Optimal Design of Tie-Rod Strengthening for Historical Masonry Structures Through a Genetic Algorithm Combined with Limit Analysis

Retrofitting and strengthening measures play a crucial role in safeguarding historical masonry structures in southern European regions against seismic events. Among these techniques, tie-rods are often the preferred solution due to their efficiency, practicality, and cost-effectiveness, while also preserving the architectural integrity of the structure. To optimize their design – considering parameters such as size, quantity, and placement – a genetic algorithm is integrated into a limit analysis-based approach developed in MATLAB. This approach models the structure through a discretization process, representing it with infinitely resistant hexahedral elements connected by quadrilateral interfaces, where plastic deformations occur according to the Mohr-Coulomb failure criterion, supplemented by a tension cutoff and a linearized compression cap. Various loading conditions can be applied, accounting for different distributions of horizontal forces and seismic input angles. A Genetic Algorithm identifies the most effective tie rod configuration that maximizes structural performance while adhering to predefined constraints, such as feasible placement zones, limits on the number of tie rods, and their orientation. The proposed procedure is validated through a case study on a single-nave church.