Form-finding Of Tensegrity Structures Research Articles

Effects of prestress implementation on self-stress state in large-scale tensegrity structure

Tensegrity structures are spatial, reticulated, and lightweight structures that are composed of struts and cables. Stability is provided by a self-stress state between tensioned and compressed members obtained by prestress. Although the form finding of tensegrity structures has attracted significant attention, few studies have focused on the structural concept implementation in large-scale systems and prestress implementation in particular. This work investigates the effects of the prestress implementation on the self-stress state in a large-scale tensegrity structure with interconnected struts. The suspended, 6.2-m-tall structure consists of stainless steel cables and carbon-fiber composite tubes. Different uniform and non-uniform prestress and support condition scenarios were applied and the effects on the self-stress state were investigated experimentally by measuring strains in the carbon tubes, stresses in cables, and reaction forces. Numerical modeling was performed using the dynamic relaxation method, whose predicted stress values were compared to experimental data. The results revealed that the cable-by-cable prestress implementation led to lower effective prestress levels than nominally predicted due to a continuous stress redistribution. Non-uniformly applied prestress resulted in a uniform stress state due to the same continuous stress redistribution. Small joint restrictions in rotational angles and small joint friction hindered geometry and stress distribution from changing when the support conditions changed. The importance of extending the analysis of tensegrity structures beyond form finding and sizing is thus demonstrated; prestress implementation and joint design also need attention.

Cellular morphogenesis of three-dimensional tensegrity structures

The topology and form finding of tensegrity structures have been studied extensively since the introduction of the tensegrity concept. However, most of these studies address topology and form separately, where the former represented a research focus of rigidity theory and graph theory, while the latter attracted the attention of structural engineers. In this paper, a biomimetic approach for the combined topology and form finding of spatial tensegrity systems is introduced. Tensegrity cells, elementary infinitesimally rigid self-stressed structures that have been proven to compose any tensegrity, are used to generate more complex tensegrity structures through the morphogenesis mechanisms of adhesion and fusion. A methodology for constructing a basis to describe the self-stress space is also provided. Through the definition of self-stress, the cellular morphogenesis method can integrate design considerations, such as a desired shape or number of nodes and members, providing great flexibility and control over the tensegrity structure generated.

Overview on the Form-Finding of Tensegrity Structure

This paper presents an overview of the previous research on the form finding structures which include tensegrity and biotensegrity structure. Tensegrity systems have been widely used for many applications due to the stability and flexibility of the structures. On technologies era nowadays, a stable structure is needed to implement for new developments especially robotics and machineries. Therefore, the importance of finding the shape or design configuration is to ensure it is in self-equilibrium which able to support itself. In order to build new structures which lies on general requirement, previous researchers have proposed several form-finding methods for instance by using force density method, advance force density method, finite element method, dynamic relaxation method, genetic algorithm, novel linear approach and Monte Carlo method. What kind of stable structures can be produced and how efficient the structures by using those methods? In this paper, understanding on the form-finding methods and various numerical examples of form-finding conducted in previous studies are presented to enhance researchers’ knowledge on the form-finding of tensegrity structures.

A Genetic Algorithm Based Form-finding of Tensegrity Structures with Multiple Self-stress States

A form-finding method of tensegrity systems is a process of finding an equilibrium configuration and a key step in the design of tensegrity. Over the past few years, several studies have been made on the form-finding methods of tensegrity systems, however, these methods are limited in the tensegrity systems with multiple self-stress states. In this study, a numerical method is presented for form-finding of tensegrity structures with multiple states of self-stress by using a force density method combined with a genetic algorithm. The proposed method can design the desired tensegrity shape through a genetic algorithm with appropriate constraints. The design variable can be uniquely defined in the case of multiple states of self-stress using only the constraint of the member types. An eigenvalue decomposition of the force density matrix and a singular value decomposition of the equilibrium matrix are performed repeatedly in order to determine a feasible solution for nodal coordinates and force densities. A genetic algorithm is then adopted to uniquely define a single integral feasible set of force densities. Several numerical examples are presented to prove efficiency in searching for self-equilibrium configurations of tensegrity structures. In all cases, the single integral feasible self-stress states can be obtained.

Form-finding of tensegrity structures using an optimization method

The process of finding an equilibrium configuration, called form-finding, is a key step in the design of a tensegrity structure. An efficient form-finding method based on the optimization method is proposed for regular and non-regular tensegrity structures. The force densities of a tensegrity are obtained by minimizing a special objective function, which satisfies the non-degeneracy necessary condition. Two examples, planar and spatial tensegrity structures, are used to prove the efficiency of the proposed method. It can be found that the results of regular tensegrity are the same as those given by the analytical method in the literatures.

유전알고리즘과 내력밀도법을 결합한 새로운 형상탐색방법

Tensegrity structures are pre-stressed pin-joint structures inclusive tensile members and compressive members. Form-finding is very important for Tensegrity structures need to determine shape and pre-stress value for self-equilibrium. In the form-finding of tensegrity structures, Infomation are usually introduced for initial geometry and pre-determined member types. In this study, Form-finding of tensegrity structures by using genetic easy and versatile form-finding processing requires only a minimal information 'topology'. Genetic Algorithms was determined the type of members. The form-finding of tensegrity structures are found by a full iteration pocedure until a state of self-stress is obtained.

Form-finding of tensegrity structures with arbitrary strut and cable members

An advanced form-finding method for tensegrity structures is presented. In the present study, determining an appropriate candidate for strut members using the discontinuity condition of struts is performed. Additionally, the self-equilibrium and stability properties of tensegrity structures are obtained by using the force density method combined with a genetic algorithm. The proposed algorithm is effectively capable of searching for appropriate strut candidates with limited information in nodal connectivity. Appropriate member types and a feasible set of the nodal coordinates and the force densities can be found efficiently. Based on numerical examples, it is found that the proposed method is very efficient and robust in searching the self-equilibrium configuration of tensegrity structures.

Form finding of tensegrity structures using finite elements and mathematical programming

Form finding of tensegrity structures using finite elements and mathematical programming

Novel Form-Finding of Tensegrity Structures Using Ant Colony Systems

Tensegrity structures have remarkable configurations and are drawing the attention of architects and engineers. They possess inextensional mechanisms and self-stress states at a static equilibrium configuration under no external loads. For geometry with its nodes fixed, different connectivity patterns of the compression bars and tension cables might bring some novel tensegrity structures. Thus, form-finding is the key to designing novel tensegrity structures. Here, we develop a discrete optimization model for the form-finding and convert it into a modified traveling salesman problem (TSP). The ant colony system (ACS) is used to search for feasible solutions, where all the predetermined nodes are taken as different cities in the network. An objective function that considers the stability and the relative stiffness is developed to obtain the optimized configurations of tensegrity structures. Examples based on some regular geometries (including a hexagon and two polyhedra) and two nonregular geometries are carried out using the proposed technique. Many different configurations of the pin-jointed assemblies are transformed into interesting tensegrity structures. To verify the proposed method, some physical models are constructed and compared to the tensegrity structures obtained from the form-finding process. We conclude that this novel algorithm can be applicable to the form-finding of both regular and nonregular tensegrity structures.

Form-finding of tensegrity structures using double singular value decomposition

A numerical form-finding procedure of tensegrity structures is developed. The only required information is the topology and the types of members. The singular value decompositions of the force density and equilibrium matrices are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required deficiencies of these two matrices, respectively. An approach of defining a unique configuration of tensegrity structure by specifying an independent set of nodal coordinates is provided. An explanation is given for the preservation in self-equilibrium status of the tensegrity structures under affine transformation. Two- and three-dimensional examples are illustrated to demonstrate the efficiency and robustness of the proposed method in searching stable self-equilibrium configurations of tensegrity structures.

Recent advances in configurations in spatial structures

This paper presents a summary of the author's recent work on the configuration of spatial structures. To better satisfy architecture and engineering requirements, the paper introduces a technique of reconstructing freestyle 3D objects with grid space structures. With this technique, irregular and complex configurations can be easily modelled, which has a great potential in modelling of sculptures and bionic structures. Then several new types of deployable structures, which are based on linkage mechanisms including Bricard linkages and double chain linkages, are proposed. The kinetic behaviour of these deployable structures is investigated by geometrical analysis. And their possible applications in retractable roofs are also explored. Meanwhile, the paper proposes a practical application of structures with changeable configurations – a novelty erection technology based on expandable mechanisms. Finally, the paper presents some new advances in form-finding of tensegrity structures and shape control of tensegrity structures.