Search

We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O’Dwyer and fully developed by Block and coworkers. Reducing the bias by the quoted authors in favor of a graphical interpretation of the method, we reformulate the original version of the TNA by discarding the dual grid and focusing only on the primal grid, thus significantly enhancing the computational performances. The proposed reformulation of the TNA is also extended by including horizontal forces in the analysis as well as holes or free edges in the vault. Furthermore, the coefficient matrices entering the solution scheme are obtained by assembling the separate contribution of each branch, thus avoiding the ad hoc node numbering and branch orientation required by alternative implementations. Numerical examples, some of which referred to vaults having a particularly complex geometry, show the effectiveness and robustness of the proposed approach in assessing the safety conditions of existing masonry vaults or in designing new ones. [ABSTRACT FROM AUTHOR]

The present paper proposes a new Genetic Algorithm NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. A given masonry vault geometry can be represented by a NURBS (Non-Uniform Rational B-Spline) parametric surface and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material is deduced, with internal dissipation allowed exclusively along element edges. The approach is capable of well predicting the load bearing capacity of any masonry vault of generic shape. It is proved that, even by using a mesh constituted by very few elements, a good estimate of the collapse load multiplier is obtained provided that the initial mesh is adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism. The proposed method turns out to be both accurate and much less computationally expensive than existing methods for the limit analysis of masonry vaults. [ABSTRACT FROM AUTHOR]