Italian Workshop on
Shell and Spatial Structures
Massimo Cuomo
Dipartimento di Ingegneria Civile e Architettura, Università di CataniaBiography
Full professor of Solids and Structural Mechanics Italian coordinator of the Italian Group of Computational Mechanics (GIMC). Coordinator of the PhD programme of National Interest Defense against natural risks and ecological transition of the built environment. His research interests spam through Computational Mechanics of Solids and Structures, Non-linear structural modelling of rods and shells, Form finding methods for cables and shells, Plasticity and damage mechanics of solids, Fibre reinforced materials, Multi-physics modelling of materials.
The research activity has been mainly developed in the field of Computational Mechanics of Solids and Structures. Among the research subjects covered in his activity are: non linear structural modeling with innovative numerical methods (isogeometric analysis, splines etc.), damage mechanics of solids and computational fracture mechanics, multi-physics modeling of materials subjected to mechanical and chemical actions, static and dynamic analysis of structures with material and geometric non linearities, elasto-plastic analysis in the field of finite deformations.
Has been coordinator of many research projects, especially PRIN and CNR projects and others In the years 1993-1997 has been scientific coordinator of the research "Ancient building materials and building technologies of Eastern Sicily, with special interest for lava stones", sponsored by the National Secretariat for Cultural Heritage.
Has been scientific coordinator of a joint project with the Universitat Politecnica de Catalunya, Barcelona, of interchange projects with the Polytechnic of Helsinki and with the University of Nantes, of a frenchitalian doctoral programme (èn cotutele) with Universitè di Marne La Vallèe, Parigi.
Variational formulations for the form finding of flexible structures
The determination of the equilibrium configuration of a structure under assigned kinematic constraints is known as form finding problem, and is especially relevant for cables, cable nets and membranes. These structures do not have a uniquely defined reference configuration, due to the absence of bending stiffness, and the stress state has to be positive definite. However, form finding is also applied to the search of the equilibrium configuration of heavy shells, which are required to satisfy assigned constraints for the stress state.
In general, in addition to the position of parts of the boundary, additional kinematic constraints (like the cable length in the case of form finding of cables) or constraints on the stress state are imposed. In the case of minimal surfaces, the goal is to reach a form that guarantees an isotropic stress state everywhere. When the geometrical constraints are such that a minimal surface cannot be reached, several stress adaptation procedures have been proposed, that allow to reach a form that generally depends on the starting geometry.
A general variational formulation for form finding will be presented, applicable to cable nets and to membranes, able to incorporate suitable constraints for the stress state of for kinematic entities. The formulation includes position and stress variables, plus Lagrange multipliers for the constraints, so that it falls within the class of mixed methods. In addition to equality constraints, like those used in the case of minimal surfaces, inequality constraints are considered that allow to reach an equilibrated form with an adapted state of stress.
An efficient numerical implementation employing NURBS interpolation and allowing a direct connection with CAD codes has been used for performing illustrative examples.