Optimal Fiber Reinforcement of Masonry Walls Loaded Out-of-Plane

The problem of the optimal external reinforcement with FRP strips of masonry walls under lateral loads is dealt with, by means of a combined homogenization-topology optimization approach. A homogenization procedure is utilized to deduce both the orthotropic elastic moduli of masonry and the out-of-plane strength domain. The elastic moduli are estimated by mini-mizing the total complementary energy of any discretized elementary cell. The out-of-plane failure surface is numerically evaluated by means of the lower bound theorem of limit analysis. Joints are reduced to interfaces obeying a Mohr-Coulomb strength criterion with tension cut-off and a cap in compression. For bricks, a classic Mohr-Coulomb criterion is employed. The out-of-plane macroscopic strength domain is deduced by integration of the stresses along the thickness. The optimization problem is written assuming perfect bonding between FRPs and masonry, meaning that a fiber-reinforced layer is modelled as an additional contribution to the out-of-plane stiffness of the underlying brickwork. Constraints on the internal actions in masonry are also imposed at any Gauss point. The proposed approach is applied to the determination of the optimal reinforcement of a rectangular panel. The numerically predicted optimal layout is compared with that given by an energy-based approach, in which the stiffness of the panel is maximized for a given amount of reinforcement.