# Parametric Analysis of Tensegrity Plate-Like Structures: Part 1--Qualitative Analysis
## 5 Conclusions  
The qualitative evaluation of truss structures presented in this paper was done for the assessment of the tensegrity plate-like structures. The qualitative analysis leads us to define the unique properties of tensegrities, which allow for the control of static and dynamic parameters. With regard to structural mechanics, the uniqueness of tensegrity structures lies in the existence of self-stress states (\(S\)) and mechanisms (\(M\)). The other features, i.e., the discontinuity of struts (\(D\)) and the inclusion of struts by tension elements (\(I\)), which are cables with no rigidity in compression (\(C\)), are determined indirectly by the identified self-stress state. Based on the presence of the characteristic tensegrity features \(T\), \(S\), \(C\), \(M\), \(D\) and \(I\), a four-category classification was proposed. The structures were classified as ideal tensegrities, \"pure\" tensegrities and structures with tensegrity features of class 1 or 2. Plates built with modified Quartex modules were considered. Starting from a single-module structure, more complex cases were sequentially analysed. The different methods of plates support were considered. The presence of self-stress states (\(S\)) and mechanisms (\(M\)) was determined by the singular value decomposition of the compatibility matrix. If any mechanism existed, the spectral analysis of the tangent stiffness matrix, which includes the self-stress state, was used to establish whether the mechanism was finite or infinitesimal. The compatibility matrix and the tangent stiffness matrix were determined using the finite element method. The geometrical and mechanical characteristics did not affect the peculiar tensegrity features, so all constants were assumed as a unit. Results for all analysed plates are summarised in Table 4. The following conclusions were obtained:  
* Only the single modified Quartex module is the ideal tensegrity. This module meets all tensegrity features, i.e., the structure is a truss (\(T\)) with a continuous net of tensile components--cables (\(C\))--including a discontinuous set (\(D\)) of the compressed elements (\(I\)) and it features the existence of one self-stress state (\(S\)) and one mechanism (\(M\)). * The plates built with four, sixteen or sixty-four modules cannot be the ideal tensegrities because of the way of connecting the modules. These structures do not satisfy the condition for the discontinuity of struts (\(D\)). * All of the plates are characterised by the existence of more than one self-stress state (\(S\)). Due to the fact that only one self-stress state accurately identifies the elements, they cannot be considered as \"pure\" tensegrities. Actually, the only one appropriate self-stress state for the all considered plate-like structures is the one that is a superposition of the self-stress state of the single module. * Considered plates can be classified as structures with features of class 1, if there is a mechanism, or class 2, if there is no mechanism (see Table 4). The complete analysis of tensegrity structures is a two-stage process. The qualitative analysis carried out in the paper is the first stage and it is the basis for a quantitative analysis, which is the second stage. A quantitative analysis, which focuses on the behaviour of tensegrities under external loads, will be provided in part 2 of the paper. The proposed classification is important due to different behaviours of the structure under external actions. If a mechanism exists for the structure, that is when the structure is assigned to the one of the first three categories, and it is possible to control static properties, like, for example, stiffness, by the change in the self-stress level. The proposed tensegrity plate-like structures can be used in the design process of standard tensegrity building structures, i.e., plates and non-standard applications. The tensegrity concept can be used in metamaterial unit cells and in deployable or smart engineering structures with monitoring, self-control, self-repair and active control.