The finite element code COMES-NOSA for the structural analysis of ancient masonry constructions

The finite element code NOSA (NOn-Linear Structural Analysis) has been developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR with the aim of testing new constitutive models for materials. It has moreover been applied to checking the algorithms used for integrating the equations of motion, as well as other numerical techniques for solving structural engineering problems. The development of NOSA began in 1980 and has continued over the ensuing years along the research lines of the Lab. In 1996, the Lab became a member of the Multi-centre Network for Computational Solid Mechanics (COMES). Since then, a large part of the group's development activities have been conducted within this framework, giving rise to the COMES-NOSA code. The first version of the code included plane, three-dimensional, axisymmetric isoparametric elements and shell elements and allowed for linear elastic analyses. Over the last two decades, constitutive models and calculation techniques have become available that enable realistic description of the static behaviour of masonry structures. Recent studies have led to a better understanding of the constitutive equation of the materials not withstanding tension, known in literature as masonry-like materials. Such equation can realistically reproduce the mechanical behaviour of masonry, at least regarding certain aspects. Within this framework, masonry is considered to be a non-linear elastic material, with zero tensile strength and infinite compressive strength. In order to study real problems, the equilibrium problem of masonry structures can be solved via the finite-element method. To this end, suitable numerical techniques have been developed. They are based on the Newton-Raphson method for solving the non-linear system obtained through discretising the structure into finite elements. Their application requires that the derivative of the stress with respect to the strain be explicitly known, as this is needed in order to calculate the tangent stiffness matrix. The numerical method studied has therefore been implemented into the COMES-NOSA code, which allows determination of the stress state and the presence of any cracking, and moreover enables modelling to be performed of any potential consolidation and restoration work, such as, for example, the fitting of chains. Moreover, the code allows for thermo-mechanical analysis of no-tension solids whose mechanical characteristics depend on temperature, in the presence of thermal loads. The code has been successfully applied to the analysis of arches and vaults as weel as of some buildings of historical and architectural interest, amongst which the chimney of the Vecchi Macelli in Pisa, the S. Nicolò's Motherhouse in Noto, the Goldoni Theatre in Livorno, the Medici Arsenal in Pisa, the Baptistery of the Volterra Cathedral, the Buti's bell tower and the San Pietro in Vinculis Church in Pisa deserve special mention. Development of the code has been made possible through the funding of C.N.R. (progetto finalizzato Informatica, progetto finalizzato Materiali Speciali per Tecnologie Avanzate, progetto finalizzato Beni Culturali) and funding of the region of Tuscany (structural funds and Regional High Tech Network).