# Parametric Analysis of Tensegrity Plate-Like Structures: Part 2--Quantitative Analysis
## 4 Examples
### Four-Module Tensegrity Plate-Like Structures
Similarly to the single module, there is significant difference in the values of the displacements obtained from the analysis using the second (II) and third (III) order theory (Figure 5). For instance, for \(S_{\rm min}\) relative error in the case of the displacement \(q_{39}\) for the analyzed models is, respectively, equal to 1988%, 2.44\(\cdot\)10\({}^{5}\)%, and 2917%, whereas for \(S_{\rm max}\), relative error is smaller and equal to 5.81%, 0.13%, and 10.32%, respectively. Analogous to the single module, the displacement in the \(x\) direction is two times higher than the displacement in the \(z\) direction. According to the second order theory, the displacement \(q_{15}\) is not dependant on the level of the initial prestress and equal to almost zero (for all models this displacement in mechanisms is equal to zero). However, calculations performed according to the third order theory show that in fact that displacement is correlated with the level of the initial prestress. The displacement is not equal to zero, but still remains small. Based on Figure 6a and Table 2, it can be concluded that the model P4-2 is the stiffest one. On average, the increase of the level of the initial prestress by 1 kN causes the increase of \(GSP\) by 0.024. For the model P4-1, the same increase in the level of the initial prestress causes the increase of \(GSP\) by 0.019, whereas for model P4-3 it increases by 0.015. The model P4-3 is significantly less stiff than the models P4-1 and P4-2. Comparing the direction of supports, all models supported along the \(x\) direction are more rigid. The values of the effort of the structure, these obtained for the models P4-1 and P4-2, are comparable, whereas those for the model P4-3 are higher (Figure 6b). For example, the difference in values of the effort for \(S_{\rm min}\) between the models P4-2 and P4-3 is equal to 5.1 percentage points for cables and 2.3 for struts, whereas for \(S_{\rm max}\) it is, respectively, 3.7 and 1.8 percentage points. Analogous to the single module, for all models, the effort of cables is higher than of struts, and the difference increases with the increment of the prestress level. For example, for the model P4-3, the effort of cables is 57.4% higher than of struts for \(S_{\rm min}\) and 59.7% for \(S_{\rm max}\). Figure 6: Impact of the initial prestress level \(S\) on the: (**a**) global stiffness parameter \(GSP\), (**b**) effort of structure \(W_{\rm max}\). In the case of the models P4-4 and P4-5, the minimum prestress level are assumed, respectively, as \(S_{\text{min}}~{}=~{}34\) kN and \(S_{\text{min}}~{}=~{}0.55\) kN. For these models, the displacements of the corresponding bottom (\(q_{18}\) for the model P4-4 and \(q_{24}\) for the model P4-5) and top (\(q_{57}\) for the model P4-4 and \(q_{60}\) for the model P4-5) nodes on free edge are compared \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(S\)} & \multirow{2}{*}{**Type of**} & \multicolumn{3}{c}{**Model P4-4 (\(S_{\text{min}}\) = 34 kN)**} & \multicolumn{3}{c}{**Model P4-5 (\(S_{\text{min}}\) = 0.55 kN)**} \\ \cline{3-8}  & & \(N_{\text{max}}\) & \(W_{\text{max}}\) & \(GPS\) & \(N_{\text{max}}\) & \(W_{\text{max}}\) & \(GPS\) \\ \cline{3-8}  & & [kN] & [\(-\)] & [\(-\)] & [kN] & [\(-\)] & [\(-\)] \\ \hline \multirow{2}{*}{\(S_{\text{min}}\)} & cables & 57.7 & 0.524 & \multirow{2}{*}{1.0} & 54.1 & 0.491 & \multirow{2}{*}{1.0} \\ \cline{2-2} \cline{5-8}  & struts & \(-\)46.3 & 0.239 & & \(-\)50.1 & 0.258 & & \\ \hline \multirow{2}{*}{60} & cables & 93.2 & 0.846 & \multirow{2}{*}{1.4} & 105.2 & 0.954 & \multirow{2}{*}{1.9} \\ \cline{2-2} \cline{5-8}  & struts & \(-\)73.1 & 0.376 & & \(-\)77.0 & 0.397 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Load-bearing characteristics of the models P4-4 and P4-5. Figure 7: Impact of the initial prestress level \(S\) on the: (**a**) bottom nodes’ displacements, (**b**) top nodes’ displacements, (**c**) global stiffness parameter \(GSP\), (**d**) effort of structure \(W_{\text{max}}\). (Figure 7a,b).