Abstract
Numerical form-finding is an effective method for determining the equilibrium configurations of tensegrity structures. However, the connectivity matrix is required to be input as initial data in most form-finding methods, and it is time-consuming and inconvenient for the designer in processing a complex structure with a large number of components. To address this issue, a novel automatic method of generating a connectivity matrix is proposed for three dimensional N-4 type tensegrity structures in this paper. The novelty of our algorithm is that the number of nodes is the only required parameter for the proposed method. Numerical examples are employed to validate our method. The results show that the proposed method is competent inform-finding for three-dimensional N-4 type tensegrity structures in terms of accuracy, efficiency and convergence.
Highlights
Tensegrity structure, first proposed by Fuller (1962), is a spatially stable structure consisting of discontinuous compression struts inside a set of continuous tension cables
Different analytical and numerical methods have been proposed for the form-finding of tensegrity structures (Masic et al.,2005, Koohestani, 2012, Ali et al, 2011, Cai and Feng, 2015), Tibert and Pellegrino classified these methods into two categories: kinematical and statical methods, and discussed their advantages and limitations (Tibert and Pellegrino, 2003)
The nodal connectivity is the last information required in the procedure of automatic form-finding of tensegrity structures
Summary
Tensegrity structure, first proposed by Fuller (1962), is a spatially stable structure consisting of discontinuous compression struts inside a set of continuous tension cables. The nodal connectivity, the initial force densities and the types of members (i.e., either strut or cable) are required to be input as initial data in most form-finding methods. The nodal connectivity is the last information required in the procedure of automatic form-finding of tensegrity structures. The rank deficiency of AA should be equal to or larger than 1, namely, the rank of AA should be defined as: rAA = rank(AA) < bb (12) In this condition, at least a non-trivial solution is guaranteed for force density vector qq or one state of self-stress. ※Stage 1: Recursively generate incidence matrices and delete isomorphic matrices, as described in Section 4.1. ※Stage 2: Assign initial force density coefficients by searching for strut candidates and specify member types, as discussed in Section4.2. ※Stage 3: Find out feasible sets of nodal coordinates and force density coefficients by performing eigenvalue decomposition of force density matrix and singular value decomposition of the equilibrium matrix, as discussed in Sec-tion 4.3. ※stage 4: List all configurations of form-finding for selecting to designers
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