Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

The analysis of masonry double curvature structures by means of the kinematic theorem of limit analysis is traditionally the most diffused and straightforward method for an estimate of the load carrying capacity. However, the evaluation of the actual failure mechanism is not always trivial, especially for complex geometries and load conditions. Usually, the failure mechanism is simply hypothesized basing on previous experience, or - due to the complexity of the problem - FE rigid elements with interfaces are used. Both strategies may result in a wrong evaluation of the failure mechanism and hence, in the framework of the kinematic theorem of limit analysis, in an overestimation of the collapse load. In this paper, a simple discontinuous upper bound limit analysis approach with sequential linear programming mesh adaptation to analyze masonry double curvature structures is presented. The discretization of the vault is performed with infinitely resistant triangular elements (curved elements basing on a quadratic interpolation), with plastic dissipation allowed only at the interfaces for possible in- and out-of-plane jumps of velocities. Masonry is substituted with a fictitious material exhibiting an orthotropic behavior, by means of consolidated homogenization strategies. To progressively favor that the position of the interfaces coincide with the actual failure mechanism, an iterative mesh adaptation scheme based on sequential linear programming is proposed. Non-linear geometrical constraints on nodes positions are linearized with a first order Taylor expansion scheme, thus allowing to treat the NLP problem with consolidated LP routines. The choice of inequalities constraints on elements nodes coordinates turns out to be crucial on the algorithm convergence. The model performs poorly for coarse and unstructured meshes (i.e. at the initial iteration), but converges to the actual solution after few iterations. Several examples are treated, namely a straight circular and a skew parabolic arch, a cross vault and a dome. The results obtained at the final iteration fit well, for all the cases analyzed, previously presented numerical approaches.