Topology optimization of the fiber–reinforcement retrofitting existing structures

The paper presents a numerical approach for the optimal design of any unidirectional fiber-reinforcement to improve the structural performance of existing structural elements. A problem of topology optimization is formulated, simultaneously searching for the regions to be strengthened and the optimal pointwise inclination of the reinforcement. Aim of the formulation is the minimization of the maximum equivalent stress in the underlying material, for a prescribed amount of fiber-reinforcement. The Tsai–Wu failure criterion is implemented to detect highly tensile-stressed regions in the existing structural components, both in case of isotropic material (e.g. concrete) and orthotropic media (e.g. brickwork or reinforced concrete). A suitable set of relaxed stress constraints is dealt with, calling for a no-compression stress state in the fiber-reinforcement. The resulting multi-constrained min–max problem is solved by mathematical programming. Numerical examples are presented to discuss the features of the achieved optimal layouts, along with their possible application as preliminary design for structural retrofitting. Performances of the adopted computational procedure are investigated as well.