Simple homogenized plate model for out-of-plane loaded masonry taking into account material and geometrical non linearity

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a simplified “homogenized” procedure. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine where second order effects are suitably considered adding a further term, quadratic in the nodal displacement, within the total energy of the discretized system. As validation of the approach proposed, the buckling behavior of some existing experimental pre-compressed four-point bending tests is reproduced; furthermore square panels in two-way bending, exhibiting the classical Rondelet’s mechanisms, are also studied. The results obtained are compared with those provided by commercial FE programs and with specifically derived analytical results.