NURBS upper bound prey-predator scheme for collapse analysis of masonry vaults

We present here an improvement in the non-uniform rational Bezier spline (NURBS)-based kinematic limit analysis approach, which has proven to be particularly effective for masonry vaults, by adding an innovative mesh adaptation scheme. The procedure is based on the application of the kinematic theorem of limit analysis on a 3D model composed of NURBS rigid blocks. The definition of curved geometries through NURBS surfaces allows using mesh of few elements without modifications of the real geometry. An adjustment of the initial mesh is needed to minimize the kinematic load multiplier. Therefore, a Prey-Predator Algorithm (PPA), an innovative meta-heuristic algorithm based on the natural interaction between a predator and preys, is implemented as core of the mesh adaptation, allowing an efficient evaluation of load-bearing capacity and collapse behavior of masonry vaults. In this work, the standard PPA is further improved by introducing a variable population size, the so-called saw-tooth model, which allows reducing the computational effort without penalizing the evaluation of the objective function. Some numerical examples, which involve a masonry arch, a skew arch, and a horizontally loaded dome, are finally analyzed. For all the cases, a comparison between the proposed PPA and a traditional Genetic Algorithm (GA) is presented.