## 4 Self-Repair  
In order to prove that tensegrity systems are capable of self-repair, an analysis of a tensegrity plate-like structure was performed. In the analysis, the structure presented in Figure 8 was considered, with the same materials, dimensions of the cross-sections, values of self-stress and loading as in the previous example. The aim of the analysis was to examine the behavior of the structure in the case of a member loss and to verify the possibility of self-repair. The failure was modelled by removing one of the cables from the system, marked with the dashed red line in Figure 12. The calculations were conducted in SOFiStFiK software, with the use of the finite element method, according to the geometrically non-linear theory. Figure 11: Structure No. 3: influence of self-stress on the internal force in a strut (\(S_{72}\)), with two levels of loading, according to the third order theory. One of the aims of the analysis was to verify the possibility of structural repair through an adjustment of self-stress in one selected module of the structure. Such a possibility would be particularly valuable from the practical point of view: it would allow one to significantly reduce the number of actuators installed on the active structural members. As is proven below, such a repair is possible in the case of the analyzed system. The scope of the analysis was a vertical displacement of the central node of the upper surface of the plate-like structure, marked with letter A in Figures 8 and 12. With the loading \(P=10\) kN and self-stress \(S_{0}=100\) kN, the value \(\delta_{\rm A}=51.36\) mm was obtained. Removal of the cable caused changes in the structure of Module Nos. 3 and 10 (Figure 12), so they could no longer be pre-stressed after the member loss. Self-stress on the level of \(S_{0}=100\) kN was maintained in twelve undamaged modules. After damage, the value \(\delta_{\rm A}=55.29\) mm was obtained. The authors tried to simulate the repair of the structure, which is to reduce the value of \(\delta_{\rm A}\) to the value from before damage, by adjusting the pre-stressing forces in single modules. Each time the level of self-stress within the considered module was changed, other modules were pre-stressed with the force \(S_{0}=100\) kN. Figure 13 shows the levels of self-stress obtained for each module that allowed regaining the given value of \(\delta_{\rm A}\). The smallest values of pre-stressing forces that led to self-repair of the structure were obtained for Module No. 11. Figure 12: Tensegrity plate-like structure with member loss (dimensions units (mm)). Figure 13: Self-stress state required for self-repair of the structure. The diagram presented below shows the distribution of the displacements of the upper structural nodes in two characteristic sections: A-A and B-B (Figure 14). Four states were taken into account:  
* State \"0\": structure before damage, the level of self-stress \(S_{0}\) = 100 kN, no external loading,
* State \"1\": structure before damage, the level of self-stress \(S_{0}\) = 100 kN, concentrated forces \(P\) = 10 kN applied to the upper nodes,
* State \"2\": structure after damage, the level of self-stress in undamaged modules \(S_{0}\) = 100 kN, concentrated forces \(P\) = 10 kN applied to the upper nodes,
* State \"3\": structure after repair, the level of self-stress in module 11 \(S_{0}\) = 308.5 kN and in other undamaged modules \(S_{0}\) = 100 kN, concentrated forces \(P\) = 10 kN applied to the upper nodes. The presented example concerns only one damage scenario in one specific tensegrity structure and does not exhaust the problem of structural repair. However, the aim of the analysis was to show that tensegrities are capable of self-repair, not to investigate all possible cases of structural damage. Tensegrity structures owe this unique property of self-repair to infinitesimal mechanisms, which are balanced with self-stress states. Repair of these structures is possible through an adjustment of prestressing forces, without any operation from the outside.