Minimal mass design of strengthening techniques for planar and curved masonry structures

We present a discrete element model of a masonry structure strengthened through the application of reinforcing elements designed to work in tension. We describe the reinforced masonry structure as a tensegrity network of masonry rods, mainly working in compression, and tension elements corresponding to fiber-reinforced composite reinforcements, which are assumed to behave as elastic-perfectly-plastic members. We optimize a background structure connecting each node of the discrete model of the structure with all the neighbors lying inside a sphere of prescribed radius, in order to determine a minimal mass resisting structure under the given loading conditions and prescribed yielding constraints. Fiber-reinforced composite reinforcements can be naturally replaced by any other reinforcements that are strong in tension (e.g., timber or steel beams/ties). Some numerical examples illustrate the potential of the proposed strategy in designing tensile reinforcements of a three-dimensional structure composed of a masonry vault and supporting walls.