Novel non-linear static numerical model for curved masonry structures based on a combined adaptive limit analysis and discrete FE computations

A new procedure for a fast and comprehensive description of the collapse behavior of curved masonry structures is presented. The first step provides the identification of the exact collapse mechanism and the load-bearing capacity through adaptive NURBS limit analysis. This method is based on the discretization of the masonry vault through very few curved elements, assumed as rigid blocks with internal dissipation allowed only at interfaces, whose shape is iteratively modified until interfaces coincide with the correct position of cracks. On the obtained mechanism, a kinematic non-linear analysis with rigid-softening behavior can be also applied to better understand how the load-bearing capacity decreases during the evolution of the mechanism. A finite element (FE) non-linear static analysis is then applied to obtain the force–displacement curve according to the real elastic-softening behavior. The NURBS optimized model is converted into a discrete FE model composed of three-dimensional elastic units joint together by interfaces where the non-linear mechanical properties are lumped. Within this assumption, non-linear interfaces are applied along the cracks previously found through the limit analysis in a fully automatic way, preventing any mesh dependency effect. Furthermore, the combination of such approaches allows overcoming the respective drawbacks of the methods. Selected masonry arches and vaults are here studied to present the reliability of the presented coupled approach.