Design of the optimal fiber-reinforcement for masonry structures via topology optimization

A novel approach for the optimal positioning of fiber reinforcements in masonry structures is presented, based on topology optimization techniques [1]. Topology optimization has already been used to generate energy-based truss-like layouts that may be straightforwardly interpreted as strut-and-tie models in concrete structures [1]. The minimization of the so-called structural compliance allows optimal load paths to be defined, which may inspire a safe disposal of steel bars if the specimen is provided by the required ductility. Due to the brittle behaviour of masonry structures, the minimization of strain energy cannot be adopted as an objective. The problem may be conveniently re-formulated as a minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. Strength criteria for masonry elements are provided by means of a recently presented lower bound limit analysis homogenization model [2], relying into a discretization of ¼ of the unit cell with six CST elements. Thanks to the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. This calls for the adoption of a multi-constrained discrete formulation that locally controls the stress field over the whole design domain [3]. The contribution discusses preliminary numerical results addressing fiber-reinforcement on a benchmark masonry wall.