XXII Congresso - Associazione Italiana di Meccanica Teorica e Applicata Genova, 14-17 Settembre 2015 Scuola Politecnica - Sede Architettura - Università di Genova Advanced numerical models of masonry vaults F. Fraternali, G. Teodosio, M. De Piano, G. Carpentieri, V.P. Berardi Department of Civil Engineering, University of Salerno, 84084 Fisciano (SA), Italy ABSTRACT This paper presents a mechanical model and a shape optimization procedure for masonry vaults. The model is based on the basic assumption that such structures exhibit a no-tension membrane state of stress across a thrust surface S. Thus, the static problem of the vault is reduced to the search for a shape of S which ensures membrane equilibrium under suitable no- tension and position constraints (optimal shape). A discrete formulation of the model is obtained through a non-conforming variational method which makes use of polyhedral approximations to the thrust surface and the potential of the membrane stress (Pucher’s approach). It leads to a representation of such a stress field by a discrete network of compressive forces. The paper includes some numerical examples underlying the performance of the proposed solution search strategy. INTRODUCTION The mechanical modeling of masonry structures is a rather complicated subject due to several reasons, such as the non-homogeneity of the material; friction effects; damage; and above all weakness of the material when it is pulled apart. As a first approximation, the elastic no-tension model can be used in engineering applications. It describes the masonry as linearly elastic in compression but unable to sustain any tensile stress. Such a model underlies, more or less consciously, the design of masonry structures since antiquity, especially in the case of vaulted structures or arches. For example, according to the well known method of Mery, the safety of a masonry arch depends on the existence of any funicular curve within the thickness of the arch. In more recent years, beginning with the famous work of J. Heyman The stone skeleton (1966), a continuing effort has been made to develop a rational limit analysis theory of masonry structures (Del Piero 1998, O’Dwyer, 1999). On the other hand, the elastic no-tension model has