Two subdivision methods based on the regular octahedron for single- and double-layer spherical geodesic domes

Abstract

The paper presents the topological–geometric analysis of a selected number of space frames configurations for geodesic domes which are generated from the regular octahedron. Two subdivision methods for spherical triangles, proposed by Fuliński, were used to create two families of structures. The first family consists of six single-layer and six double-layer geodesic domes shaped on the basis of the first method of subdivision, while the second family contains six single-layer and six double-layer geodesic domes shaped on the basis of the second method of subdivision. The calculated results of the geometric parameters of the analyzed structures were used to create original formulas that allow for more advanced structures to be achieved, that is, with a larger number of nodes and struts. The geometric results were also used to create nomograms showing the range of struts of the same length for double-layer geodesic domes. In both single-layer and double-layer domes, the number of groups of struts of equal lengths and the number of faces with different areas are smaller for structures created according to the first method of subdivision. The comparison of the resulting element quantities of two methods shows that the largest differences appear between the domes with a larger number of struts (up to 67%). Here, the analysis might help the designer reach a final decision on the better choice of topology, in particular, when this aspect is combined with other design goals, such as efficiency, economy, utility, and elegance in the design of the structure and the cover of large areas.

Numerical Analysis of Steel Geodesic Dome under Seismic Excitations

“…The study assesses the effect of seismic excitations on the geodesic domes, which were designed in accordance with two different methods for creating these types of structures. As mentioned earlier, these methods have been described in detail in the papers [ 52 , 53 , 54 ]. The numerical program RFEM and the Time History method were used for the analysis.…”

“…The analysed records had different durations and intensities. The dynamic (seismic) analysis was carried out on the basis of the numerical models presented in [ 52 , 53 , 54 ]. The above-mentioned publications applied the rule that the most stressed strut in a given group was at a level of 90%.…”

“…More parts give smoother spheres. The mentioned methods were developed in detail in the paper by Pilarska [ 54 ]. Figure 2 shows the difference in the shaping of geodesic domes using the first and second subdivision methods.…”

“…Two geodesic strut domes were subjected to numerical analysis, taking into account the seismic excitations. These structures were designed according to the two different methods of creating geodesic domes proposed by Fuliński [ 55 ], which are presented in Section 2.1 and described in detail in the papers by Pilarska [ 52 , 53 , 54 ]. The basis for generating the meshes of both structures was a regular octahedron.…”

“…The paper presents the numerical analysis of the geodesic domes under seismic excitations. The developed structures were created on the basis of the regular octahedron, which was a polyhedron that has not been considered in great detail so far [ 52 , 53 , 54 ]. Two different methods for the subdivision of the spherical triangle proposed by Fuliński [ 1 , 55 ] were used to design the two geodesic domes under seismic analysis.…”