A new automatic procedure for nonlinear analysis of masonry arches subjected to large support movements

To predict the settlement and the collapse mechanisms of masonry arch structures caused by largely moving supports and the value of the support movement leading to collapse, an automatic procedure based on the use of Somigliana's distortions is proposed. The proposed procedure is an incremental method that computes the inner forces at the joints of the arch, composed of rigid blocks and deformable mortar joints, at each increase of the support movement. Somigliana's distortions are introduced at the joints to nullify the inadmissible forces, basically the tensile ones, and to restore material continuity at the cracked joints (equilibrium and congruence). The Somigliana distortions method allows for material and geometric nonlinear analysis, avoiding updating the stiffness matrix. The strength and robustness of the procedure are ascertained by analyzing case studies from the literature. The results are consistent with experimental and numerical outcomes provided by other authors.