On the strength and stability of elliptic toroidal domes

Abstract

The thin toroidal shell offers exciting possibilities as a lightweight enclosure for working and recreational spaces. In this paper, we use shell theory to investigate the strength and stability of thin toroidal domes of prolate elliptic cross-section. We assume the shell is provided with membrane-type supports so that bending effects at the edges of the shell are insignificant. Focussing attention on the effects of self-weight and the weight of any cladding that may be attached to the shell, we derive the membrane stress resultants for arbitrary values of the shell geometrical parameters, and explore the influence of these parameters on the distribution of stresses in the shell. We then conduct a linear eigenvalue buckling analysis of the shell using a finite-element programme, in order to gain some insight on the stability behaviour of the shell. The main conclusions are that stresses due to gravitational loads are very small in toroidal domes of the type in question, while for the range of geometric parameters (ratio a/b of semi-axes of the toroid; ratio a/A of horizontal semi-axis to mean radius of the toroid) likely to be encountered in practice, buckling is unlikely to govern the design of the shell.