A new numerical approach for determining optimal thrust curves of masonry arches

In this paper a new numerical approach for determining admissible thrust curves for masonry arches is proposed. Arbitrary loading conditions, including distributed loads applied to the extrados and to the intrados of the arch, but also horizontal inertial forces simulating the effects of seismic actions are considered for arches of any geometry. The admissible solutions, corresponding to equilibrium thrust curves entirely contained in the thickness of the arch, are consistent with the lower bound theorem of Limit Analysis and, thus, are “safe” solutions from a structural point of view. The well-established Milankovitch's theory for the equilibrium of masonry arches is reviewed and generalized. Then, a specific formulation of the theory is presented, allowing the construction of an effective and efficient numerical procedure based on the Point Collocation Method and enriched by a constrained optimization routine. The latter is aimed at determining, among all the admissible equilibrium solutions, the optimal solution matching specific requirements of interest for applications, as the solution corresponding to the maximum or minimum thrust. The proposed procedure is discussed and validated with reference to the cases of circular, parabolic and pointed arches. In particular, maximum and minimum thrust solutions have been determined for all the examined cases.