Simple lower bound limit analysis model for masonry double curvature structures

A new Lower Bound LB plate and shell limit analysis Finite Element FE model for the analysis at collapse of masonry double curvature structures is presented. The discretization relies into hexahedrons assumed infinitely resistant and quadrilateral interfaces where all plastic dissipation occurs. On such interfaces, the flexural behavior is ruled by the interaction between bending moment and axial load, whereas the shear and torsional behavior are modeled by means of an in-plane tangential force, out-of-plane shear and a plate torque. The resultant limit analysis problem obtained by such a formulation is particularly straightforward and the number of variables to deal with very limited. Equilibrium is indeed imposed only on hexahedrons and admissibility on interfaces between adjoining elements. Masonry can be modeled obeying a classic no-tension material or with more complex linearized failure surfaces, for example derived from suitable homogenization techniques. A simple Linear Programming LP problem is so derived, where the actual thickness of the structure is accurately accounted for, a key feature to assess the stability of a vault in case of the no-tension material assumption. The numerical model is validated by means of several meaningful structural examples. A detailed comparison with numerical data available in the literature, obtained for the same examples with alternative numerical approaches shows the accuracy of the method proposed and its usefulness for a fast and reliable prediction of the load carrying capacity of masonry double curvature structures.