A Comparative Study of the Structural Performance of Different Types of Reticulated Dome Subjected to Distributed Loads

Willem Gythiel,Mattias Schevenels,Christiaan Mommeyer,Tom Raymaekers

doi:10.3389/fbuil.2020.00056

Abstract

Whereas reticulated domes (i.e. domes composed of bars) are very material-efficient in general, the geodesic dome is claimed to be superior according to its patent holder, Richard Buckminster Fuller. Recent studies on the optimal design of reticulated domes do not allow a direct comparison between the geodesic dome and other dome types because the test cases are not subjected to the same loads. This paper aims to determine which type of reticulated dome is superior in terms of material efficiency by comparing the minimized weight of different dome types, taking into account stress and buckling constraints. The study includes hemispherical Schwedler, Kiewitt and geodesic domes with a diameter of 16 m, and a gravity load of 2 kN/m². Full enumeration is used to optimize the discrete variables (number of rings, subdivisions along each ring,...), while a gradient-based algorithm is used for the continuous variables (member sections). The results show that the claim of uniform stressing in a geodesic dome is legitimate: if all members are assigned the same size, a geodesic dome is generally more evenly stressed and up to 28% lighter than other dome types of similar size. However, if all members are sized individually, the Schwedler dome is the lightest.

Highlights

Reticulated domes with various patterns (Figure 1) have been built to span large surfaces, demonstrating their material efficiency
To determine which dome type is superior in terms of material efficiency, the minimized weight of each variant is compared for various subdivision frequencies
This claim suggests that the geodesic dome is a fully stressed design, which is a measure for optimal material-efficiency under certain conditions

Summary

Introduction

Reticulated domes (i.e., domes composed of bars) with various patterns (Figure 1) have been built to span large surfaces, demonstrating their material efficiency. The geodesic dome is often assumed to be superior because its patent holder, Richard Buckminster Fuller, claimed that the resulting framework will be characterized by more uniform stressing of the individual members than is possible with any construction heretofore known (US patent 2,682,235A). This -unverified- claim implies that it is a fully stressed design, which is a measure for optimal material use under certain conditions (Patnaik and Hopkins, 1998). Often unrealistic loads were applied: distributed loads were not considered in most studies, they are the predominant load for reticulated domes

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