Thrust Network Analysis of Masonry Arches and Domes of Any Stereotomy with Finite Compressive Strength: Multi-constrained Minimization Problem versus Stability Area Method

In this research, equilibrium analysis of curved structures is carried out via a computational approach based on the constrained force density method, with the aim of taking into account both the effects of a finite compressive strength of the material and any possible stereotomy of the voussoirs composing the structures. The procedure relies on independent sets of branches for networks with fixed plan projection. At each joint, a suitable set of local constraints is formulated to take into account the moment capacity. Then, a multi-constrained minimization problem is stated. In order to validate this approach, a benchmark case study is examined, i.e., a dome with arbitrary stereotomy. To this purpose, a classical semi-analytical graphical method, originally devised by the French scholar Durand-Claye is adopted. A re-visited version of this method, formulated in terms of the static theorem of Limit Analysis, is exploited in order to determine the complete set of admissible solutions with respect to both the equilibrium conditions and the strength requirements of the material.