A new computational framework for the minimum thrust analysis of axisymmetric masonry domes

Abstract

An original computational framework is presented for the minimum thrust analysis of axisymmetric masonry domes with arbitrary meridian curve, subject to their self-weight. The formulation is characterized by the ability to account for an arbitrary meridional stereotomy, which is reflected in the exact treatment of the dome self-weight and in the representation of the stress resultants. The classical equilibrium equations of axisymmetric shells are resorted to for formulating the equilibrium of the dome as that of its mid-surface, and the admissibility conditions on the stress resultants are consequently stated. The proposed formulation is proven to provide a unitary framework in which competing formulations for masonry domes available in the literature, classified as lunar-slices and membrane formulations, can be derived as particular cases. Furthermore, it fosters an extremely efficient and robust computational approach, which amounts to the solution of a straightforward Linear Programming problem. Numerical results are discussed, as parametric analyses of ogival domes with normal or vertical meridional stereotomies, and of domes with superellipse meridian curve, at varying of the rise-to-midspan ratio and of the shape exponent. Finally, the merit of the proposed procedure is shown in application to a real case.