A NURBS-based numerical approach for the assessment of masonry vaults undergoing differential settlements

In this paper, we propose a NURBS-based adaptive approach to the three-dimensional analysis of masonry vaults undergoing foundation settlements. A given masonry vault of arbitrary geometry is described through its NURBS (Non-Uniform Rational B-Spline) parametric representation in the three-dimensional Euclidean space. The vault surface is then discretized into an initial set of rigid elements. Such discretization is obtained by suitably subdividing the NURBS parameters space. Jumps of displacement are allowed solely at the interfaces. Given a known displacement on the external boundary, which comprises possible settlements, the resulting displacement field is computed by minimizing the total potential energy of the system by means of a linear programming optimization algorithm. Moreover, a mesh adaptation scheme based on a suitable Genetic Algorithm (GA) is used to determine the crack pattern yielding the mechanism actually induced by the settlement. The procedure is here demonstrated through a numerical example.