1,721,221 research outputs found
Some recent results in computational variational fracture
No full textThe present work deals with the convergence analysis two different computational approaches to the variational modeling of fracture: a weak discontinuity scheme for Griffith's theory of brittle fracture based on eigendeformations (eigenfracture), and a strong discontinuity approach based on r-adaptive meshes.
Regarding the first topic, we present a weak approach to brittle fracture, which approximates Griffith's energy functional by a family of functionals depending on a small parameter and two fields: the displacement field and an eigendeformation describing the fractures that may occur in the body. The mathematical outline of such an approach is briefly sketched, discussing Gamma-convergence of the eigendeformation functional sequence to Griffith's energy. Some numerical examples illustrate the convergence features of a numerical implementation based on a variationally informed element erosion technique.
Concerning strong discontinuity approaches, we discuss the numerical implications of a recent convergence result for 3D r-adaptive finite element models. For a given h>0 and an arbitrary (rectifiable) crack pattern, we consider the convergence properties of the triangulations of the body with size greater or equal to h, thus covering a large variety of available finite element implementations of variational fracture
Free discontinuity finite element models in two-dimensions for in-plane crack problems
Full text linkTwo different free discontinuity finite element models for studying crack initiation and propagation in 2D elastic problems are presented. Minimization of an energy functional, composed of bulk and surface terms, is adopted to search for the displacement field and the crack pattern. Adaptive triangulations and embedded or r-adaptive discontinuities are employed. Cracks are allowed to nucleate, propagate, and branch. In order to eliminate rank-deficiency and perform local minimization, a vanishing viscosity regularization of the discrete Euler–Lagrange equations is enforced. Converge properties of the proposed models are examined using arguments of the Γ-convergence theory. Numerical results for an in-plane crack kinking problem illustrate the main operational features of the free discontinuity approach
Dispositivo di isolamento sismico
No full textDispositivo isolatore sismico conformato per essere posizionato in corrispondenza della base di un edificio per assorbire una vibrazione derivante da un movimento sismico, comprendente una struttura stratiforme (100) in cui uno strato intermedio (12) realizzato in un materiale pentamode è compreso tra un elemento laminare superiore ed un elemento laminare inferiore realizzati in un materiale rigido
FORMULAZIONE VARIAZIONALE DEL PROBLEMA DI EQUILIBRIO DI SOLIDI ELASTICI NON REAGENTI A TRAZIONE
No full text
Error estimates for a lumped stress method for plane elastic problems
Full text linkThe variational properties and the convergence order of a Lumped Stress Method (LSM) for 2D anisotropic elasticity are presented. Such a method can be thought of as a rational procedure to approximate a plane continuous body by a truss-like structure. The traction problem of plane elasticity is considered, making use of the Airy stress function. Under suitable assumptions, the convergence of the LSM is proved on using arguments of the mathematical theory of mixed finite element methods. The given result is useful in order to prove the accuracy of the discrete-continuum approximation in technical applications
Complementary energy variational approach for plane elastic problems with singularities
No full textPresented is the numerical analysis of plane elastic problems involving stress concentrations and/or singularities using a physically meaningful complementary energy variational approach. The continuum body is modeled by a non-conventional truss structure. Stress distributions in laminated composite bodies and orthotropic sheets with a through crack are obtained. The present results are compared with the analytical solutions for different numerical methods
Multiscale Mechanical Modeling of CNT Structures
No full textWe deal in the present work with the following tasks: - multiscale modelling of hysteresis and strain localisation in nanoparticle lattices endowed with bistable elastic potentials; - mechanical modelling and structural identification of CNT foams and CNT multilayer assemblies. A rational approach to the limiting energies at the mesoscopic scale energies consists of determining the continuum limits of the discrete interaction potentials, which characterize the microscopic response (bistable elastic potentials). We formulate a multiscale mechanical model of CNT structures under compressive loading, which is inspired by some distinctive features of the micromechanical response reported earlier in the literature for such materials (see, e.g., Cao et al., 2005; Hutchens et al., 2010) The given model make uses of multiscale chains of lumped masses connected by nonlinear springs, and captures the characteristic ‘three-phase’ response of the examined structures (a:linear response; b:buckling; c:densification). We show that a series of bistable elastic springs indeed exhibits such a kind of response, and through-the-thickness localisation of the axial deformation, mimicking the snap-buckling events and the macroscopic hysteresis observed in real CNT arrays
ELEMENTO DI RINFORZO PER MATERIALI COMPOSITI E RELATIVO METODO DI PRODUZIONE
Full text linkLa presente monografia riguarda un elemento di rinforzo per materiali compositi e il relativo metodo di produzione.
Più precisamente, la presente monografia riguarda elementi di rinforzo per materiali compositi, aventi una sezione trasversale e/o un profilo longitudinale aventi una forma geometrica complessa basata su uno o più algoritmi di tipo frattale.
Allo stato della tecnica sono noti elementi di rinforzo per materiali compositi, aventi superfici laterali lisce o dotati di risalti superficiali, nervature e/o scanalature, aventi forme ricavate dalla geometria classica in particolare rette e piani. In diverse applicazioni di interesse tecnico, tali forme semplici non consentono un ancoraggio ottimale dell’elemento di rinforzo alla matrice del materiale composito, e pertanto non risultano particolarmente efficaci per il rinforzo di tali materiali.
Scopo della presente monografia è quello di sviluppare elementi di rinforzo aventi una struttura tale che permetta una più pronunciata aderenza alla matrice del materiale composito, rispetto agli elementi di tecnica nota.
Un ulteriore scopo del presente studio è quello di sviluppare tali elementi di rinforzo mediante un metodo che permetta la rapida elaborazione di tali elementi
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