# Parametric Analysis of Tensegrity Plate-Like Structures: Part 2--Quantitative Analysis
## 4 Examples
### Sixteen-Module Tensegrity Plate-Like Structures and Plate Strips  
The plate consisting of the sixteen modified Quartex modules (Figure 10a) is taken into account as the next. Six models (models: P16-1-P16-6) with different ways of support were considered in Part 1 [45]. One of them, i.e., the model P16-1 (Figure 10b), is the structure with tensegrity features of class 1. The quantitative analysis is carried for this model and, for comparison, for the structure with tensegrity features of class 2--the model P16-2 (Figure 10c). The minimum prestress level depends on the way of support, whereas the maximum is assumed as \(S_{\text{max}}~{}=~{}60\) kN. Figure 8: Impact of the initial prestress level \(S\) on the displacements: (a) \(q_{37}\), (b) \(q_{39}\), (c) \(q_{15}\). Figure 9: Impact of the initial prestress level \(S\) on the: (a) global stiffness parameter \(GSP\), (b) effort of structure \(W_{\text{max}}\). Simultaneously, plate strips built with four modified Quartex modules are analyzed. The qualitative analysis [45] showed an analogy between the corresponding models of sixteen-module plates and plate strips (i.e., P16-1 and PS-1, P16-2 and PS-2, etc.). Therefore, simply supported and cantilever plate strips are analyzed for comparison. The support along the \(x\) and \(y\) axes is considered, it means four models, i.e., PS-1x, PS-1y and PS-2x, PS-2y (Figure 11) are compared. The simply supported models (P16-1, PS-1x, PS-1y) are loaded by uniformly distributed load \(q~{}=~{}-10~{}\mathrm{kN/m^{2}}\) applied on the top surface of the structure, whereas the cantilever models (P16-2, PS-2x, PS-2y)--by \(z\)-directional forces \(P_{z}~{}=~{}-5~{}\mathrm{kN}\) applied to the top nodes on the free edge. The influence of the initial prestress level \(S\) on some displacements is showed in Table 4.  
Based on Table 4, it can be noticed that there is no significant difference in the results, thus the use of the simplified plate strip models instead plate is legitimate. In the case of the simply supported models, which are featured by the presence of the mechanisms, the initial prestress level \(S\) influences on the displacements. Additionally, for the lower levels of the initial prestress, there are significant differences in the results obtained according to the second (II) and the third (III) order theory. For example, relative errors for the displacement \(q_{39}\) for \(S_{\mathrm{min}}\) is equal 1258% and for \(S_{\mathrm{max}}\)--1.19%. In the case of the cantilever models (without mechanisms) the initial prestress level \(S\) does not influence on the displacements, and the second order theory is sufficient for the purpose of analysis. Figure 11: Models of the tensegrity plate strips. Figure 10: Sixteen-module tensegrity plate-like structure: (**a**) top view, (**b**) model of structures with tensegrity features of class \(1\), (**c**) model of structures with tensegrity features of class \(2\). In qualitative analysis [45], the direction of support does not matter, as the number of mechanisms and self-stress states is the same. In this paper, a support along the \(x\) and \(y\) axes in plate strips is considered. For example, in Table 5, the load-bearing characteristics of the models PS-1x and PS-1y are presented. It can be seen that also in the quantitative analysis, the direction of the support of four-module plate practically does not influence the results. At the end, the influence on the initial prestress level \(S\) on the global stiffness parameter \(GSP\) (Figure 12a) and the effort of the structure \(W_{max}\) (Figure 12b) are presented. The results confirm previous conclusions. In the case of the models with mechanisms, i.e., PS-1x and PS-1y, the initial prestress level \(S\) influences the global stiffness parameter. The increase of the level of the initial prestress by 1 kN causes that \(GSP\) increases by 0.20.