A computational scheme for investigating statically admissible internal forces in masonry domes and vaults

A shell model recently introduced by the authors for the limit analysis of masonry domes is reconsidered. The model is set within the framework of the static theorem of limit analysis. Masonry is assumed to fulfill Heyman’s hypotheses. An enhanced computational scheme is presented, which enables searching for statically admissible distributions of internal forces, by accounting for both membrane forces and bending moments. The main advantage of the method lies in its ability to select stress distributions that minimise the error in the equilibrium equations among a given set satisfying the requirements for the masonry material. The solution is pursued numerically by solving a convex optimisation problem. The case of the semi-dome subjected to different load distributions and constraint conditions is presented for model validation. The results obtained are critically discussed and a comparison is made with classical results available in the literature.