Fast kinematic limit analysis of masonry walls with out-of-plane loading

Masonry structures represent one of the commonest structural typologies for buildings worldwide. In particular, masonry walls constitute, by far, the prevailing elementary structural unit in the majority of masonry constructions both modern and historical. This contribution validates an approach proposed by the authors for the limit analysis masonry vaults, now extended to a new general procedure for the structural assessment of masonry walls with out-of-plane loading based on an upper bound formulation. A given masonry panel of arbitrary form possibly with openings is described through its NURBS (Non-Uniform Rational B-Spline) parametric representation in the three-dimensional Euclidean space. An initial set of rigid elements subdividing the original wall geometry is identified through the definition of a suitable lattice of nodes. An upper-bound limit analysis formulation, taking into account the main characteristics of masonry material through homogenization, is deduced where internal dissipation is allowed along element edges only. As shown in a number of examples, a good estimate of the collapse load is obtained, provided that the initial net of yield lines is suitably adjusted by means of a Genetic Algorithm (GA).