Limit analysis of masonry structures based on fictitious associative-type contact interface laws

We illustrate an original method for the limit analysis of masonry structures modeled as assemblies of dry rigid blocks with Coulomb-type (non-associative) contact interface laws. The method resorts to a fictitious system characterized by cohesive-type contact interface laws that depend on the axial forces of the real block system. Two theorems establish the connection between the collapse state of the real (frictional) block assembly and that of the fictitious one. Hence, an alternative problem of mathematical programming is presented to evaluate the minimum collapse load multiplier. According to the proposed formulation, the complementarity condition is not introduced as constraint but is obtained as Karush-Khun-Tucker condition. Several numerical results concerning with masonry arches, portals and panels are provided to illustrate the application of the proposed approach, which is also validated through the comparison with some existing methods.