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

A novel approach for the rational positioning of fiber reinforcements on masonry structures based on topology optimization is presented. Due to the brittle behavior of masonry, the minimization of the strain energy cannot be implemented to generate truss-like layouts that may be interpreted as strut-and-tie models in the discontinuity regions of reinforced concrete structures. To cope with the brittleness of brickwork, the optimal problem can be conveniently reduced to the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. A strength criterion recently proposed for masonry is employed, based on a lower bound limit analysis homogenization model (Milani, 2011) and relying upon a discretization of 1/4 of any unit cell by six CST elements. Thanks to the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. This criterion is implemented into the multi-constrained discrete formulation of the topology optimization algorithm, to locally control the stress field over the design domain. For comparison, the phenomenological Tsai–Wu strength criterion for anisotropic solids is also implemented. The contribution discusses three sets of numerical results, addressing the fiber-reinforcement of some benchmark masonry walls. The optimal reinforcement layouts are found to be affected by the choice of the masonry strength criterion only to a limited extent, as far as failure in the masonry element is mainly due to tensile stresses. Contrary to intuition, placing the reinforcing fibers along the direction of the principal tensile stresses in masonry is also found to be not necessarily the most effective solution, for certain geometries and load conditions.