Antonio Cazzani

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.

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.

AN UNSYMMETRIC STRESS FORMULATION FOR REISSNER-MINDLIN PLATES: A SIMPLE AND LOCKING-FREE RECTANGULAR ELEMENT

In the present paper a simple mixed-hybrid element for the linear analysis of Reissner-Mindlin plates is discussed. The element is derived from a modified Reissner functional and standard bilinear (isoparametric) interpolation for displacement and rotations is assumed whereas local stresses (rather than stress resultants and moments) are explicitly modelled. It is assumed that in plane shear stresses are not a priori symmetric. This choice allows to decouple the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling degrees of freedom. Out-of-plane shear stresses are then obtained such that equilibrium equations are exactly satisfied. The proposed element does not exhibit locking effects at all: i.e. the shear deformation energy is zero in the thin plate limit. Details of the formulation are provided, and the performances of the element are assessed with reference to well-established benchmark problems.

FEM-DEM modeling for out-of-plane loaded masonry panels: a limit analysis approach

In this work the performances of the Discrete Element Method (DEM) applied to kinematic limit analyses of the out-of-plane behavior of masonry wall panels (with different textures) are investigated. A discrete model of masonry is proposed, which assumes that rigid blocks are connected by a mortar interface: this is ap- propriate for historical masonry, where mortar is much more deformable than blocks and joints thickness is negligible. Therefore blocks can be modeled as rigid bodies connected by zero thickness Mohr-Coulomb-type interfaces. The applied method is known as FEM/DEM, which combines finite and discrete element models. A comparison with well-known and meaningful examples presented by Giuffre has been carried out in order to validate this method for studying the behavior of masonry. For this purpose, 2D DEM models reproducing walls sections have been considered: they reproduce masonry walls with different staggered blocks, in particular stack bond and running bond patterns, subjected to lateral loads.

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

AbstractA 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/...

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.

On the true extrema of Young’s modulus in hexagonal materials

Abstract In a paper, which has been recently published in Applied Mathematics and Computations , Khan and Ahmad (2012) [1] deal with the detection of the extrema of Young’s modulus, E , in hexagonal materials. A few issues presented in that paper, which deserve being outlined and thoroughly discussed, are tackled. Moreover, in the case of hexagonal materials, a suitable classification is suggested, an exhaustive panoramic view of the possible shape of the surface E ( n ) generated by Young’s modulus for all possible orientations n is illustrated, and some meaningful numerical examples are proposed.

Di un principio controverso della meccanica analitica di lagrange e delle molteplici sue applicazioni

I principj ed i metodi generali esposti dal sommo Lagrange nella Meccanica Analitica vennero in molta parte abbandonati dai geometri che dopo di lui trattarono questioni di Matematica applicata. L’essere alcuni di quei principj, o non dimostrati, o dimostrati incompletamente, pare sia la cagione principale di quell’abbandono, e ne abbiamo quasi una prova nel vedere adoperate tuttora le formole date da Lagrange nella Sezione IV della seconda parte, le quali, appunto perche rigorosamente dimostrate, non vennero lasciate in disparte anche dopo i lavori di Hamilton e di Jacobi sullo stesso argomento. Fra questi principj il piu importante per le applicazioni e certamente quello indicato dall’autore nella Sezione II, ed esposto con maggior chiarezza nella Sezione IV della prima parte della M. A., intorno al modo di introdurre l’effetto delle forze interne nella equazione generale per l’equilibrio e pel moto, e che il difetto di dimostrazione rese quasi sterile pei successori di Lagrange.

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.