Limit analysis of axisymmetric masonry domes under vertical loads: parametric studies and statically admissible stress fields

A parametric analysis of the safety level of masonry domes subjected to their self-weight is conducted by varying a given set of geometric parameters. By adopting the well-known Heyman hypotheses that allow proving the theorems of limit analysis, statically admissible stress fields inside the dome are sought. The dome is modelled as a thin shell where both membrane forces and bending moments may arise. This allows exploring a much broader set of possible equilibrium states than the established analysis techniques found in the literature, thus enabling improved estimation of the dome safety level. The equilibrium problem is solved by the collocation method, and a convex optimisation problem is devised to search for the best stress field distribution. The case of spherical domes and equilateral pointed domes with a top opening are analysed. Finally, the results in terms of minimum admissible thickness and the corresponding stress field are illustrated.