Flavio Stochino

Constitutive models for strongly curved beams in the frame of isogeometric analysis

The current development of the isogeometric approach in various fields of mechanics is explained by the high-accuracy results which can be achieved at a reduced computational cost by codes based on non-uniform rational B-splines (NURBS). In the case of strongly curved beams the simple diagonal de Saint-Venant’s constitutive model can lead to significant errors as it has been reported in the classic literature. Other models such as Winkler’s have been proposed and seem more suitable for these kinds of structures. Unfortunately several numerical codes are based on a diagonal constitutive model which neglects the coupling effect of elongation and curvature even if a highly refined geometry description can be developed by means of NURBS. The results obtained by means of numerical codes based on isogeometrical analysis for curved beams are here reported and basic choices, computational costs and numerical accuracy of the above-mentioned constitutive models are discussed, from a qualitative and quantitative point of view. This comparison, in the authors’ opinion, is necessary to avoid an excessive gap between the computational efficiency of NURBS, which are capable of very accurate geometry description, and a simplistic representation of the constitutive relations that is efficient for straight beams but not so much for curved beams whose curvature is large. The results of some selected tests are presented and discussed to highlight differences between the two approaches, showing that the small increase of computational cost of Winkler’s model is well compensated by the accuracy gain.

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.

The Sardinia Radio Telescope: A comparison between close-range photogrammetry and finite element models:

The Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope endowed with an active-surface system. Its primary mirror has a quasi-parabolic shape with a diameter of 64 m. The configuration of the primary mirror surface can be modified by means of electro-mechanical actuators. This capability ensures, within a fixed range, the balancing of the deformation caused, for example, by loads such as self-weight, thermal effects and wind pressure. In this way, the difference between the ideal shape of the mirror (which maximizes its performances) and the actual surface can be reduced. In this paper the authors describe the characteristics of the SRT, the close-range photogrammetry (CRP) survey developed in order to set up the actuator displacements, and a finite element model capable of accurately estimating the structural deformations. Numerical results are compared with CRP measurements in order to test the accuracy of the model.

Structural Response and Reliability Analysis of RC Beam Subjected to Explosive Loading

The random nature of the explosion load, associated with the random nature of material properties, and geometric dimensional characteristics, implies the need to consider them into the reliability analysis in order to have a more correct estimation of the structural behavior. Therefore, when the randomness of these parameters in the analysis is considered, the response of the structure assumes probabilistic nature, and this makes it necessary to look into the reliability measure. This paper presents results from a parametric investigation of the reliability of reinforced concrete (RC) beam subjected to blast load. The probabilistic responses of the maximum displacement for a reinforced concrete flexural member under blast loadings are evaluated by means of nonlinear dynamic analysis with simplified equivalent single-degree-of-freedom (SDOF) system. Results of numerical simulations have shown the response of structures, in terms of maximum displacement in relation also to the blast load and the geometrical and mechanical characteristics of the beams. Monte Carlo simulation of dynamic response of the equivalent SDOF system is performed to estimate the reliability.

Modal analysis of laminates by a mixed assumed-strain finite element model:

Fibre-reinforced plates and shells are finding an increasing interest in engineering applications; in most cases dynamic phenomena need to be taken into account. Consequently, effective and robust computational tools are sought in order to provide reliable results for the analysis of such structural models. In this paper the mixed assumed-strain laminated plate element, previously used for static analyses, has been extended to the dynamic realm. This model is derived within the framework of the so-called First-order Shear Deformation Theory (FSDT). What is peculiar in this assumed-strain finite element is that in-plane strain components are modeled directly; the corresponding stress components are deduced via constitutive law. By enforcing the equilibrium equations for each lamina, and taking continuity requirements into account, the out-of-plane shear stresses are computed and, finally, constitutive law provides the corresponding strains. The resulting global strain field depends only on a fixed number of parameters, regardless of the total number of layers. Since the proposed element is not locking-prone, even in the thin plate limit, and provides an accurate description of inter-laminar stresses, an extension to the dynamic range seems to be particularly attractive. The same kinematic assumptions will lead to the formulation of a consistent mass matrix. The element, developed in this way, has been extensively tested for several symmetric lamination sequences; comparison with available analytical solutions and with numerical results obtained by refined 3-D models are also presented.

On the analysis of the stellar vault of Santa Maria del Monte in Cagliari

The aim of this paper is to study the statics of the stellar (i.e. star-shaped) vault of the church of Santa Maria del Monte in Cagliari. This church, which was built during the second half of the 16th century, is a beautiful example of Gothic-Catalan style and the ribbed stellar vault is one of the most representative of this type in the town of Cagliari. A comparison between a static finite element non-linear analysis carried out with the commercial code Diana and a limit analysis performed with a method recently developed by the research team of the University of Ferrara is presented.

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.

Dynamics of Strongly Curved Concrete Beams by Isogeometric Finite Elements

The standard finite elements approach for the dynamics of curved beam is usually based on the same energy functional used for straight beam, in other words an energy form that is essentially derived from de Saint–Venant’s theory. In case of strongly curved elements this approximation yields to not negligible errors, in particular for stress assessments. For this reason, in this work a different formulation, based on the Winkler’s simple kinematic assumptions, is adopted. In this way a non diagonal constitutive matrix is obtained and the computational efficiency of NURBS (Non Uniform Rational B–Splines) shape functions is added to an accurate representation of the constitutive relations. In this paper the natural frequencies and mode shapes of plane curved concrete beams are obtained. Computational cost and results accuracy is assessed with respect to closed form solutions and literature results.