On the shape optimisation of the force networks of masonry structures

A novel lumped stresses network approach for the analysis of the mechanical behaviour of masonry structures is presented. It is formulated through a network of lumped stresses, making use of polyhedral stress functions and a variational approximation of the continuous equilibrium problem. The proposed method allows for modelling masonry structures as no-tension elements and gives, in the case of curved masonry members, the optimised surface through a predictor-corrector procedure and the stress function describing the membrane stress. The given approach offers a useful tool for predicting the crack pattern of unreinforced masonry structures and the associated stress fields. It is validated against some benchmark case studies dealing with a hemispherical dome, a groin vault, a cloister vault and a masonry beam.