Simple topology optimization strategy for the FRP reinforcement of masonry walls in two-way bending

A multi-constrained topology optimization approach is employed to define the layout of the reinforcing layers that minimizes the structural compliance (i.e. that maximizes the structural stiffness) of retrofitted out-of-plane loaded masonry walls, for a given amount of reinforcement. The reinforcement is supposed to be symmetrically placed on both sides of the wall. The macroscopic elastic properties of brickwork in bending are derived through an original homogenization approach, which relies upon the discretization of 1/4 of any unit cell by six CST elements. Topology optimization is then applied to the determination of the optimal reinforcement of solid and windowed panels. The increase in stiffness given by the numerically predicted reinforcement layout respect to the unreinforced panels is pointed out.