scholarly journals Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 374 ◽  
Author(s):  
Qian Zhang ◽  
Xinyu Wang ◽  
Jianguo Cai ◽  
Jingyao Zhang ◽  
Jian Feng
Keyword(s):  
Closed Form ◽  
The Self ◽  
Eigenvalue Decomposition ◽  
Force Density ◽  
Triangular Prism ◽  
Form Finding ◽  
Tensegrity Structures ◽  
Closed Form Solutions ◽  
Tensegrity Structure ◽  
Stable Conditions

An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.

Form-Finding of Tensegrity Structures with Boundary Constraints Using Parallel Computation of Singular Value Decomposition

2019 ◽  
Author(s):  
Xiaodong Feng ◽  
Shirong Huang ◽  
Can Chen ◽  
Yaozhi Luo ◽  
Sergio Zlotnik
Keyword(s):  
Singular Value Decomposition ◽  
Parallel Computation ◽  
Singular Value ◽  
Force Density ◽  
Form Finding ◽  
Tensegrity Structures ◽  
Boundary Constraints ◽  
Tensegrity Structure ◽  
Equilibrium Configurations ◽  
Value Decomposition

A novel analysis method is presented for form-finding of tensegrity structures subjected to boundary constraints. Dummy members are introduced to free the fixed nodes as to transform the tensegrity structure with boundary constraints into free-standing self-stressed system without supports. The geometrical topology, the dimension of the structure and the element prototype are the only information that is required in the proposed form-finding process. Parallel computation of singular value decomposition of the force density matrix and the equilibrium matrix are performed iteratively to seek the feasible sets of nodal coordinates and force densities. A rigorous definition is given for the required rank deficiencies of the force density and equilibrium matrices that lead to a stable non-degenrate d-dimensional self-stresssed tensegrity structure. Several illustrative examples are presented to demonstrate the efficiency and robustness in searching self-equilibrium configurations of tensegrity structures subjected to boundary constraints.

A Novel Ortho-Triplex Tensegrity Derived by the Linkage-Truss Transformation With Prestress-Stability Analysis Using Screw Theory

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Liheng Wu ◽  
Jian S. Dai
Keyword(s):  
Stability Analysis ◽  
Quadratic Form ◽  
Screw Theory ◽  
Structural Parameters ◽  
Triangular Prism ◽  
Tensegrity Structures ◽  
Tensegrity Structure ◽  
Revolute Joints ◽  
Rigidity Analysis

Abstract This paper presents a novel tensegrity structure derived from the tensegrity triplex (also called the simplex or regular triangular prism) by using the linkage-truss transformation. In this paper, the tensegrity triplex is first transformed into a 6R linkage with vertical members as revolute joints and is coined the triplex linkage. With this, a novel 6R linkage was derived, whose joint axes are perpendicular to the joint axes of the triplex linkage and is coined the ortho-triplex linkage. Rigidity analysis based on screw theory demonstrates that both obtained linkages with infinitesimal mobility are prestress stable. Finally, transforming the ortho-triplex linkage to a truss, by using cables for tensional members and struts for compressional members, leads to a novel tensegrity that is coined ortho-triplex tensegrity. A non-dimensional quadratic form is further provided to analyze the sensitivity of prestress-stability in terms of the structural parameters. The process of derivation of this novel tensegrity presents a new way of designing tensegrity structures with prestress-stability analysis based on screw theory.

scholarly journals Force Density Relation and Lightweight Modeling of Single Layer Tensegrity Structures

2020 ◽  
Author(s):  
Haoyu Yang ◽  
Ruiwei Liu ◽  
Ani Luo ◽  
Heping Liu ◽  
Chuanyang Li
Keyword(s):  
Single Layer ◽  
Force Balance ◽  
Connection Matrix ◽  
Force Density ◽  
Structural Parameter ◽  
Tensegrity Structures ◽  
Tensegrity Structure ◽  
Density Relation ◽  
Density Relationship ◽  
Vector Matrix

A mathematical model is established using the space coordinates of nodes and vector matrix of components to study the construction method and lightweight nature of single-layer tensegrity structures on the basis of their geometric parameters. Connection matrix and configuration of the single-layer tensegrity structures are built using MATLAB software. The force balance equations of nodes of a three-bar tensegrity structure are established by introducing the force-density method, and the force-density relationship amongst the components is analysed. Thus, the configuration principle of single-layer tensegrity structure is verified. The force-density relationship between the components in the single-layer tensegrity structure is obtained. The change rule of the force-density relationship in different single-layer tensegrity structures is also analysed. Notably, p-1 stable configurations are present in the p-bar tensegrity structure. The force-density relationships of these p-1 configurations are in symmetrical distribution, that is, the j-th and (p-j)th configurations have the same force-density relationship. The lightweight nature of the structure is studied using the force-density relationship between the components, and the optimal structural parameter relationship is obtained when the structure has the lightest mass.

A Mesomechanical Model for Brittle Deformation Processes: Part II

1989 ◽  
Vol 56 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Dragoslav Sumarac ◽  
Dusan Krajcinovic
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Inelastic Strain ◽  
The Self ◽  
Crack Interaction ◽  
Brittle Deformation ◽  
Closed Form Solutions ◽  
Consistent Model ◽  
Self Consistent ◽  
Deformation Processes

The approximate, closed-form solutions for the inelastic strain and compliances are derived for some simple plane stress and plane strain cases. The computations are performed for a model-ignoring crack interaction as well as for the case of the self-consistent model.

Genetically Finding Algorithm for a Tensegrity Structure

2012 ◽  
Vol 450-451 ◽  
pp. 861-864
Author(s):  
Buntara Sthenly Gan ◽  
Manabu Yamamoto
Keyword(s):  
Initial Structure ◽  
Form Finding ◽  
Numerical Examples ◽  
Tensegrity Structures ◽  
Fitness Evaluation ◽  
Tensegrity Structure ◽  
Connectivity Information ◽  
Design Variables ◽  
Structure Configuration ◽  
Initial Geometry

In the form-finding process of a tensegrity structure, some constraints and assumptions are usually introduced for initial geometry and/or pre-determined member types to ensure the uniqueness of solution. The tensegrity structures are indeterminate problems in most cases. In this study, a novel and versatile numerical form-finding procedure which requires only a minimal knowledge of initial structure configuration is adopted. The procedure needs only the prototype of each member, i.e. either compression or tension, and the connectivity information of members. The connectivity of members and its prototype information are encoded to form an individual population used in genetic algorithm searching problems. As for the fitness evaluation to each population, the existence of self-stressed state in each population is sought. At the end, some numerical examples are given to show the efficiency of the present study and its ability in searching new configurations of tensegrity structures with less design variables.

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