Fast kinematic limit analysis of FRP reinforced masonry vaults through a new genetic algorithm nurbs-based approach

In the present contribution, a novel Genetic Algorithm NURBS-based approach for the limit analysis of FRP reinforced masonry vaults based on an upper bound formulation is developed. Vaults geometry can be described by a NURBS representation of their mid-surface, which can be generated within any commercial free form modeler, together with information about the local thickness at each point of the surface. By exploiting the properties of NURBS functions, a mesh of the given surface, which still provides an accurate representation of the vaulted surface, can be obtained. Each element of the mesh is a NURBS surface itself and is idealized as a rigid body. Starting from the obtained rigid bodies assembly, an upper bound limit analysis problem with very few optimization variables can be devised and in which dissipation is allowed along element edges only. A possible dissipation at the interfaces between FRP and masonry is also considered in order to take into account, in an approximate but effective way, the possible delamination of the strips from the supports. Due to the very limited number of rigid elements used, the quality of the collapse load so found depends on the shape and position of the interfaces, where dissipation is allowed. Mesh adjustments are therefore needed which is carried out by adopting a simple meta-heuristic (like a standard Genetic Algorithm GA) approach of mesh adjustment. The strength of the proposed GA-NURBS method lies in the fact that even by using a mesh made of very few elements (which therefore require a negligible computational time to have an estimate of collapse loads), it is possible to obtain accurate load multipliers and failure mechanisms, thus exhibiting an edge over existing methods for the collapse analysis of masonry vaults in terms of computational efficiency.