Anti-funicular networks in masonry vaults with stereotomy, friction and strength requirements: a multi-constrained min/max problem validated through Durand-Claye’s method

This contribution, framed within the theoretical background of limit analysis, aims at assessing the equilibrium of masonry arches and domes. Anti-funicular networks are searched accounting for both the stereotomy of the voussoirs and the mechanical properties of masonry, by assuming a nil tensile strength, a limited compressive strength and a limited friction coefficient. A computational approach based on the constrained force density method is implemented in order to handle the equilibrium of the loaded nodes, by considering networks with a fixed plan geometry. At the interfaces between the voussoirs, a suitable set of local constraints is formulated to take into account the moment and shear capacity at the cross-sectional level. Then, a multi-constrained minimization/maximization problem is stated, which is solved by means of a sequential convex programming. The results obtained via the numerical method described above are validated by means of a modern re-visitation of Durand-Claye’s stability area method, which allows for determining the complete set of admissible solutions respecting both equilibrium and strength/friction requirements. Some significant case studies of masonry arches and domes with a non-conventional stereotomy are examined; moreover, critical issues related to the non-standard plastic behaviour of the material, arising from the hypothesis of a limited friction coefficient, are discussed.