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Analisi di strutture reticolari in elasticità finita con applicazione a materiali nanostrutturali
Full text linkLe strutture reticolari con non linearità geometriche e materiali vengono spesso analizzate mediante approcci numerici. Soluzioni dell’equilibrio in forma chiusa si trovano solamente per casi semplici di riferimento e sotto l’ipotesi di materiale elastico lineare. Tale ipotesi non è consistente con l’effettivo comportamento di solidi reali soggetti a grandi deformazioni. Pertanto, il lavoro di tesi riporta una formulazione analitica interamente non lineare per il problema dell’equilibrio e stabilità di strutture reticolari.
Le aste della struttura reticolare sono riguardate come solidi iperelastici di materiale omogeneo, comprimibile e isotropo. I campi di spostamento e deformazione sono considerati grandi, senza alcuna restrizione. Il problema a valori al contorno viene risolto, ricavando così le equazioni che governano l’equilibrio. Di conseguenza, la stabilità delle configurazioni di equilibrio viene studiata attraverso un criterio energetico. La formulazione è dapprima sviluppata per il traliccio di von Mises (arco a tre cerniere), il quale rappresenta il caso più semplice di struttura reticolare. Nonostante la sua apparente semplicità, tale sistema esibisce diversi tipi di comportamento post-critico, tra cui snap-through e biforcazione. La trattazione viene poi estesa al caso della struttura reticolare a tre aste, la quale rappresenta un importante problema di riferimento, poiché mostra diversi punti critici e configurazioni di equilibrio stabili non simmetriche. Si riportano alcune applicazioni della teoria a materiali polimerici, utilizzando il modello di Mooney-Rivlin per l’energia di deformazione elastica delle aste della struttura. I risultati hanno particolare importanza per quanto concerne la validazione di simulazioni agli elementi finiti o di altre procedure numeriche.
La trattazione non lineare per l’analisi di strutture reticolari in elasticità finita si applica anche allo studio del comportamento meccanico di materiali nanostrutturali. Nello specifico, in questo lavoro si analizza il grafene soggetto a grandi deformazioni piane. Gli atomi del reticolo cristallino esagonale rappresentano nodi connessi tra loro da elementi strutturali continui, le cui caratteristiche sono determinate attraverso un’equivalenza energetica con il potenziale interatomico dei legami chimici. L’equilibrio viene risolto per i casi di carico uniassiale ed equibiassiale. I risultati del lavoro dimostrano l’isotropia del grafene per piccole deformazioni, proprietà che viene persa per grandi deformazioni dando origine a un comportamento anisotropo. Si osservano inoltre soluzioni multiple e instabili dopo valori critici di deformazione.
A differenza di molti altri studi in letteratura, il modello presentato in questo lavoro di tesi tiene conto delle non linearità geometriche e materiali. Ciò è necessario per una modellazione accurata del comportamento meccanico del grafene, in quanto questo materiale può raggiungere deformazioni a rottura superiori a 15-20%. I risultati dello studio permettono quindi di approfondire la comprensione dei meccanismi di deformazione del grafene e del suo complesso comportamento meccanico.The analysis of truss structures involving geometric and material nonlinearities is often performed by means of numerical approaches. Closed-form solutions of the equilibrium are provided only for simple benchmark problems, under the inconsistent hypothesis of linear constitutive behavior of the material. This hypothesis does not reflect the actual behavior of solids subjected to large deformations. Therefore, in this thesis, a fully nonlinear analytical formulation of the equilibrium and stability of truss structures is presented.
The bars of the truss are regarded as hyperelastic bodies composed of a homogeneous, compressible and isotropic material. Both displacement and deformation fields are large, without any restriction. The boundary-value problem is written and the equations governing the equilibrium are derived. The stability of the equilibrium configurations is assessed through an energy criterion. The formulation is firstly obtained for the von Mises (or two-bar) truss, which is the simplest case of truss structure. Despite its apparent simplicity, it exhibits various types of post-critical behaviors, such as snap-through and bifurcation. The formulation is then extended to the three-bar truss, which is an important benchmark test because it shows a number of critical points and stable asymmetric configurations. Several applications to rubber-like materials are performed by assuming a Mooney-Rivlin law for the stored energy function of the bars. The results are of great importance for the validation of finite element simulations and other numerical procedures.
The nonlinear formulation for the analysis of truss structures can be applied to the study of the mechanical behavior of nanostructured materials. In particular, this work is focused on the response of graphene subjected to large in-plane deformations. The atoms of the graphene lattice structure are viewed as nodes connected by continuum elements, whose properties are determined through an energy equivalence with the interatomic potential of the chemical bonds. The equilibrium solutions are given for the cases of uniaxial and equibiaxial tensile loads. The results show that graphene is isotropic only for small deformations, while anisotropy arises for large deformations. Multiple and unstable solutions are found after critical values of deformation.
Differently from many other studies in literature, the model presented in this work accounts for both geometric and material nonlinearities. This is necessary for an accurate analysis of the mechanical behavior of graphene, because it can easily experience strains larger than 15-20% prior to failure. The results allow therefore to deepen the understanding of the mechanics of deformation of graphene and provide insights into its complex mechanical behavior
degrading Bouc-Wen model parametrers identification under cyclic load
No full textThe Bouc–Wen model of hysteresis is used in structural engineering to describe a wide range of
nonlinear hysteretic systems, as consequence of its capability to produce a variety of hysteretic
patterns. This research focuses on the application of the Bouc–Wen model to predict the hysteretic
behaviour of reinforced concrete bridge piers. The purpose is to identify the optimal values of the
parameters so that the output of the model matches as well as possible the experimental data. Two
repaired and retrofitted reinforced concrete bridge pier specimens (in a 1:6 scale of a real bridge pier)
tested physically in a laboratory are considered in this paper. An identification of Bouc–Wen model’s
parameters is performed using the force–displacement experimental data obtained after cyclic loading
tests on these two specimens. The original model involves many parameters and complex pinching
and degrading functions and this makes the identification solution unmanageable and with numerical
problems. Furthermore, from a computational point of view, the identification takes too much time.
The novelty of this work is the proposal of a simplification of the model allowed by: simpler pinching
and degrading functions; reduction of the number of parameters. The latter innovation is much
effective in reducing computational efforts and is performed after a deep study of the mechanical
effects of each parameter on the pier response. This simplified model is implemented in a MATLAB
code and the numerical results are well fitting the experimental ones and are reliable in terms of
manageability, stability, and computational time
Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening
Full text linkThe von Mises truss has been widely studied in the literature because of its numerous applications in multistable and morphing structures. The static equilibrium of this structure was typically addresses by considering only geometric nonlinearities. However, Falope et al. (2021) presented an entirely nonlinear solution in finite elasticity and demonstrated that material nonlinearities play an important role in the prediction of both snap-through and Euler buckling. In such work, the von Mises truss was subjected to a vertical load and thus the system was symmetric and the deformations were relatively small. The present contribution extends the investigation to the case of a horizontal load, which is much more complex due to asymmetry and very large deformations. Since most rubbers employed in technological applications exhibit hardening under large stretches, we propose a new hyperelastic model capable of reproducing this behavior. The advantage of such model compared to the ones available in the literature is that the equilibrium solution maintains a straightforward mathematical form, even when considering compressibility of the material. In addition, in this work we present a new formulation in nonlinear elasticity to predict Euler buckling. The formulation takes into account shear deformation. The analytical prediction agrees well with both finite element (FE) and experimental results, thus demonstrating the accuracy of the proposed model
Instability of compressed members in timber trusses assembled with punched metal plates
No full textThis study addresses the instability of wooden trusses assembled with punched metal plates. The instability of compressed wooden elements is a complex problem due to the specific boundary conditions, the timber orthotropy, and the difficult quantification of the defects. This research presents an analytical framework based on the Eurocode approach for predicting the instability of compressed wooden elements, considering the effect of boundary constraints representative of punched metal plates. The general aspects of this research are twofold: (i) proposing an analytical approximate expression for assessing the theoretical buckling load of compressed beams with elastic boundary constraints; (ii) deriving the buckling design curves as a function of the geometric imperfection of the structural element. The authors refer to the constraints exerted by punched metal plates, experimentally characterized to determine the response along the six degrees of freedom. The experimental results were used to generate a high-fidelity finite element (FE) model of the connection, validate it using digital image correlation, and estimate by extrapolation the stiffness properties of a selection of punched metal plates. Additionally, a secondary FE model was developed to simulate the out-of-plane deflection of structural elements with different types of punched metal plates, predict the failure load from static incremental analysis, and estimate the buckling design curves. In conclusion, the research aims to specialize the design method of compressed members according to the Eurocode, taking explicitly into account the boundary constraints representative of punched metal plates. It is found that while the theoretical instability load of beams with elastic constraints closely approximates that of the clamped condition, the instability load under imperfections resembles the pinned condition more closely. This observation leads to systematically higher imperfection coefficients for elastic constraints than pinned conditions
A degrading Bouc–Wen model for the hysteresis of reinforced concrete structural elements
No full textThis paper presents a smooth hysteresis model for reinforced concrete (RC) structural elements based on the differential equation of the Bouc–Wen model. Stiffness degradation and strength degradation are defined by introducing a damage index that includes both dissipated energy and maximum displacement. The pinching effect acts directly on the stiffness of the system and is controlled by an activation energy. The degrading functions are connected to the actual processes with which the damage occurs, thereby giving each parameter a physical meaning. The simple formulation of the model allows a straightforward identification of the best-fitting parameters and an easy interpretation of the results. Applications to the cyclic behaviour of RC structural elements demonstrate that the model is well capable of describing complex hysteretic behaviours involving degradation and pinching effects
Effect of pinching on structural resilience: performance of reinforced concrete and timber structures under repeated cycles
No full textThis article attempts to define pinching of two structural joints, reinforced concrete (RC) and wood ones. In particular, the research outlines differences and analogies between pinching of an RC portal and a Light Timber Frame (LTF) wall. This is done by focusing on the concavity of pinching in their response under repeated cycles, which produces differences in the energy dissipation. The response of the two structural archetypes under pseudo-static and dynamic simulations is analysed using the Atan hysteresis model modification. The truncated incremental dynamic analysis (TIDA) of the two systems modelled as single-degree-of-freedom (SDOF) oscillators yielded the fragility curves, approximated by a lognormal cumulative distribution (CDF). The stability of RC under repeated cycles reveals its significant resilience compared to LTF structures. The examination of the fragility functions supports a discussion about the relation between the pinching concavity and the notion of structural resilience by introducing a robustness index ranging from 0 to 1. Ultimately, a parametric analysis of a fictitious structural system derived from the timber one by varying the concavity of the pinching path leads to the estimation of the robustness index as a function of the pinching concavity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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