Masonry vaults represent one of the most widespread structural typologies in the historical buildings of both Eastern and Western architecture. Therefore, the interest for their preservation is growing over time along with the need for developing new efficient tools to analyze and evaluate their load-bearing capacity. As pointed out in , it can be affirmed that the modern theory of limit analysis of masonry structures, which has been developed mainly by Heyman , is the most reliable tool to assess the ultimate load bearing capacity of masonry vaults. Modern approaches stem out from lower bound formulations (e.g. the so-called Thrust Network Method ) or upper bound formulations (like finite-element based methods, see e.g. ) of limit analysis. The present paper proposes a new NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. NURBS (i.e. Non-Rational Uniform Bi-Spline) are special approximating base functions widely used in the field of 3D modeling . A given masonry vault geometry can be represented by a NURBS parametric surface, which can be generated within a commercial 3D modeling software. By exploiting the properties of NURBS functions, a mesh of the given surface which still provides an exact representation of the vaulted surface, can be obtained. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation is deduced, with internal plastic dissipation allowed exclusively along element edges, capable of well predicting the load bearing capacity of any masonry vault under consideration. 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 meta-heuristic approaches (e.g. Genetic Algorithms) in order to enforce that element edges coincide with the actual failure mechanism. The proposed method turns out to be much less computationally expensive than existing methods for the limit analysis of masonry vaults and can be easily integrated with commercial 3D modeling software.
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