Adaptive limit analysis of historical masonry structures modeled as NURBS solids

In this work, we propose an adaptive upper bound limit analysis based on the representation of geometry through NURBS-solids. A NURBS-solid is a closed volume identified by boundary NURBS surfaces (Non-Uniform Rational Bezier Spline). Differently from using NURBS surfaces representing masonry shell-elements, NURBS-solids allow an accurate representation of masonry three-dimensional macro-blocks, such as vaults or walls with variable thickness. The initial model is subdivided into very few macro-elements, each one is still a NURBS solid and is considered as a rigid block. Since dissipation occurs only along interfaces, NURBS boundary surfaces represent possible fracture zones. An upper bound limit analysis is applied. The minimum kinematic multiplier is found by modifying the initial subdivision of solids until the real collapse mechanism is reproduced. This automatic research is performed through a Genetic Algorithm. A simple numerical example is finally reported.