On the thrust surface of unreinforced and FRP-/FRCM-reinforced masonry domes

We employ a r-adaptive finite element model to search for a 'safe' thrust surface of a masonry dome, which minimizes the maximum tensile stress carried by the unreinforced portion of the material. A numerical procedure based on a Breeder Genetic Algorithm is employed to drive the movement of the nodes of a membrane model within a suitable design domain, which coincides with the region comprised in between the intrados and extrados of the dome in correspondence with the unreinforced portion of the structure. The presence of externally bonded Fiber Reinforced Polymer and/or Fabric Reinforced Cementitious Mortar reinforcements is accounted for by allowing the thrust surface to move outside the physical domain of the structure in correspondence with the reinforced regions. A benchmark example shows that the proposed procedure leads to detect if a masonry dome is safe or not, according to the master 'safe' theorem of the masonry vault theory. In addition it allows to optimally design reinforcement strategies that are aimed at preventing or mitigating crack damage, and increasing the load carrying capacity of the structure.