# Parametric Analysis of Tensegrity Plate-Like Structures: Part 2--Quantitative Analysis
## 5 Summary and Conclusions  
The quantitative evaluation of truss structures presented in this paper was used for the assessment of the behaviour of tensegrity plate-like structures. The complete analysis of tensegrity structures is a two-stage process. The quantitative analysis carried out in this paper is the second stage and completes the qualitative analysis [45], which is the first stage. Defined in [45], the unique properties and the proposed classification of tensegrity structures (tenesgrities were divided into four classes) are important due to the different behaviours of the structure under external actions. In this paper, it is proved that the stiffness of ideal and \"pure\" tensegrity structures and structures with tensegrity features of class 1 (structures in which mechanisms are identified) depends not only on the geometry and material properties, but also on the prestress level and external loads. However, it should be emphasized that the influence of self-equilibrium force system on the stabilization of the structure can be demonstrated only at the load that causes the displacements consistent with the infinitesimal mechanism. In other cases, the displacements are insensitive to changes of the prestress level. The existence of a state of self-stress in structures with tensegrity features of class 2 (structures in which mechanisms are not identified) allows for prestressing them, but they are insensitive to changes in the force level. In this paper, a static parametric analysis of plates built with modified Quartex modules was carried out. Starting from a single-module structure, more complex cases were sequentially analyzed. The influence of the initial prestress level on the displacements, the effort and the stiffness of the structure was studied. For the determination of the structural stiffness, the global stiffness parameter (\(GSP\)) was proposed. This parameter determines the impact of self-stress state on the total rigidity of the structure at a given load. The calculation procedure, including the analysis of geometrically non-linear rod systems, was written in the Mathematica environment. The program makes it possible to freely define the geometry of the structure, material parameters, and loads, and then identify the self-stress state and track the behaviour of selected static and geometric parameters in the function of this state. Before proceeding with the quantitative analysis of the tensegrity structure, a qualitative assessment is required. It leads to the classification of tensegrity structures. Stiffness control is possible only in structures characterized by the presence of an infinitesimal mechanism, which is the case of ideal or \"pure\" tensegrities and structures with tensegrity features of class 1. The stiffness of these structures depends not only on the geometry and material properties, but also on the prestress level (which stabilizes the infinitesimal mechanisms that occur) and the level of external load. External load induces additional stress in the system, and the impact of the load is most significant for the low values of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(S\)**[kN]**} & \multirow{2}{*}{**Type of Element**} & \multicolumn{3}{c}{**Model \(P64\)-1 (\(S_{\text{min}}\)=16 kN)**} & \multicolumn{3}{c}{**Model \(P64\)-2 (\(S_{\text{min}}\)=45 kN)**} & \multicolumn{3}{c}{**Model \(P64\)-3 (\(S_{\text{min}}\)=38 kN)**} \\ \cline{3-10}  & & \(N_{\text{max}}\) & \(W_{\text{max}}\) & \(GPS\) & \(N_{\text{max}}\) & \(W_{\text{max}}\) & \(GPS\) & \(N_{\text{max}}\) & \(W_{\text{max}}\) & \(GPS\) \\  & & [**kN**] & [\(-\)] & [\(-\)the initial prestress forces. As the level of prestress increases, the effect of the external load decreases. Moreover, the initial prestress forces have a greater influence on the total stiffness of the structure with smaller external loads. Similarly, like for stiffness of tensegrity structures, in the case of effort, the influence of self-stress state decreases with increasing loads.