1,721,150 research outputs found
Influenza dell’interfaccia fibre-matrice nella formulazione di modelli di resistenza macroscopici per materiali compositi
No full textAim of the work is the definition of domains apt to describe the overall strength properties of composite materials reinforced by long, parallel fibers, with a fiber-matrix interface of finite strength. To this end, a homogenization procedure for periodic media is employed in the framework of limit analysis theory, which allows one to define the macroscopic strength domain, Ghom, according to the known strength domains of the components (fiber, matrix and interface). By formulating suitable microscopic stress fields and failure mechanisms for a representative volume of the composite, inner and outer bounds to Ghom can be defined. Analytical expressions are also derived to approximate the composite strength under particular stress conditions in the case of matrix and interface complying with von Mises or Tresca yield conditions. Finally, further developments are outlined to improve the model and reduce the gap between the obtained bounds
A Method of Cells-type approach to estimate the macroscopic elastic and creep coefficients of brick masonry
No full textThe problem of obtaining reliable analytical expressions for the macroscopic elastic and creep coefficients of brick masonry with a regular pattern according to the mechanical properties of the individual constituents (e.g. mortar and units) is dealt with. Starting from the microscopic displacement field estimated over any Representative Volume Element by a refined finite element model with suitable periodicity boundary conditions, a kinematic solution is proposed that depends on a limited number of degrees of freedom and matches the numerical predictions with fair accuracy. According to this field, the macroscopic constitutive law is derived in closed form at various degrees of approximation. A minimization of the potential energy of the RVE under any macroscopic stress respect to all the model d.o.f.s is shown to give values for the macroscopic elastic constants in excellent agreement with the FE results taken as a benchmark. Eventually, the results are extended to the description of the global creep behaviour of brickwork under service loads, assuming both units and mortar to obey Zener rheological model. Using the concept of effective modulus, the proposed approach is found to accurately predict also the macroscopic delayed moduli of brickwork given by the FE model
Omogeneizzazione di compositi fibrorinforzati a matrice elastoplastica
No full textA numerical model was developed for the evolutive analysis of unidirectional fiber composites. The model is based on homogenization theory for periodic media and requires a single representative volume element (RVE) to be analyzed. The related structural problem is numerically solved by the finite element method. Particular attention is given to the boundary conditions that ensure the continuity of the displacement field across adjacent RVEs and the periodicity of the microscopic strain field. The results obtained for metal composites are compared with the findings of other authors: the importance of a correct enforcement of the boundary conditions to reliably estimate the macroscopic response is emphasized. For perfectly plastic composites, the numerical results agree with previously obtained theoretical predictions as far as the ultimate strength is concerned
Corso di scienza delle costruzioni 2
No full textGli argomenti trattati nel testo corrispondono a quelli trattati abitualmente nei corsi di ‘Scienza delle Costruzioni II’ del Politecnico di Milano. Il testo consta essenzialmente di due parti. La prima inizia con alcuni richiami di Meccanica dei Solidi, con particolare riguardo al ruolo dell’equazione dei lavori virtuali in meccanica strutturale e alle formulazioni energetiche del problema elastico lineare. Si passa poi allo studio dei problemi piani di elasticità e di alcune teorie ingegneristiche per l’analisi di travi e piastre. Vengono quindi presentati i fondamenti teorici del metodo degli elementi finiti, limitatamente all’ambito elastico lineare, e alcuni fra gli elementi più utilizzati nella pratica ingegneristica per la determinazione di soluzioni approssimate per solidi elastici generici, sistemi di travi e piastre inflesse. Nella seconda parte si illustra dapprima il comportamento meccanico dei materiali schematizzabili come elastici-perfettamente plastici e di travi pressoinflesse costituite da tali materiali. Dopo aver mostrato come la capacità portante di una struttura possa essere valutata attraverso un’analisi evolutiva in campo non lineare, si conclude la trattazione presentando i fondamenti della teoria dell’analisi limite, che consente di stimare direttamente tale capacità e che costituisce pertanto un potente strumento di progetto e verifica per l’ingegnere, non solo civile
Lower and upper bounds to the macroscopic strength domain of a fiber reinforced composite material
No full textThe macroscopic strength domain of a composite material reinforced by long, parallel fibers is, in general, unknown but for its theoretical definition. In this note it is shown how a homogenization technique applied to yield design theory allows the derivation of two domains (in the space of macroscopic stresses) that are a lower and an upper bound to the composite strength domain. The dependence of these domains on the fiber content and on the shape of the fiber array is pointed out. Analytical equations for the approximate uniaxial macroscopic strength of composites with Drucker-Prager or Von Mises type matrix are derived. For more complex stress conditions, the relevant strength domains are numerically evaluated as well. The discrepancy between the two bounds is in many cases relatively small. In particular, the two bounds yield the same value for the uniaxial strength of the composite along the fiber direction, which, by consequence, is exactly determined
Delimitazione bilaterale del dominio di resistenza macroscopico di un materiale fibrorinforzato
No full textThe macroscopic strength domain or a composite material reinforced by long, parallel fibers is, in general, unknown but for its theoretical definition. In this note it is shown how a homogenization technique applied to yield design theory a1lowed to derive (in the space or macroscopic stresses) two domains, which are a lower and an upper bound to the real strength domain. The dependence or these domains on the fiber content and on the shape or the fiber array is discussed
Analysis of the Behavior of Brick Masonry with Calcium Silicate Units under Sustained Loads
No full textThe numerical modeling of the time evolution of stresses and strains in brickwork made with Ca2SiO4 units under sustained loads is dealt with, within the framework of linear viscoelasticity. The research aims at investigating the influence of the brick pattern on the creep behavior (global deformation; stress redistribution) of any wall under typical load conditions, and at assessing whether a simplified 2D layered model can be employed to get reliable predictions. To this end, finite element analyses were carried out, using two 3D models representative of header bond masonry and Flemish bond masonry; the results were compared with those given by the layered model. The influence of the mortar properties on the stress redistribution was also investigated. Whereas the layered model provides a fairly good prediction of the global creep deformation for both masonry textures under vertical (uniform and eccentric) load, it cannot be applied under more complex load conditions. Under uniform vertical load, 3D models taking the real masonry pattern into account must be used to predict the local stress evolution accurately. The uncertainties regarding the mortar Poisson’s ratio basically affect the time evolution of the transversal stress in the units and the joints
Closed-form expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry
Full text linkApproximate expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry with a regular pattern are derived in closed form, using a homogenization approach for periodic media. A microscopic displacement field fulfilling suitable periodicity boundary conditions, and depending on a
limited number of degrees of freedom, is formulated over any masonry Representative Volume Element (RVE). According to this field, closed-form expressions for the macroscopic elastic constants are obtained at various degrees of approximation, either using a Method of Cells-type approach, or minimizing the potential energy of the RVE subjected to any given macroscopic stress. Eventually, the results are extended to the description of the global creep behavior of brickwork under service loads, assuming the creep laws of units and mortar to be expressed by Prony series. Using the FE solution as a benchmark, the proposed approach is found to accurately match both the macroscopic constitutive law in linear elasticity and the time evolution of the macroscopic strains of brickwork under sustained macroscopic stress
Meccanica dei sistemi di travi
No full textIl testo affronta lo studio dei sistemi piani di travi (che comprendono le strutture a telaio, ampiamente utilizzate nel campo delle costruzioni civili), dal punto di vista sia tensionale (calcolo delle sollecitazioni), sia deformativo (calcolo degli spostamenti). La trattazione è limitata al campo elastico lineare. L’ultima parte del testo è dedicata alla verifica di stabilità delle travi compresse.
Il testo si presta a quegli insegnamenti dei corsi di laurea in Ingegneria e Architettura (quali Scienza delle Costruzioni, Meccanica delle Strutture, ecc.) in cui il problema dell’analisi dei sistemi di travi viene affrontato indipendentemente dallo studio della Meccanica dei Solidi.
La trattazione teorica è accompagnata da numerosi esercizi svolti, riportati alla fine di ciascun capitolo
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