Efficient meta-heuristic mesh adaptation strategies for NURBS upper–bound limit analysis of curved three-dimensional masonry structures

We propose a new adaptive NURBS upper-bound limit analysis approach for the assessment of general three-dimensional curved masonry structures, based on different meta-heuristic mesh adaptation schemes. The method, which can easily be integrated within CAD modeling environments, allows to establish the actual failure mechanism and load bearing capacity of a masonry structure by iteratively adjusting a tentative pattern of yield lines, defined upon a suitable initial mesh of NURBS rigid elements, by means of a suitable meta-heuristic algorithm which searches for the minimum collapse load multiplier, thus enforcing the upper-bound theorem of limit analysis. In particular, we investigate and discuss the efficiency of several meta-heuristic algorithms in delivering the optimal solution: a specifically devised Prey Predator Algorithm (PPA) is compared with the Particle Swarm Optimization (PSO) Algorithm, the Firefly Algorithm (FA) and a suitable Genetic Algorithm (GA). Four masonry vaults have been chosen as case studies. In particular, the modified PPA proves to be the most efficient mesh-adjustment scheme for the proposed adaptive NURBS-based limit analysis procedure.