Fast kinematic limit analysis of FRP-reinforced masonry vaults. II: Numerical simulations

A new approach for limit analysis of masonry vaults retrofitted with fiber-reinforced polymers (FRPs) based on an upper bound formulation is presented. Part I of this paper was devoted to detailing the theory on which this approach relies. The main idea consists of exploiting properties of nonuniform rational b-spline (NURBS) functions to develop a computationally efficient adaptive limit analysis procedure, which allows quick evaluation of the collapse load multiplier of any given FRP-reinforced masonry vault starting from its three-dimensional (3D) model, which can be generated within any free-form modeler natively working with NURBS entities. A suitably devised genetic algorithm (GA) governs mesh adaption. The present Part II is devoted to validating and discussing through numerical simulations the proposed GA-NURBS procedure. Several structural examples of masonry vaults, including two distinct arches (a straight parabolic barrel vault and a skew parabolic arch, respectively), a hemispherical dome, and both cloister and cross vaults are investigated. Each example is analyzed considering both the unreinforced configuration and the presence of FRP reinforcements. Moreover, comparisons with both nonlinear finite-element (FE) simulations and data collected from experiments (where existing) are presented to assess the proposed GA-NURBS limit analysis procedure. It is shown that, for all cases analyzed, this model allows reliable prediction of both collapse mechanisms and failure loads. The present GA-NURBS approach turns out to be a promising tool that may be conveniently used by practitioners who seek a quick and reliable way to evaluate the outcome of restoration interventions based on the application of FRP composites.