Relations between static-structural aspects, construction phases and building materials of San Saturnino Basilica (Cagliari, Italy)

The construction site was used several times: in a first phase, in the republican era of Roman domination it hosted, probably, a temple whose height could reach 25 meters; in a second phase, during the Roman Empire, it was used as a burial area. Then around IV-V century AD a first Christian Basilica made of a naved building with an apse was built there, at the center of a large monastery. Subsequently in a third phase in VI century AD a Byzantine Martyrium, with a Greek cross-shaped plan, was built: the central part of it, supporting a dome is still standing. Finally after 1089 the church was given to Marsilian monks who deeply renovated it and changed its shape converting the plan to a Latin cross. A macroscopic material analysis shows the presence of various rocks, whose use appears to be inhomogeneous during all construction phases. Sedimentary rocks (limestones, sandstones, calcarenites etc belonging to local geological formations) are generally used for masonry structures. Marbles, mostly coming from abroad and previously used in Roman buildings have been adopted for architectural elements (columns, capitals, and so on). At a lower extent there are masonry blocks in Oligo-Miocenic volcanic rocks and seldom stone materials which are not originally from Sardinia. Both mineralogical and petrographic tests (e.g. XRF, XRD) and the most important physical properties (porosity, density, water absorption coefficients, compressive, flexural and tensile strength, etc) show that many of the more representative samples of rock materials (like limestonss, calcarenits) are often highly decayed, with a corresponding reduction of their mechanical strength. A structural analysis is particularly useful for helping in clarifying the historical evolution of the building, checking reconstruction hypotheses and assessing the true residual strength of the more important parts. An example, a FEM analysis of the Byzantine domed part is presented here

Stabilization by deflation for sparse dynamical systems without loss of sparsity

Multiple-input, multiple-output models for coupled systems in structural dynamics including unbounded domains, like soil or fluid, are characterized by sparse system-matrices and unstable parts in the whole set of solutions due to spurious modes. Spectral shifting with deflation can stabilize these unstable parts; however the originally sparse system-matrices become fully populated when this procedure is applied. This paper presents a special consecutive treatment of the deflated system without losing the numerical advantages from sparsity. The procedure starts with an LU-decomposition of the sparse undeflated system and continues with restricting the solution space with respect to deflation using the same LU-decomposition. An example from soil-structure interaction shows the benefits of this consecutive treatment

An analytical assessment of finite element and isogeometric analyses of the whole spectrum of Timoshenko beams

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values provided by several finite element models, based on either the traditional Lagrangian interpolation or on the recently developed isogeometric approach. Comparison of results is performed on both spectrum error (in terms of the detected natural frequencies) and on the l2 relative error (in terms of the computed eigenmodes): this double check allows detecting for each finite element model, and for a discretization based on the same number of degrees-of-freedom, N, the frequency threshold above which some prescribed accuracy level is lost, and results become more and more unreliable. Hence a quantitative way of measuring the finite element performance in modeling a Timoshenko beam is proposed. The use of Fast Fourier Transform is finally employed, for a selected set of vibration modes, to explain the reasons of the accuracy decay, mostly linked to a poor separation of the natural frequencies in the spectrum, which is responsible of some aliasing of modes

On the whole spectrum of Timoshenko beams. Part II: Further applications

The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general rootfinding methods for nonlinear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models

On the whole spectrum of Timoshenko beams. Part I: a theoretical revisitation

The problem of free vibrations of the Timoshenko beam model is here addressed. A careful analysis of the governing equations allows identifying that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided. This allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. Among all possible combination of end constraints which can be applied to single-span beams, the case of a simply supported beam is considered. These theoretical results can be used as benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. traditional Lagrangian-based finite element models or the newly developed isogeometric approach

Isogeometric analysis of plane-curved beams

A curved beam element based on the Timoshenko model and non-uniform rational B-splines (NURBS) interpolation both for geometry and displacements is presented. Such an element can be used to suitably analyse plane-curved beams and arches. Some numerical results will explore the effectiveness and accuracy of this novel method by comparing its performance with those of some accurate finite elements proposed in the technical literature, and also with analytical solutions: for the cases where such closed-form solutions were not available in the literature, they have been computed by exact integration of the governing differential equations. It is shown that the presented element is almost insensitive to both membrane- and shear-locking, and that such phenomena can be easily controlled by properly choosing the number of elements or the NURBS degree

Sardinia radio telescope finite element model updating by means of photogrammetric measurements

The 64 m diameter Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope with an active surface. Among its peculiarities is the capability of modifying the configuration of the primary mirror surface by means of electromechanical actuators. This capability enables, within a fixed range, balancing of the deformation caused by external loads. In this way, the difference between the ideal shape of the mirror (which maximizes its performance) and the actual surface can be reduced. The control loop of the radio telescope needs a procedure that is able to predict SRT deformation, with the required accuracy, in order to reduce deviation from the ideal shape. To achieve this aim, a finite element model that can accurately predict the displacements of the structure is required. Unfortunately, the finite element model of the SRT, although very refined, does not give completely satisfactory results, since it does not take into account essential pieces of information, for instance, thermal strains and assembly defects. This paper explores a possible update of the finite element model using only the benchmark data available, i.e. the photogrammetric survey developed during the setup of the reflecting surface. This updating leads to a significant reduction in the differences between photogrammetric data and results of the numerical model. The effectiveness of this tuning procedure is then assessed

A simplified model for railway catenary wire dynamics

In this paper, a simplified analytic model for the dynamic behaviour of railway catenary wire is presented. The model is discussed and validated with the help of numerical results obtained by a finite element code, for the case of a typical Italian railway installation. The simplified model is convenient from the computational point of view and is useful for sensitivity analysis. Some parametric studies have been developed by considering as free parameters the velocity and the distance of the train pantographs and looking at their effect on catenary dynamics

ArchNURBS: NURBS-Based Tool for the Structural Safety Assessment of Masonry Arches in MATLAB

A new approach toward a fully computer-aided design (CAD) integrated structural analysis of arched masonry structures is proposed and a new MATLAB-based computational tool, named ArchNURBS, is developed. It is addressed to professionals dealing with the restoration or structural rehabilitation of historical constructions, who need to assess the safety of masonry arches under assigned load distributions. By using it, they can easily produce estimates of the carrying capacity of curved masonry members, and specifically arches of arbitrary shape. A CAD environment, which is very popular among professionals, can be employed to provide a nonuniform rational B-splines (NURBS) representation of arch geometry. On the basis of this representation, it is possible to perform both an elastic isogeometric analysis and a limit analysis of the structure up to the collapse load. Moreover, the developed tool is devised for handling the presence of fiber-reinforced polymers reinforcement strips at the extrados and/or intrados. This allows for the design of properly dimensioned reinforcement and its verification according to current building codes. The entire procedure relies upon a sound theoretical background. ArchNURBS is going to be freely distributed as an open-source project (http://sourceforge.net/projects/archnurbs/)

Continuous transition between traveling mass and traveling oscillator using mixed variables

The interaction between cars or trains and bridges has been often described by means of a simplified model consisting of a beam loaded by a traveling mass, or by a traveling oscillator. Among others, two aspects are essential when dealing with masses traveling along flexible vibrating supports: (i) a complete relative kinematics; and (ii) a continuous transition between a traveling mass, rigidly coupled, and a traveling oscillator, elastically coupled with the support. The kinematics is governed by normal and tangential components - with respect to the curved trajectory - of the acceleration. However in literature these parts are oriented with reference to the undeformed beam configuration. This model is improved here by a non-linear second-order enriched contribution. The transition between a traveling oscillator and a traveling mass is governed by the stiffness k of the elastic or viscoelastic coupling which, in the latter case (i.e. rigid coupling), has to tend towards infinity. However, very large stiffness values cause high frequencies and significant problems are mentioned in the literature in order to establish numerically stable and reliable results and in order to realize a continuous evolution between absolute and relative formulations. By using mixed state variables, generalized displacements and coupling forces, the contribution from the stiffness changes from k to its inverse 1/k, the coupling force itself becomes a member of the solution-space and the problems, which have been mentioned in the literature, disappear. As a matter of fact, the coupling force can also take into account a viscoelastic contribution; moreover, a larger number of traveling oscillators can be considered, too. Finally, for a periodic sequence of moving oscillators the dynamic stability is treated in the time-domain along several periods, as well as in the spectral domain, by using Floquet's theorem