Seismic vulnerability of masonry historical structures: A simple adaptive nurbs FE approach for the limit and the subsequent non-linear static analysis with few dofs

The present contribution deals with an innovative evaluation of the vulnerability and static seismic behavior of existing masonry structures and monumental buildings. For a given masonry construction, a discretization through few NURBS surfaces is realized. NURBS surfaces are converted into shell elements which are assumed rigid and infinitely resistant. The non-linearities typical of the masonry material (almost no tensile strength, frictional behavior in shear, and relatively larger resistance in compression) are imposed at interfaces between adjacent elements, which represent in this way possible fracture lines. Once defined a horizontal load configuration, an adaptive upper bound limit analysis is applied. As final result, the collapse mechanism and the collapse load multiplier are found. Then, to provide the complete non-linear structural response, a FE model composed of elastic elements representing macro-blocks and non-linear contact-based interfaces or plastic damaging strips corresponding to the cracks is derived. On such model, static non-linear analyses can be performed easily at a fraction of the computational burden needed by standard approaches. Several examples including masonry churches, vaults, and buildings are presented. Finally, a novel limit analysis computational technique based on a discretization through NURBS solid elements is introduced and future perspectives of the research are drawn.