Optimal strengthening of no–tension structures with externally bonded reinforcing layers or ties

An innovative approach is proposed to define the optimal distribution of a prescribed amount of reinforcement to be externally bonded to 2D no-tension structural elements, with the aim of maximizing the overall stiffness of the strengthened element. Only tensile stresses are allowed in the reinforcing layers. An algorithm based on Topology Optimization is employed to simultaneously enforce negativity of the principal stresses in the original body, and positivity of the stress in the reinforcement. A few numerical simulations are presented to assess the capabilities of the proposed procedure in defining the optimal reinforcement layouts for laterally loaded walls and arches. In the case of curved elements, suitable fasteners have to be employed to ensure bonding of the strengthening layer at the intrados. Fiber-reinforcement is found to spontaneously arise where cracks would occur in the unreinforced element. The proposed formulation can also be employed to define the optimal location of reinforcing ties for arches and barrel vaults.