Enrico Babilio

Dynamics of Functionally Graded Beams on Viscoelastic Foundation

In the present contribution, the nonlinear dynamics of beams under axial time-dependent excitation is studied. The beams, which rest on a linear viscoelastic foundation, are assumed as axially graded both in terms of geometrical and material properties. The transversal motion equation is derived under two main hypotheses, namely the beams satisfy the requirements of Euler–Bernoulli theory and undergo moderately large deflections (MLDs).

A Numerical Method for Fracture of Rods

We consider fracture problems for one-dimensional bodies, such as rods, through energy minimization. For an elastic-brittle body β occupying in the reference configuration the domain Ω, the energy depends on both some unknown closed crack set K and a displacement field u, smooth on Ω ∖ K. On Ω ∖ K a bulk energy density and on K an interface energy density are defined. As a result of this assumption the total potential energy is a nonconvex functional. We propose a new numerical method for the search of minimal states of rods by minimizing the energy both on K and u. To seek a minimizer (\( \tilde K \); ũ) a nonlinear gradient iterative procedure is employed. During the process of minimization both the displacement field u and the set K evolve toward local minima. To illustrate our approach, some examples are reported.

Limit Analysis for Unilateral Masonry-like Structures

Abstract: This paper is devoted to the application of unilateral models to the stress analysis of masonry structures. Some 2d applications of what we can call the simplified masonry-like model for masonry, are discussed and studied. The results here presented demonstrate that the unilateral model for masonry can be a useful tool for modeling real masonry structures. The main technique here employed for applying the No-Tension model to structures is the systematic use of singular stress and strain fields within the frame set by the theorems of Limit Analysis. A number of simple examples is discussed to illustrate the method.

A damping device based on bistable springs

A device for earthquake energy dissipation in shear-type structures is introduced. The idea is basically to employ chains made of bistable springs, that exhibit hysteretic behavior.

The Dynamics of Shear-Type Frames Equipped with Chain-Based Nonlinear Braces

In recent years a number of bracing devices have been proposed, analyzed, and applied to real cases, since in engineering applications the construction of frames equipped with braces is a widespread practice. In the present contribution, a nonlinear bracing system is introduced and applied to the case of shear-type moment-resistant frames. The frame is considered here as the primary structure and is assumed to have linear elastic behavior and the bracing system is considered as a secondary, additional structure. The bracing system is made of two chains, each of them constructed as the assemblage of two axial elements (springs) undergoing axial force, only. The springs that are assumed to have linear elastic behavior are connected to each other in the chain and to the frame through hinges. The global behavior of the system is nonlinear, since the restoring force of the bracing system is a piecewise-defined function. In order to asses the performance of the whole nonlinear system, its behavior is compared with that of the linear primary structure alone, through a suitable concise descriptor.

Capacity Design Criteria of 3D Steel Lattice Beams for Applications into Cultural Heritage Constructions and Archaeological Sites

Three-dimensional lattice beams are highly efficient technical solutions to cover large spans, especially when the single members do not have intermediate restraints able to prevent lateral-torsional buckling phenomena. Hence, lattice structures are widely applied in any field of civil and industrial engineering. In the present paper, in the framework of a research project funded by both the Campania Region and the European Community, a compound structure made of welded lattice beams and structural glass slabs is proposed as a structural system for valorisation and protection of monumental constructions and archaeological sites. Due to both the risk exposure of monumental heritage to be protected and the use of structural glass, the definition of an appropriate design criterion is mandatory in order to avoid development of brittle collapse mechanisms, mainly under static and dynamic vertical loads. The attention is herein paid to the design procedure, with a brief description of basic ideas behind the project itself and the main focus on the parametric capacity design of structural members. The proposed procedure, whose validity is quite general, has been subsequently verified by linear and non-linear numerical analyses calibrated on the basis of experimental investigations carried out on both the beam material and full-scale beam prototypes.

Nonlinear Dynamics of a Slender Axially Graded Beam Embedded in a Viscoelastic Medium

In the present contribution the nonlinear dynamics of beams under axial time-dependent excitation is studied. The beams, which are embedded in a linear viscoelastic medium, are assumed as axially graded in terms of material properties. The transversal motion equation is derived under two main hypotheses, namely the beams satisfy the requirements of Euler-Bernoulli theory and undergo moderately large deflections.Copyright

Static Analysis of Cross Vaults: The Case of the Cathedral of Casertavecchia

In the present paper, on assuming that the material has infinite friction and no cohesion, i.e. it is No-Tension in the sense of Heyman, we study the equilibrium of cross vaults of unequal rise, such as those of some Romanesque and Gothic churches. In particular the case study of the lateral cross vaults of the Cathedral of the old town of Caserta is analyzed. The scope of the paper is not to study in detail and quantitatively any particular vault, rather we give a compressive equilibrium solution (compatible with the unilateral material assumption) for the general case of cross vaults, constructed on arches of unequal rise, and loaded by a uniform load. For the purpose of the structural analysis, the vault is modelled as a thin shell made of Rigid No-Tension material. The webs of the vault that we consider, are supported on two crossing ribs. To obtain the axial force inside the ribs, equilibrated and singular stress fields (that is stress fields concentrated on curves and balanced with the loads) are constructed. An estimate of the thrust forces transmitted by the vault to the peripheral arches and walls is also obtained, so that the stability of these structures can be checked.