Optimal fiber-reinforcement of no-tension masonry walls through a stress-based formulation

A topology optimization problem is dealt with, which aims at distributing a prescribed amount of fiber-reinforcement over any masonry wall, so as to maximize the overall stiffness of the strengthened element. A no-tension (NT) model is adopted to account for the negligible tensile strength of brickwork. The equilibrium of the NT body is enforced through an energy-based method, which replaces brickwork by an equivalent orthotropic medium with constraints on the stress state. The inability if the reinforcement to carry compressive stresses is also taken into account in a similar way. The stress analysis of the reinforced NT body can be straightforwardly embedded within the topology optimization formulation, with no need for demanding incremental approaches. Both the regions to be strengthened and the local orien-tation of the optimal FRP strips are identified. To improve accuracy in the enforcement of the stress constraints, an efficient formulation that uses stresses as main variables of the elastic problem is implemented. Also, the structural compliance is computed through the evaluation of the complementary strain energy. A preliminary numerical example is shown, to assess the capabilities of the proposed procedure.