar systems. The work studies the kinematics and the mechanics of the investigated structures through analytic and numerical methods. Two folding motions are examined: to open and close the modules and to track sun rays. The rapid prototyping of a physical mock-up permits an experimental validation of the force–displacement response in a given configuration of the sun-tracking motion. A procedure for the computation of the fundamental vibration modes and vibration frequencies of a quadrangular solar module is also given, and the expected response of the system under wind loading is outlined.

The paper contains a parametric analysis of tensegrity structures subjected to periodic loads. The analysis focuses on determining the main region of dynamic instability. When load parameters fall within this region, the resulting vibration amplitudes increase, posing a risk to the durability of structures. The study considers structures built using commonly used modules. The influence of the initial prestress on the distribution of the instability regions is examined. Additional prestress can significantly reduce the extent of instability regions, potentially narrowing them by up to 99%. A nondimensional parameter is introduced to accurately assess changes in the extent of the instability region. A geometrically non-linear model is employed to evaluate the behavior of the analyzed structures. [ABSTRACT FROM AUTHOR]

Copyright of Revista: Módulo Arquitectura CUC is the property of Corporacion Universidad de la Costa, CUC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper contains a parametric analysis of tensegrity structures subjected to time-independent external loads. A complete dynamic stability analysis is a three-step process. The first stage involves the identification of self-stress states and infinitesimal mechanisms. The next stage concentrates on the static and dynamic behavior of tensegrities under time-independent external loads, whereas the third is under periodic loads. In this paper, the first two stages are carried out. The structures built with the most popular tensegrity modules, Simplex and Quartex, are considered. The effect of the initial prestress on the static parameters and frequency is analyzed. To assess this behavior, a geometrically non-linear model is used. [ABSTRACT FROM AUTHOR]

To effectively guide the erection of the tensegrity structures, the forming process was simulated, and the intermediate equilibrium states were predicted. A kind of prismatic tensegrity structures with redundant cables was defined. The change rules of its mechanical properties including self-stress states and structural stiffness with the change of the twist angle were investigated analytically. Based on the topology of this kind of structures, a reasonable forming scheme was proposed in which some temporary lifting points were set and two groups of vertical cables were tensioned in batches. A simplified dynamic relaxation method was employed to track the forming process inversely. The results show that when the removal of the active cables and the relaxation or tension of the passive cables are simulated by controlling the axial stiffness of the members, the structural topology keeps invariant regardless of the withdrawal of the slack cables, and the stability of the algorithm is good. Combining with the inverse analysis, the dynamic relaxation method can accurately predict the intermediate states in the erection of tensegrity structures, and determine the key structural parameters such as the nodal coordinates and the internal forces of members, which provides a theoretical basis for the construction of such structures. [ABSTRACT FROM AUTHOR]

The paper contains a parametric analysis of tensegrity structures subjected to periodic loads. The analysis focuses on determining the main region of dynamic instability. When load parameters fall within this region, the resulting vibration amplitudes increase, posing a risk to the durability of structures. The study considers structures built using commonly used modules. The influence of the initial prestress on the distribution of the instability regions is examined. Additional prestress can significantly reduce the extent of instability regions, potentially narrowing them by up to 99%. A nondimensional parameter is introduced to accurately assess changes in the extent of the instability region. A geometrically non-linear model is employed to evaluate the behavior of the analyzed structures.

A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained through a ground structure method combined with mixed integer programming; in the second step, the cable connectivities are optimized through nonlinear programming to obtain a feasible tensegrity structure. The same ground structure used in the first step is adopted in the second step, which is beneficial to find a more symmetric cable layout. The independent continuous mapping method is used in the second step to convert the 0–1 binary variables of cable connectivities to continuous variables to transform the combinatorial optimization problem into a nonlinear programming problem. The number of strut lengths is adopted as a control parameter and a symmetry objective function is proposed to generate a variety of regular and symmetric tensegrity structures. A multi-stage computation scheme is proposed to improve the computational efficiency. Typical examples are carried out to validate the proposed method. The computational efficiency of the method is benchmarked with existing methods fully based on mixed integer programming. Results demonstrate that the computational efficiency of the proposed method is significantly improved compared to the existing methods. [ABSTRACT FROM AUTHOR]

The form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. This form-finding problem leads to the evaluation of both the self-stress in the elements and the shape of the tensegrity structure. This paper presents a novel method for determining feasible integral self-stress states for tensegrity structures, that is self-equilibrated states consistent with the unilateral behaviour of the elements, struts in compression and cables in tension, and with the symmetry properties of the structure. In particular, once defined the connectivity between the elements and the nodal coordinates, the feasible self-stress states are determined by suitably investigating the Distributed Static Indeterminacy (DSI). The proposed method allows for obtaining feasible integral self-stress solutions by a unique Singular Value Decomposition (SVD) of the equilibrium matrix, whereas other approaches in the literature require two SVD. Moreover, the proposed approach allows for effectively determining the Force Denstiy matrix, whose properties are strictly related to the super-stability of the tensegrity structures. Three tensegrity structures were studied in order to assess and discuss the efficiency and accuracy of the proposed innovative method.

The successful construction of a tensegrity structure requires not only design techniques but also a means to account for any manufacturing or assembly errors. As a tensegrity is prestressed and is often stabilised by its prestress, it requires a form-finding technique to determine the balanced configuration in the design phase; this property also makes it challenging for engineers to evaluate the effect of manufacturing imperfections on the self-equilibrated configuration. In this paper we investigate the sensitivity of tensegrity structures to manufacturing imperfections, using a stiffness-matrix-based form-finding technique in combination with the Monte Carlo simulation method to introduce manufacturing length errors. The effects at the structural level are captured, and two general relationships between the variance of the input manufacturing error and the output distribution of the member tensions, between the variance and the mean across all groups, are observed. By identifying the most sensitive member group, this work provides a design and analysis strategy when the natural length errors of members are considered for tensegrity structures. • Analysis of length error effects on tensegrity structures using Monte Carlo simulations; • Nodal position, member failure, and stiffness modes are considered in sensitivity analysis; • A linear relationship is found between the variance of the output normalised load and input length error distribution; • The most highly loaded members are most sensitive to manufacturing imperfections; • A versatile analysis framework that could be extended to include various loading cases. [ABSTRACT FROM AUTHOR]

A modified dynamic relaxation algorithm for the form-finding of tensegrity robots in task space is proposed in this paper. There are some form-finding problems of tensegrity structures that are hard to be handled by the node-based dynamic relaxation algorithm. For tensegrity structures with multiple interconnected rods or rigid rods, the node-based dynamic relaxation algorithm is usually difficult to perform this type of form-finding. The node-based dynamic relaxation algorithm becomes rather cumbersome if several different ratios between rod lengths and cable lengths are desired, which restricts its applicability to less regular structural forms. The performance of the algorithm is affected by the relative difference in stiffness between members(cables and rods). To solve these problems, we extend the general dynamic relaxation algorithm from node space to task space. The proposed algorithm considers multiple interconnected rigid rods as an entire rigid body to derive its motion in six degrees of freedom. We simulated the motion process of the rigid body approaching its self-equilibrium position under the force exerted by all surrounding cables. In the form-finding process, the relative location relationship of all interconnected rods on a complex rigid body is maintained. The algorithm is valid for the form-finding of tensegrity structures which are with several different ratios between rod lengths and cable lengths. Besides, the modified algorithm is not affected by the stiffness of interconnected rods on rigid bodies. To demonstrate the capability of the method, four examples, including a two-segment spine robot, a bio-inspired tensegrity arm, a multi-segment spine robot, a tensegrity robot with disconnected and interconnected rigid rods, are presented in this paper.

The paper contains a parametric analysis of tensegrity structures subjected to time-independent external loads. A complete dynamic stability analysis is a three-step process. The first stage involves the identification of self-stress states and infinitesimal mechanisms. The next stage concentrates on the static and dynamic behavior of tensegrities under time-independent external loads, whereas the third is under periodic loads. In this paper, the first two stages are carried out. The structures built with the most popular tensegrity modules, Simplex and Quartex, are considered. The effect of the initial prestress on the static parameters and frequency is analyzed. To assess this behavior, a geometrically non-linear model is used.

This paper gives a new formulation to design adaptive structures through total energy optimization (TEO). This methodology enables the design of truss as well as tensegrity configurations that are equipped with linear actuators to counteract the effect of loading through active control. The design criterion is whole-life energy minimization which comprises an embodied part in the material and an operational part for structural adaptation during service. The embodied energy is minimized through simultaneous optimization of element sizing and actuator placement, which is formulated as a mixed-integer nonlinear programming problem. Optimization variables include element cross-sectional areas, actuator positions, element forces, and node displacements. For tensegrity configurations, the actuators are not only employed to counteract the effect of loading but also to apply appropriate prestress which is included in the optimization variables. Actuator commands during service are obtained through minimization of the operational energy that is required to control the state of the structure within required limits, which is formulated as a nonlinear programming problem. Embodied and operational energy minimization problems are nested within a univariate optimization process that minimizes the structure's whole-life energy (embodied + operational). TEO has been applied to design a roof and a high-rise adaptive tensegrity structure. The adaptive tensegrity solutions are benchmarked with equivalent passive tensegrity as well as adaptive truss solutions, which are also designed through TEO. Results have shown that since cables can be kept in tension through active control, adaptive tensegrity structures require low prestress, which in turn reduces mass, embodied energy, and construction costs compared to passive tensegrity structures. However, while adaptive truss solutions achieve significant mass and energy savings compared to passive solutions, adaptive tensegrity solutions are not efficient configurations in whole-life energy cost terms. Since cable elements must be kept in tension, significant operational energy is required to maintain stable equilibrium for adaptation to loading. Generally, adaptive tensegrity solutions are not as efficient as their equivalent adaptive truss configurations in mass and energy cost terms. [ABSTRACT FROM AUTHOR]

This work studies the dispersion relation of a Maxwell type mass–spring chain formed by lumped masses and the parallel arrangement of two different types of tensegrity prisms. Use is made of the Bloch–Floquet theory of discrete systems in association with a linearized model of the response of the tensegrity units under compression loading. Such a modeling is aimed at studying the propagation of compression waves under small perturbations of the initial equilibrium state of the system. For a given value of the cable's prestress, the tensegrity systems connecting the lumped masses react as elastic springs, which exhibit axial deformations accompanied by relative twisting rotations of the terminal bases. The twisting motion of the chain affects the expression of the kinetic energy, and is accounted for by introducing a suitable definition of equivalent masses. The bandgap structure of the analyzed system is analytically determined and numerical results are obtained for a chain formed by physical models tensegrity θ = 1 prisms aligned in parallel with minimal tensegrity prisms. The given results highlight the highly tunable frequency bandgap properties of tensegrity mass–spring chains exhibiting internal resonance capabilities. • Bandgap structure of a tensegrity mass–spring chain equipped with resonant units. • Coupling of longitudinal and twisting motions. • Compatibility constraints are required to permit the propagation of mechanical waves. • Definition of equivalent masses. • Strong influence of coupling effects on the frequency bandgap edges. [ABSTRACT FROM AUTHOR]

Finding form is a critical step in designing tensegrity structures. On the condition that the partial node coordinates, topology, and a bar/cable attribute (the force density of bar is -1 and the force density of cable is 1.) are known, a form-finding method, which is used to find the remaining node coordinates and the force density relation between elements, is proposed in this paper. Firstly, the equilibrium conditions of the tensegrity system are analyzed, and the equilibrium equation is established. Secondly, the variables that must be solved are set and substituted into the equilibrium equation, and the target equation with the variables is built. The Levenberg-Marquardt method with a damping parameter updating strategy is introduced to solve the least squares problem by transforming the equilibrium equation problem into the least squares problem. The form-finding process is performed by solving the least squares formula. Three examples demonstrate the efficiency and accuracy of searching for self-equilibrium configurations. [ABSTRACT FROM AUTHOR]

This study proposes a general framework for topology-finding or topology optimization of tensegrity structures. The existing topology-finding formulation of tensegrity structures based on mixed-integer linear programming (MILP) was improved and transformed into a formulation based on mixed-integer semidefinite programming (MISDP) which considers the global stability condition of tensegrity. We illustrated and analyzed two undesirable phenomena, loss of prestress stability and loss of integrity, caused by the missing global stability condition in previous MILP-based approaches. A branch-and-bound algorithm combined with a primal-dual interior-point algorithm is employed to solve the proposed MISDP model. Some numerical examples illustrated the improvements and effectiveness of the proposed approach. The proposed approach successfully can avoid the two undesirable phenomena and ensure the global stability of the found tensegrity structures. By using different stability conditions in the topology-finding process, the proposed approach can find general stable tensegrity structures and superstable tensegrity structures. [ABSTRACT FROM AUTHOR]

Traditional tensegrity structures comprise isolated compression members lying inside a continuous network of tension members. In this contribution, a simple numerical layout optimization formulation is presented and used to identify the topologies of minimum volume tensegrity structures designed to carry external applied loads. Binary variables and associated constraints are used to limit (usually to one) the number of compressive elements connecting a node. A computationally efficient two-stage procedure employing mixed integer linear programming (MILP) is used to identify structures capable of carrying both externally applied loads and the self-stresses present when these loads are removed. Although tensegrity structures are often regarded as inherently 'optimal', the presence of additional constraints in the optimization formulation means that they can never be more optimal than traditional, non-tensegrity, structures. The proposed procedure is programmed in a MATLAB script (available for download) and a range of examples are used to demonstrate the efficacy of the approach presented. [ABSTRACT FROM AUTHOR]

Tensioned cable nets can be used as a lightweight supporting formwork in the construction of thin concrete architectural shells. Meeting the structural and mechanical specifications of such shells requires precise positioning of the nodes of the cable net. We develop and experimentally verify a control strategy that uses measurements of the nodal positions to identify model parameters and calculate adjustments to the boundary cable lengths to achieve the desired form. As cable net lengths adjustments on the construction site are time-consuming, the number of control adjustments is minimized via a sparsity-promoting optimization-based method. [ABSTRACT FROM AUTHOR]

This paper presents a mechanical study on the use of tensegrity lattices for the design of energy efficient sun screens, inspired by the dynamic solar façades 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 developed an analytic formulation of the deformation mapping associated with such an actuation motion, giving rise to a morphing-type behavior. We also estimated the energy required to activate the analyzed shading system, and established a comparison between its weight and that of the original screens of the Al Bahar Towers. The proposed tensegrity design concept leads to the realization of shading screens that are markedly lightweight, operate on very low energy consumption and can be usefully employed to harvest solar and wind energies.

This study performs a novel control efficiency assessment approach that compares performance of optimal control algorithms regarding vibration of tensegrity structures. Due to complex loading conditions and the inherent characteristics of tensegrities, e.g. geometrical nonlinearity, the quantization of control efficiency in active control of tensegrity constitutes a challenging task especially for different control algorithms. As a first step, an actuator energy input, comprising the strain energy of tensegrity elements and their internal forces work, is set to constant levels for the linear-quadratic regulator (LQR). Afterwards, the actuator energy of the linear-quadratic Gaussian (LQG) is iterated with identical actuator energy input in LQR. A double layer tensegrity grid is employed to compare the control efficiencies between LQR and LQG with five different control scenarios. The results demonstrate the efficiency and robustness in reducing the dynamic response of tensegrity structures, and a theoretical guideline is provided to search optimal control options in controlling actual tensegrities. [ABSTRACT FROM AUTHOR]

Abstract Tensegrity structures are an intriguing kind of structures by virtue of their deployability, scalability and high stiffness to mass ratio. Fraddosio et al. recently proposed a family of five innovative V-Expander elementary tensegrity cells, characterized by an increasing degree of geometrical complexity, and designed as a morphological evolution of a concept originally proposed by Motro and Raducanu. Here, we study the mechanical behavior of these innovative V-Expander elementary tensegrity cells by referring to different topologies; in particular, we analyze for such cells the feasible self-stress states in the cases in which the components in compression are composed of 2, 3, 4 and 6 struts, respectively. In addition, we evaluate the minimal mass of the cells taking into account the buckling strength of members in the self-equilibrium states according to the indications of standard building codes. [ABSTRACT FROM AUTHOR]

A major deficiency of tensegrity structures which may prevent wide spread application of them in practice is their low structural efficiency in terms of initial stiffness and ultimate strength. Further, the collapse of these structures can be initiated by the buckling of a few struts, which may propagate to other elements of these systems and finally cause overall collapse. Using force-limiting devices (FLDs) and high-stiffness cables can be the primary enhancement techniques for abrupt collapse prevention as well as achieving efficient behavior to ensure the satisfactory performance of these structures exposed to extreme events. In the present study, static and dynamic collapse analyses have been conducted to evaluate the effects of FLDs and high-stiffness cables on the collapse behavior and structural efficiency of these structures. From the results, it is found that an increase of 145% in the cable elastic modulus increases the initial stiffness of tensegrity structures by approximately 135%. Using FLDs in a small selection of the most critical struts can lead to increases of up to 52% in tensegrity structures strength. Irrespective of cable stiffness, using FLDs can be more beneficial in altering the collapse mechanism of these structures. [ABSTRACT FROM AUTHOR]

This work studies tensegrity bracing systems to be used as energy dissipation devices in next generation, earthquake-proof timber buildings. The examined lightweight and high-strength structures with re-centering capabilities are formed by timber members and pretensioned elements with a superelastic response, which may consist of shape memory alloy wires, cables or bars with energy dissipation capacity. In the case of bars, we assume that such members can be protected against buckling through their encasement in buckling-restrained devices, so as to respond both in tension and in compression. The work on the analyzed bracing systems presents novel results on this type of bi-directional response and the effects derived from the pretension of the superelastic elements, within an analytic formulation of the mechanical response of the structure. It includes an example dealing with a full-scale glued laminated timber frame, which compares the responses of different bracing systems in terms of the lateral force vs. drift ratio curve and ductility factor. The beneficial effects deriving from the use of buckling-restrained devices in an inverted V-braced timber frame are discussed. The presented results highlight the high potential of superelastic braces with tensegrity architecture for the design of timber frames exhibiting markedly high ductility ratios, which considerably surpass those of full-timber or timber-steel systems. [ABSTRACT FROM AUTHOR]

An optimization approach based on force density method and mixed integer nonlinear programming is proposed for optimization of tensegrity structures on member connectivities and nodal positions. The member connectivities, nodal coordinates and force densities are simultaneously used as design variables and the number of nodes is the only necessary parameter needed to be given in advance. The proposed approach possesses a general-purpose formulation which can be degenerated into both conversional form-finding formulation and previous member connectivities-finding formulation. Various properties such as the number of cables, nodal coordinates and evenness of member internal forces can be controlled and optimized by introducing appropriate constraints and objective functions. Numerical examples are carried out to verify the proposed approach and illustrate that not only classical tensegrity systems but also novel tensegrity systems can be obtained by the proposed approach. [ABSTRACT FROM AUTHOR]

The paper introduces a modified symbiotic organisms search (mSOS) algorithm to optimization of pin-jointed structures including truss and tensegrity ones. This approach is refined from the original SOS with five modifications in the following three phases: mutualism, commensalism and parasitism. In the mutualism one, benefit factors are suggested as 1 to equally represent the level of benefit to each organism, whilst the best organism is replaced by a randomly selected one to increase the global search capability. With the aim of improving the convergence speed, randomly created coefficients in the commensalism phase are restricted in the range [0.4, 0.9]. Additionally, an elitist technique is applied to this phase to filter the best organisms for the next generation as well. Finally, the parasitism phase is eliminated to simplify the implementation and reduce the time-consuming process. To verify the effectiveness and robustness of the proposed algorithm, five examples relating to truss weight minimization with discrete design variables are performed. Additionally, two examples regarding minimization a function of eigenvalues and force densities of tensegrity structures with continuous design variables are considered further. Optimal results acquired in all illustrated examples reveal that the proposed method requires fewer number of analyses than the original SOS and the DE, but still gaining high-quality solutions. Furthermore, the mSOS also outperforms numerous other algorithms in available literature in terms of optimal solutions, especially for problems with a large number of design variables. [ABSTRACT FROM AUTHOR]