Design of Tensegrity Structures with Static and Dynamic Modal Requirements

Tensegrity structures, characterized by enhanced stiffness, slender struts, and superior buckling resistance, have found wide-ranging applications in fields such as engineering, architecture, art, biology, and robotics, attracting extensive attention from researchers. The form-finding process, a critical step in the design of tensegrity structures, aims to discover the self-equilibrated configuration that satisfies specific design requirements. Traditional form-finding methods based on force density often require repeated steps of eigenvalue decomposition and singular value decomposition, making the process complex. In contrast, this paper introduces a new intelligent form-finding algorithm that uses the force density method and combines the Coati optimization algorithm with Graph Neural Networks. This algorithm avoids the complex steps of eigenvalue and singular value decomposition and integrates the physical knowledge of the structure, making the form-finding process faster and more accurate. In this algorithm, various force densities are initially randomized and input into a trained Graph Neural Networks to predict a fitness function’s value. Through optimizing the constrained fitness function, the algorithm determines the appropriate structural force density and coordinates, thereby completing the form-finding process of the structure. The paper presents seven typical tensegrity structure examples and compares various form-finding methods. The results of numerical examples show that the method proposed in this paper can find solutions that align with the super-stable line more quickly and accurately, demonstrating its potential value in practical applications.

Tensegrity structures are three-dimensional networks of truss members loaded in tension or compression. The location of the end points of the truss members, denoted as the nodes, and the associated node-member connectivity matrices are the fundamental descriptors in the modeling and design of tensegrity structures. This paper presents systematic analytical formulas for such node locations and connectivity matrices for tensegrity plates of two different topologies. The formulas apply to plates of any thickness, diameter, and complexity. As application examples, dynamic simulations demonstrating a strategy for morphing the planar plates toward domes are studied. The presented formulas allow for efficient computations and can be employed in the numerical analysis and design of shape-controllable antennas and mirrors, architectural constructions, and other applications based on tensegrity plate and dome-like structures.

This paper presents a new approach to simultaneously obtain the optimal design parameters of tensegrity structures, including pre-stress force and sectional area of elements. The proposed method is based on minimizing the static compliance in terms of some linear and nonlinear constraints using a genetic algorithm tool. This work is devoted to optimize the concurrent cross sectional area of element and pre-stress of a tensegrity system which works under the applied external loading along with a fixed topology and shape. An increase in the rigidity of systems is one of the outcomes of modifying of tensegrity structures according to optimal design parameters. The validation, efficiency and characteristics of proposed algorithm to find the optimum values for design variables of tensegrity structures is tested through three known tensegrity structures.

While form-finding and optimization methods in shell structures have been widely advanced, discourses regarding an ideation process of how a designer or engineer may synthesize a precedent into novel designs have been less explored, as such ideation mainly relies on his/her intuition in representing structural problems. In this paper, we present a computational method to synthesize shell designs through the interplay between mechanical idealization and visual computation using traditional craft as a reference. Examples of how to generate a folding structure from weaving and tensegrity structure from folding show not only the way to convert craft logic from one type to another in shell structures but also the method to explicitly interpret the designer’s ideation process in generating a certain structural design.

This research investigates the optimisation of deployable antennas by focusing on material selection, structural design, and drive mode. Deployable antennas are crucial for applications such as satellite communication and remote sensing. The study aims to enhance their efficiency and reliability through a comprehensive optimisation approach. A systematic review identifies suitable materials based on mechanical, electrical, and environmental properties. The structural design analysis explores various deployment mechanisms, such as foldable, inflatable, and tensegrity structures. Additionally, the drive mode optimisation examines actuation methods, including motor-driven, shape memory alloy, and piezoelectric systems, assessing their precision, energy consumption, and adaptability. The findings contribute to the development of more efficient, reliable, and versatile deployable antennas, improving the capabilities of communication systems.

The functional capacity of the human lung as gas exchanger is to a large extent determined by structural design. Quantitative structure-function correlations can be established by morphometry. A very large surface of air-blood contact, together with a very thin tissue barrier, are required to permit adequate oxygen uptake under work conditions. However, these design features also pose problems, such as how to ventilate and perfuse this large surface evenly and efficiently, or how to ensure mechanical stability against surface forces with a minimum of supporting tissue. The discussion focuses on the extent to which novel design principles are used to overcome such problems by designing the airways as a fractal tree and the fibre support system as a tensegrity structure.

Nodal flexibility and kinematic indeterminacy analyses of symmetric tensegrity structures using orbits of nodes

Lightweight structures comprise of actual pieces or segments that give the crucial ability to function while weighing less than other possibilities as well. The aerospace industry invented this particular branch of expertise, which is sometimes referred to as lightweight engineering or lightweight construction. This paper focuses on how lightweight structures are developed and applied in the field of structural engineering which is essential to achieving the high standards and breakthroughs of modern science. Comparison is made depending on different types of lightweight materials such as titanium alloys, shape memory alloys, magnesium, aluminum alloys, and wood composites, benefits, and applications of each type of material are discussed. Recent technologies and innovations in the field of lightweight design are performed including deployable and morphing structures, 3D printing, embedded sensors and actuators, and advanced joining technologies. Moreover, research is also being done on these structure types of evolution, uses, and significance, as well as their design techniques and innovations. Truss, tensegrity, pantographic, cable, origami, and sandwich structures are identified by explaining their properties and working mechanisms. The usage of several lightweight structures in the fields of aerospace, robotics, civil engineering, architecture, automotive, and biomedicine is examined in this paper. Additionally, the comparison is made between the application of tensegrity, truss, pantographic, and sandwich structures in aircraft applications in detail, while the importance of shape morphing and deploying of pantographic and origami structures is explained in the field of aerospace and robotics. In addition, different types of bridge structures and architecture are mentioned according to applications of suspension cables, stayed cables truss structures, and tensegrity techniques. Furthermore, the paper covers the improvement of computational and numerical techniques in the analysis and design of lightweight structures including the force method, dynamic relaxation method, and finite element method (FEM), trends in optimization techniques and their applications are included mentioned sequential quadratic programming (SQP) and interior point optimization, with applications on different types of lightweight structures. Also, perspectives and future directions of lightweight design through sustainability and smart construction are taken into account, importance of lightweight design in the form of environment and innovation is clearly supported.

PurposeThis paper aims to propose a study on the static behavior of prismatic tensegrity structures and an innovative form for determining the effect of mechanical properties and geometric parameters on the minimal mass design of these structures.Design/methodology/approachThe minimal mass design in this paper considers a stable class-two tensegrity tower built through stable models. Using the proposed structures, comprehensive parametric studies are performed to examine the mass (in which the masses of joints are ignored), the mass ratio between a class-two tensegrity tower and a single element, both having the same diameter and length and afterward determine a reliable mass saving structure under various circumstances.FindingsThe simulations show that the mass ratio versus the number of units is a nonlinear regressive curve and predicts that the proposed model outperforms the standard model when the variation parameter considered is a vertical force. The difference in mass between these structures is visible when the gap gradually decreases while the number of units increases. On the geometrical aspect, the gap between the masses is not significant.Originality/valueThis paper helps to understand the influences of geometric parameters and the mechanical properties on the design of cylinder tensegrity structures dealing with a compressive force.

Design of tensegrity structures for supporting deployable mesh antennas

A reduced-order model for the dynamic and post-buckling behavior of tensegrity structures

Tensegrity structures represent a special class of spatial structures, having a continuous network of members in tension and a discontinuous network of members in compression. These members can serve simultaneously as sensors, actuators, and load carrying elements. Hence, structure and control design must be carried out together. This paper illustrates the use of tensegrity structures as adaptive structures. The paper addresses static design problems, presents the mathematical structure of the linear dynamic models, deals with the actuator locations, and integrates structure and controller design for output variance control problems. Through integration of static design, actuator selection and controller design, better performances are achieved compared with the case in which these tasks are carried out separately.

An optimization approach is presented for force design of tensegrity structures by enumeration of the vertices of the feasible region of the prestresses, which is defined as the linear combinations of the coefficients of the self-equilibrium force vectors. The unilateral properties of the stresses in cables and struts are taken into consideration. In order to design the stiffest structure against uncertain external loads as well as specific external loads, a multiobjective optimization problem is formulated for simultaneous maximization of the lowest eigenvalue of the tangent stiffness matrix and minimization of the compliance against a specified set of external loads. In the numerical example, Pareto optimal solutions are found by enumerating the vertices of the feasible region of prestresses of a tensegrity grid, and the monotonicity properties of the objective functions are investigated.

A novel method for topology design of tensegrity structures

Distribution and level of self-stress has a profound impact on the structural behavior of tensegrity systems. The problems associated with self-stress implementation preclude designing tensegrity structures for civil engineering application. To achieve the feasible self-stress state of a tensegrity shell structure, an efficient procedure based on solving an optimization problem in conjunction with multi constraint equations on group subdivisions is presented in the current study. Several tensegrity shell configurations are utilized to demonstrate the capability of the proposed procedure. The method provides superior performance compared with the other conventional methods of obtaining desired self-stress distributions. For a given shell configuration, group division is of paramount importance with respect to the regularity and uniformity of self-stress distributions.