# Parametric Analysis of Tensegrity Plate-Like Structures: Part 2--Quantitative Analysis
## 4 Examples
### Four-Module Tensegrity Plate-Like Structures  
The structure built with the four modified Quartex modules (Figure 4a) is considered in succession. Ten models (models: P4-1-P4-10) with different ways of support were considered in Part 1 [45]. The quantitative analysis shows that the initial prestress level \(S\) influences on static parameters only when infinitesimal mechanisms occur in the structure. It means that the control of static parameters is possible only if the structure is the ideal tensegrity, \"pure\" tensegrity, or the structure with tensegrity features of class 1. Five out of ten considered models feature the presence of the mechanisms (structures with tensegrity features of class 1), i.e., the models: P4-1-P4-5 (Figure 4b), so the results for these models are shown in this paper. For comparison, the results for the structure with tensegrity features of class 2 (in this structure mechanism does not occur)--the model P4-10 (Figure 4c)--are also presented. The minimum prestress level depends on way of support, whereas the maximum is assumed as \(S_{\text{max}}~{}=~{}60\) kN. The models P4-1-P4-3 are loaded by uniformly distributed load \(q~{}=~{}-10\) kN/m\({}^{2}\) applied on the top surface of the structure, whereas the models P4-4 and P4-5 are loaded by two concentrated \(z\)-directional forces \(P~{}=~{}-5\) kN applied to the top nodes on the free edge. For the model P4-4, forces were applied to the 18 th and 19 th nodes (\(P_{54}~{}=~{}P_{57}~{}=~{}P\)), and for the model P4-5, to the 20 th and 21 st nodes (\(P_{60}~{}=~{}P_{63}~{}=~{}P\)). For the models P4-1-P4-3, the influence of the initial prestress level \(S\) on some displacements are illustrated in Figure 5, whereas the influence on the effort (\(W_{max}\)) and the global stiffness parameter (\(GSP\)) are shown in Figure 6. Additionally, the values of the analyzed static parameters for the minimum and maximum prestress level are shown in Table 2. The results of analysis for the models P4-4 and P4-5 are presented in Figure 7 and in Table 3.  
Figure 4: Four-module tensegrity plate-like structure: (**a**) geometry, (**b**) models of structures with tensegrity features of class 1, and (**c**) model of structure with tensegrity features of class 2. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(S\)} & \multirow{2}{*}{
\begin{tabular}{c} **Type of** \\ **Element** \\ \end{tabular} } & \multicolumn{3}{c}{**Model P4-1 (\(S_{\text{min}}\) = 1.15 kN)**} & \multicolumn{3}{c}{**Model P4-2 (\(S_{\text{min}}\) = 0.01 kN)**} & \multicolumn{3}{c}{**Model P4-3 (\(S_{\text{min}}\) = 1.4 kN)**} \\ \cline{2-11}  & & \(N_{max}\) & \(W_{max}\) & \(GPS\) & \(N_{max}\) & \(W_{max}\) & \(GPS\) & \(N_{max}\) & \(W_{max}\) & \(GPS\) \\  & & [**kN**] & [\(-\)] & [\(-\)] & [**kN**] & [\(-\)] & [\(-\)] & [\(-\)] & [\(kN\)] & [\(-\)] & [\(-\)] \\ \hline \multirow{2}{*}{\(S_{\text{min}}\)} & cables & 49.54 & 0.450 & \multirow{2}{*}{1.0} & 48.8 & 0.443 & \multirow{2}{*}{1.0} & 54.4 & 0.493 & \multirow{2}{*}{1.0} \\ \cline{2-11}  & struts & \(-\)37.0 & 0.191 & & \(-\)36.6 & 0.189 & & \(-\)41.0 & 0.211 & \\ \hline \multirow{2}{*}{60} & cables & 100.5 & 0.912 & \multirow{2}{*}{2.1} & 101.5 & 0.921 & \multirow{2}{*}{2.4} & 105.6 & 0.958 & \multirow{2}{*}{1.9} \\ \cline{2-11}  & struts & \(-\)71.2 & 0.367 & & \(-\)71.93 & 0.371 & & \(-\)75.4 & 0.389 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Load-bearing characteristics of the models P4-1–P4-3. Figure 5: Impact of the initial prestress level \(S\) on the displacements: (**a**) \(q_{37}\), (**b**) \(q_{39}\), (**c**) \(q_{15}\). In the case of the models P4-1-P4-3, the lowest minimum level of the initial prestress is observed for the model P4-2, whereas the highest is the model P4-3. The minimum level of the initial prestress for these models are, respectively, \(S_{\rm min}~{}=~{}0.01\) kN and \(S_{\rm min}~{}=~{}1.4\) kN. For the model P4-1, the minimum level of the initial prestress is equal to \(S_{\rm min}~{}=~{}1.15\) kN.