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The preservation and definition of the correct retrofitting interventions of historic masonry buildings represents a relevant topic nowadays, especially in a country characterized by high seismicity zones. Considering the Italian Cultural Heritage, most of these buildings are constructed in ancient unreinforced masonry (URM) and showed a high level of vulnerability during the recent 2009 (L'Aquila), 2012 (Emilia Romagna) and 2016 (Centro Italia) earthquakes. In this paper, the seismic assessment of an historic masonry building damaged during 2016 Centro Italia seismic event is presented considering different types of retrofitting interventions. Starting from the results obtained by the post-earthquake survey, different finite element models have been implemented to perform linear and non-linear analyses useful to understand the seismic behaviour of the building and to define the appropriate retrofitting interventions. In particular, reinforced plaster layer and cement-based grout injections have been applied in each masonry wall of the building in order to improve their horizontal load-bearing capacity, and an additional wall made with Poroton blocks and M10 cement mortar has been built adjacent to the central stairwell. In addition, in view of the need to replace the roof seriously damaged during the seismic event, a cross-laminated roof solution characterized by a thickness equal to 14 cm (composed by seven layers, each 2 cm thick) has been proposed. The results show that the proposed retrofitting interventions have led to a significant improvement in the seismic behaviour of the building. [ABSTRACT FROM AUTHOR]

75 Lekszycki T, dell'Isola F. A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials. Francesco dell'Isola trained generations of scholars in many subsets of Continuum Mechanics where he himself fine-tuned his knowledge. 177 Eremeyev VA, dell'Isola F. On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains. An interesting aspect of dell'Isola's scientific production is that periodically the lines of research that he had followed intersect and influence each other: it is remarkable that, parallel to the study of the problem of the synthesis of circuits with Porfiri, dell'Isola approached with Pierre Seppecher and Jean-Jaques Alibert (Toulon) the problem of synthesis in the mechanical field [[55]]. This very large amount of collaborations fully emerges in two papers published in 2019 [[138]]: on one hand, in the study by dell'Isola et al. [[138]] all the obtained results on pantographic metamaterial are recalled within the main contributions given by a large part of "old" dell'Isola's etal. [Extracted from the article]

It was with Maugin that Francesco dell'Isola met Paul Germain for the first time. It is in this perspective that some of dell'Isola's works in the field of Economics, such as dell'Isola and del Monte [[18]] or his recent book [[19]], should be framed. Graph We are very pleased to dedicate this Special Issue of I Mathematics and Mechanics of Solids i to Francesco dell'Isola for celebrating his 60th birthday. Francesco dell'Isola's academic formation can be ascribed to a double matrix: the primary Italian one, for which it is even possible to draw up a genealogy, and the French one, mediated by his numerous collaborations with French scientists and inspired by his fruitful contact, as a young scholar, with Paul Germain. [Extracted from the article]

A rather unexplored question and a very challenging problem consist in the synthesis and modeling of composite metamaterials consisting of at least two phases. The study of this problem may have a huge impact in the field of Civil Engineering, where such kind of composite materials found several applications, for instance, in application to architectural and civil engineering heritage. More precisely, the aim of this work is to study the mechanical properties of a fibrous metamaterial embedded in a softer matrix. Numerical simulations, obtained by means of a commercial Finite Element code, are carried out on a soft matrix reinforced by stiffer fibers arranged according to a geometry defined by the fiber directions and compared with results achieved using an effective model in which the micro-structure is homogenized. The role of the fibers and the matrix is reinterpreted with regard to these models. Finally, the employed models are calibrated to reproduce the mechanical behavior of a simple experiment. [ABSTRACT FROM AUTHOR]

The mechanical behavior of fibrous metamaterials is mainly determined by the interactions between the fibers composing the architecture. These interactions are usually of two different kinds: those directly depending on the positions of the fibers and those that need mediators, usually consisting of hinges, either inelastic or perfect, inducing restrictions on the kinematics of the fiber joints. In cases of interest, it has been observed that hinges can either have a certain torsional stiffness or behave as perfect joints, simply ensuring that the fibers remain interconnected, but not applying any constraint on the relative rotations between them. Here the effect of torsional stiffness of inelastic hinges is studied in two shear tests for a selected fibrous metamaterial. It is shown that the stiffness of hinges can be tailored to avoid, or at least reduce, out-of-plane deformations. Moreover, it is shown that, after reaching a threshold, permanent deformations are observed. This phenomenon is treated in a simplified way, by introducing damage in the continuum model. [ABSTRACT FROM AUTHOR]

The central theme of this study is to investigate a remarkable capability of a second-gradient continuum model developed for pantographic structures. The model is applied to a particular type of this metamaterial, namely the wide-knit pantograph. As this type of structure has low fiber density, the applicability of such a continuum model may be questionable. To address this uncertainty, numerical simulations are conducted to analyze the behavior of a wide-knit pantographic structure, and the predicted results are compared with those measured experimentally under bias extension testing. The results presented in this study show that the numerical predictions and experimental measurements are in good agreement; therefore, in some useful circumstances, this model is applicable for the analysis of wide-knit pantographic structures. [ABSTRACT FROM AUTHOR]

In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those equations that specify a desired behavior. Addressing this problem has led to the synthesis of second gradient materials. In the second stage, it has been necessary to develop numerical integration schemes and the corresponding codes for solving, in physically relevant cases, the chosen equations. Finally, it has been necessary to physically construct the theoretically synthesized microstructures. This has been possible by means of the recent developments in rapid prototyping technologies, which allow for the fabrication of some complex (micro)structures considered, up to now, to be simply some mathematical dreams. We show here a panorama of the results of our efforts (1) in designing pantographic metamaterials, (2) in exploiting the modern technology of rapid prototyping, and (3) in the mechanical testing of many real prototypes. Among the key findings that have been obtained, there are the following ones: pantographic metamaterials (1) undergo very large deformations while remaining in the elastic regime, (2) are very tough in resisting to damage phenomena, (3) exhibit robust macroscopic mechanical behavior with respect to minor changes in their microstructure and micromechanical properties, (4) have superior strength to weight ratio, (5) have predictable damage behavior, and (6) possess physical properties that are critically dictated by their geometry at the microlevel. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Gustav Kirchhoff has been credited, among many other renowned achievements, as the first scientist who tackled and solved the problem of studying the transversal vibrations of beams with variable cross-section. His contribution, which was presented in 1879 and published in the following year, is nowadays almost forgotten in the international scientific community, with the only exception of the German-speaking countries. For this reason it is rediscovered and thoroughly discussed here, with an exegetical approach. For completeness' sake an unabridged translation into English (the first one, to the best of the authors' knowledge) is provided in the appendix for the interested readers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 fiberreinforced 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/). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Free vibrations of straight beams which are partially supported by an elastic foundation are analyzed. For the sake of simplicity, only the Euler-Bernoulli beam model coupled with a Winkler-type elastic foundation is considered. This structural system can be used to study, in a rather accurate way, the dynamic response of partially embedded piles (like those used for telecommunications) when dealing with the problem of identifying their mechanical properties during operative conditions. The study makes clear that different kinds of vibration modes may occur in the part of the beam which is supported by the continuous elastic foundation: indeed apart from the classical modes, corresponding to the dynamics of a free beam, it is possible to have vibration modes which are similar to the static deflection of a beam on an elastic support or even corresponding to rigid-body modes. For the same beam it is shown that transition between these vibration modes can appear when switching from the fundamental natural frequency to subsequent ones. This effect is the focus of the presented numerical examples. In particular, the analytic expression of the transcendental functions governing the vibration modes, and of the coefficients of the eigenfunctions for all occurring cases, are given here - to the best of the author's knowledge - for the first time. From the practical point of view, the reported results allow to define a suitable range of the elastic stiffness parameter such that the behavior of a partially supported beam can be conveniently approximated with that of a single-span beam, having one built-in end and the other free. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]