# Parametric Analysis of Tensegrity Plate-Like Structures: Part 2--Quantitative Analysis
## 4 Examples
### Single Modified Quarex Module  
The first considered structure is a single modified Quarex module (Figure 2a). This module is classified as the ideal tensegrity with one mechanism \(\mathbf{x}_{16}\) and one self-stress state \(\mathbf{y}_{16}\) (Figure 2b) [45]. The minimum prestress level is assumed as \(S_{\text{min}}~{}=~{}0.01\) kN, whereas the maximum--\(S_{\text{max}}~{}=~{}110\) kN. The module is loaded with a \(z\)-directional force applied to 8 th node. Three cases of a load value \(P_{24}^{1}~{}=~{}-10\) kN, \(P_{24}^{2}~{}=~{}-15\) kN, and \(P_{24}^{3}~{}=~{}-20\) kN are considered. The influence of the initial prestress level \(S\) on the non-zero displacements of the eighth node (\(q_{22},~{}q_{24}\)), the global stiffness parameter (\(GSP\)), and the effort (\(W_{max}\)) is illustrated in Figure 3. Additionally, in Table 1, values of analyzed static parameters for the minimum and maximum prestress level are shown. Figure 2: _Cont._  
The values of the displacements obtained from the static analysis correspond to the values of the displacement of the mechanism \((x_{22},\ x_{24})\) identified in [45]. The \(x\)-directional displacement (\(q_{22}\)) is two times bigger than the \(z\)-directional one (\(q_{24}\)), and that tendency is preserved for all levels of the external load (Figure 3a,b). The differences between values of the displacements obtained using the second (II) and third (III) order theory are significant when the prestress level is low. As the values of prestressing forces increase, the differences between the calculations made according to the second and third order theory are becoming smaller. This means that the effect of non-linearity is most significant at low values of the initial prestress forces. The differences between theories are also more significant for higher external load. For example, for the minimum prestress level \(S_{\text{min}}\) and the smallest values of external load (\(P_{24}^{1}\ =\ -10\) kN) relative error (which is a relative difference between the displacements in reference the third order theory) is equal to \(2.9\cdot 10^{5}\%\) (\(q_{22}\)) and \(2.8\cdot 10^{5}\%\) (\(q_{24}\)), whereas for the largest values of external load (\(P_{24}^{3}\ =\ -20\) kN) relative error is equal to \(4.5\cdot 10^{5}\%\) (\(q_{22}\)) and \(4.3\cdot 10^{5}\%\) (\(q_{24}\)). With the increase of the prestress level, differences become less significant. For the maximum prestress level \(S_{\text{max}}\) and \(P_{24}^{1}\ =\ -10\) kN, relative error is equal to \(0.71\%\) (\(q_{22}\)) and \(0.22\%\) (\(q_{24}\)), whereas for \(P_{24}^{3}\ =\ -20\) kN, \(4.45\%\) (\(q_{22}\)) and \(3.34\%\) (\(q_{24}\)). This means that the effect of non-linearity is the most significant at low values of the initial prestress forces. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{\(S\)**} & \multirow{2}{*}{**Type of**} & \multicolumn{3}{c}{\(P_{24}^{1}\)**=\(-\)**10 kN**} & \multicolumn{3}{c}{\(P_{24}^{2}\)**=\(-\)**15 kN**} & \multicolumn{3}{c}{\(P_{24}^{3}\)**=\(-\)**20 kN**} \\ \cline{2-11}  & & \(N_{max}\) & \(W_{max}\) & \([\)**kN**\(]\) & \([-]\) & \([\)**kN**\(]\) & \([-]\) & \([\)**kN**\(]\) & \([-]\) & \([\)**kN**\(]\) & \([-]\) & \([\)**GPS** \\ \hline \multirow{2}{*}{0.01} & cables & 26.5 & 0.241 & \multirow{2}{*}{1.0} & 35.7 & 0.324 & \multirow{2}{*}{1.0} & 44.1 & 0.400 & \multirow{2}{*}{1.0} \\ \cline{2-11}  & struts & \(-\)35.6 & 0.184 & & \(-\)47.8 & 0.246 & & 59.1 & 0.305 & \\ \hline \multirow{2}{*}{110} & cables & 87.3 & 0.792 & \multirow{2}{*}{3.7} & 91.1 & 0.826 & \multirow{2}{*}{2.9} & 95.3 & 0.865 & \multirow{2}{*}{2.5} \\ \cline{2-11}  & struts & \(-\)117.2 & 0.604 & & \(-\)122.2 & 0.630 & & \(-\)128.0 & 0.660 & \\ \hline \end{tabular}
\end{table} 
Table 1: Load-bearing characteristics of the single modified Quartex module. Figure 2: The single modified Quartex module: (**a**) geometry, (**b**) normalised self-stress state \(\mathbf{y}_{16}\).