A mixed lumped stress–displacement approach to the elastic problem of masonry walls

We present a novel approach to the elastic problem of masonry walls, which generalizes the lumped stress method presented in Fraternali, 2001, Fraternali, 2007 and Fraternali, 2010 and Fraternali et al. (2002). The generalization consists of a mixed lumped stress–displacement approach to the elastic problem of a wall that incorporates no-tension elements. Such an approach depends on the nodal values of the Airy stress function and the displacements of selected (“pivot”) nodes. The latter coincide with inter-element and boundary nodes. The mixed lumped stress–displacement method can be conveniently coupled with standard finite element and boundary element approaches. Numerical applications dealing with recurrent structural elements are given, showing that such a method is able to capture some essential features of the actual response of masonry constructions.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We present a mixed approach to the elastic problem of a masonry wall based on polyhedral stress functions and nodal displacements (LSDM). ► The wall is composed of a collection of elastic elements including members that do not react in tension. ► The stress field is represented through a network of lumped stresses, while the deformation is characterized through the displacements of interelement and boundary nodes. ► We show that the LSDM is able to predict arch-type stress flow, distribution of compression rays and fracture of the material within recurrent structural elements made up of unreinforced and steel-reinforced masonry.