The paper concerns steel domes with regard to the special structures named tensegrity. Tensegrities are characterized by the occurrence of self-stress states. Some of them are also characterized by the presence of infinitesimal mechanisms. The aim of this paper is to prove that only tensegrity domes with mechanisms are sensitive to the change of the level of initial prestress. Two tensegrity domes are considered. In addition, a standard single-layer dome is taken into account for comparison. The analysis is carried out in two stages. Firstly, the presence of the characteristic tensegrity features is examined (qualitative analysis). Next, the behavior under static external loads is studied (quantitative analysis). In particular, the influence of the initial prestress level on displacements, effort, and stiffness of the structure is analyzed. To evaluate this behavior, a geometrically non-linear model is used. The model is implemented in an original program written in the Mathematica environment. The analysis demonstrates that for a dome with mechanisms, the adjustment of pre-stressing forces influences the static properties. It has been found that the stiffness depends not only on the geometry and properties of the material but also on the initial prestress level and external load. In the case of the non-existence of mechanisms, structures are insensitive to the initial prestress level.

The aim of the paper is to find the appropriate self-stress state of the tensegrity structures. The first approach provides exact solutions but is suitable for simple structures. In the second approach proposed in this research, it is assumed that the forces of the self-stressed state are a set of randomly selected values, which are then optimized by a genetic algorithm. This procedure is intended for more elaborate structures, for which the spectral analysis identifies many self-stress states that need to be superimposed. Two approaches are used, i.e., the spectral analysis of the compatibility matrix and the genetic algorithm. The solution procedures are presented on the example of a simple two-dimensional truss. Next, three different tensegrity domes are considered, i.e., Geiger, Levy and Kiewitt. The significant difference between these domes lies in the cable system. The obtained results are compared with those documented in the literature. It follows from the considerations that the self-stressed states found in the literature are not always accurate (forces do not balance themselves). The presented results confirm the effectiveness of the genetic algorithm for finding self-balanced forces of the existing structures. The method is relatively simple and provides sufficiently accurate results.

This paper provides a parametric analysis of cable–strut tensegrity domes subjected to periodic loads. This analysis aims at determining the main regions of dynamic instability (unstable regions). From the point of view of the physical interpretation of the phenomenon, if the load occurs in these regions, the amplitudes of the resulting vibrations increase, posing a risk to the durability of the structures. The consideration includes cable–strut structures called Geiger domes. Four dome design solutions known from the literature are compared, i.e., regular (patented by Geiger) and modified domes with a closed and an open upper section. In contrast to conventional cable–strut structures, Geiger domes are characterized by a self-equilibrated system of internal forces (initial prestress), which affects the shape and range of unstable regions. The main purpose is to answer the question as to which type of design solution is more sensitive to the risk of excitation vibrations. A nondimensional parameter $\lambda$ is introduced for this quantitative assessment. This parameter reliably determines the change in the area of unstable regions as the initial prestress level increases. The range of the parameter $\lambda$ is defined as a value between 1 and 0. In the case of $\lambda =1$, there is potential for the excitation of unstable motion, whereas in the case of $\lambda =0$, such a risk is absent. The analysis presented in this paper can be employed in the process of optimizing the initial prestress level, which will constitute the subsequent stage of this research. A geometrically non-linear model is used to evaluate the behavior of the considered structures.

The paper contains a parametric dynamic analysis of cable-strut domes. The special structures named tensegrity are considered. Two qualitative different tensegrity domes, i.e., the Geiger dome and the Levy dome are taken into account. The aim of the study is to compare the dynamic behaviour of...