Form-finding of tensegrity structures via rank minimization of force density matrix

2021 ◽  
Vol 227 ◽  
pp. 111419
Author(s):  
Yafeng Wang ◽  
Xian Xu ◽  
Yaozhi Luo
Keyword(s):  
Density Matrix ◽  
Force Density ◽  
Rank Minimization ◽  
Form Finding ◽  
Tensegrity Structures

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.

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.

Analytical form-finding of tensegrities using determinant of force-density matrix

2018 ◽  
Vol 189 ◽  
pp. 87-98 ◽  
Author(s):  
Li-Yuan Zhang ◽  
Shi-Xin Zhu ◽  
Song-Xue Li ◽  
Guang-Kui Xu
Keyword(s):  
Density Matrix ◽  
Analytical Form ◽  
Force Density ◽  
Form Finding

Form-finding design of electrostatically controlled deployable membrane antenna based on an extended force density method

2018 ◽  
Vol 152 ◽  
pp. 757-767 ◽  
Author(s):  
Yongzhen Gu ◽  
Jingli Du ◽  
Dongwu Yang ◽  
Yiqun Zhang ◽  
Shuxin Zhang
Keyword(s):  
Force Density ◽  
Form Finding ◽  
Density Method ◽  
Force Density Method
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