A quadrilateral plate-type finite element to model stress singularities in no-tension materials

The assessment of masonry constructions and, in general, of only-compression structures requires accurate modelling of stress patterns activated by external loads and boundary settlements. To this aim, previous research introduced the continuous Airy-based stress singularities (CASS) method, a convex optimisation strategy that selects the solution of the boundary value problem in the space of admissible Airy-based stress states. In this sense, the stress tensor solution is evaluated as the curvature of the Airy stress potential. However, the CASS application range was limited to only rectangular elements. This paper reformulates the CASS method to analyse domains with curved geometries, thus enabling the modelling of curved structures largely present in architectural heritage. Specifically, a novel approach to evaluating curvature in non-rectangular finite elements is introduced. Several benchmarks are proposed to validate the novel computational approach. First, the numerical strategy is validated against analytical solutions on a masonry panel subjected to lateral loads. In particular, the method's accuracy is assessed by comparing the regular and irregular finite elements. After that, the method is benchmarked on a semicircular arch against well-known solutions represented by the minimum and maximum thrust conditions and the minimum thickness problem. Finally, its robustness and potential are showcased in a real case study represented by the church of Santa Maria Immacolatella della Pietà dei Turchini in Naples, Italy.