Topology Optimization of the Fiber-Reinforcement of No-Tension Masonry Walls

An innovative approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension (NT) bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. Perfect bonding is assumed at the wall-reinforcement interface. To account for the negligible tensile strength of brickwork, the material is replaced by an equivalent orthotropic material with negligible stiffness along the direction(s) undergoing tensile principal stress(es). Compressive principal stresses in the reinforcement are not allowed. A single constrained optimization problem allows both the equilibrium of the NT body to be enforced, and the optimal reinforcing layout to be spotted out, without any demanding incremental approach. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.