The paper presents the author’s non-linear FEM solution of an initially stressless deformed flat frame element, in which the nodes are situated along the axis of the bar initially straight. It has been assumed that each node may sustain arbitrary displacements and rotation. The solution takes into account the effect of shear, the geometrical non-linearity with large displacements (Green-Lagrange’s strain tensor) and moderate rotations (i.e. such ones which allow a linear-elastic behaviour of the material) and alternative small rotations when the second Piola-Kirchhoff stress tensor is applied. This solution is based on [1], concerning beams without any initial bow imperfections. The convergence of the obtained results at different numbers of nodes and Gauss points in the element was tested basing on the example of circular arcs with a central angle of 120°÷180°. The analysis concerned elements with two, three, five, seven, nine and eleven nodes, for the same number of points of numerical integration and also with one more or less. Moreover, the effect of distributing the load on the convergence of the results was analyzed.

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.