Optimal FRP reinforcement of masonry walls out-of-plane loaded: A combined homogenization–topology optimization approach complying with masonry strength domain

• Rational FRP reinforcement of out-of-plane loaded masonry walls.
• Utilization of a topology optimization approach combined with homogenization.
• Homogenization plate model for masonry at failure (strength domains evaluation).
• Topology optimization of the FRP-reinforcement with stress constraints and orthotropic material.
• Application to windowed panels out-of-plane loaded.

A novel approach for the rational arrangement of fiber reinforcements on masonry structures based on topology optimization is presented. Following previous experiences on the automatic achievement of strut-and-tie models in reinforced concrete structures, the minimization of the strain energy can be implemented to derive optimal layouts of reinforcement for any structural element. To cope with the brickwork limited strength, the optimal problem can be conveniently reformulated as the minimization of the amount of reinforcement that is required to keep tensile stresses in any masonry element below a prescribed threshold. The out-of-plane macroscopic elastic properties and strength domain of brickwork are derived through an original homogenization approach, which relies upon the discretization of 1/4 of any unit cell by six constant moment elements. Thanks to the limited number of variables involved, fast evaluations of masonry macroscopic strength domains can be obtained. This criterion is implemented into the multi-constrained discrete formulation of the topology optimization algorithm, to locally control the internal actions field over the design domain. Topology optimization is then applied to the investigation of the optimal reinforcement of plain and windowed panels, comparing the conventional energy-based method and the proposed stress-based approach.