Parametric Analysis of Tensegrity Plate-Like Structures: Part 1—Qualitative Analysis

Abstract

The study includes parametric analysis of special spatial rod grids called tensegrity plate-like structures. Tensegrity structures consist of only compression and tension components arranged in a system, whose unique mechanical and mathematical properties distinguish them from conventional cable–strut frameworks. Complete analysis of tensegrity structures is a two-stage process. The first stage includes the identification of self-stress states and infinitesimal mechanisms (qualitative analysis). The second stage focuses on the behaviour of tensegrities under external loads (quantitative analysis). In the paper, a qualitative analysis of tensegrity plate-like structures built with modified Quartex modules was conducted. Starting from a single-module structure, more complex cases were sequentially analysed. The different ways of plate support were considered. To carry out a qualitative assessment, a spectral analysis of the truss matrices and singular value decomposition of the compatibility matrix were used. The characteristic features of tensegrity structures were identified. On this basis, the plates were classified into one of the four groups defined in the paper, i.e., ideal tensegrity, “pure” tensegrity and structures with tensegrity features of class 1 or class 2. This classification is important due to different behaviours of the structure under external actions. The qualitative analysis carried out in the paper is the basis for a quantitative analysis.

Qualitative and quantitative analysis of tensegrity domes

“…The most common methods were described in [35]. The methods often used include, e.g., the spectral analysis of linear stiffness matrix, the analytical solutions, the force density method, the dynamic relaxation, and the singular value decomposition (SVD) of the compatibility matrix B [29,30,34,36]. The SVD method is considered due to its ease of application and can be used both for simple and more complex structures.…”

Dynamic Stability of Tensegrity Structures—Part I: The Time-Independent External Load

“…To illustrate the behavior of the structures characterized by self-stress states and infinitesimal mechanisms, the simplest truss consisting of two elements is considered ( Figure 2 a) [ 33 , 34 ]. The elements are characterized by the Young modulus , the cross-sectional area and the length .…”

The application of the immanent tensegrity properties to control the behavior of double-layered grids

“…It should be noted that the self-stress states also occur in geometrically invariable structures. In the paper, the finite elements method is used [8][9][10][11][12]. In a global coordinate system (𝑥, 𝑦, 𝑧), a finite element 𝑒 is described by a Young's modulus 𝐸 𝑒 , a cross-sectional area 𝐴 𝑒 , a length 𝐿 𝑒 and by a compatibility matrix B 𝑒 (∈ R 1×6 ) [11,13]:…”