13 research outputs found
Analytical and numerical analysis on the collapse mode of circular masonry arches
No full textIn this paper, an analytical and numerical analysis on the collapse mode of circular masonry arches is presented. Specific reference is made to the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a masonry arch subjected to its own weight (Heyman 1977). The note reports the results of an on-going research project at the University of Bergamo. First, analytical solutions are derived in the spirit of limit analysis, according to the classical three Heyman hypotheses and explicitly obtained in terms of the unknown angular position of the intrados hinge at the haunch, the minimum thickness to radius ratio and the non-dimensional horizontal thrust (Colasante 2007, Cocchetti et al. 2010). Results are then compared to
Heyman solution. Though only the first of these three characteristics is perceptibly influenced in engineering terms, especially at increasing opening angle of the arch, the treatment settles an important conceptual
difference on the use of the true line of thrust, along the line of Milankovitch work. Second, numerical simulations by the Discrete Element Method (DEM) in a Discontinuous Deformation Analysis (DDA) computational
environment are provided, to further support the validity of the obtained solutions, with good overall matching of the obtained results (Rusconi 2008, Rizzi et al. 2010)
On limit analysis of masonry arches
No full textIn this paper, the so-called Couplet–Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general opening angle, subjected only to its own weight is reexamined. Classical analytical solutions provided by J. Heyman are first rederived and explored in details. Such derivations make obviously use of equilibrium relations. These are complemented by a tangency condition of the resultant thrust force at the haunches’ intrados. Later, given the same basic equilibrium conditions, the tangency condition is more correctly restated explicitly in terms of the true line of thrust, i.e., the locus of the centers of pressure of the resultant internal forces at each theoretical joint of the arch. Explicit solutions are obtained for the unknown position of the intrados hinge at the haunches, the minimum thickness to radius ratio and the nondimensional horizontal thrust. As expected from quoted Coulomb’s observations, only the first of these three characteristics is perceptibly influenced, in engineering terms, by the analysis. This occurs more evidently at increasing opening angle of the arch, especially for over-complete arches. On the other hand, the systematic treatment presented here reveals the implications of an important conceptual difference, which appears to be relevant in the statics of masonry arches. Finally, similar trends are confirmed as well for a Milankovitch-type solution that accounts for the true self-weight distribution along the arch
Analytical and Numerical Analysis on the Collapse Mode of Circular Masonry Arches
No full textIn this paper, an analytical and numerical analysis on the collapse mode of circular masonry arches is presented. Specific reference is made to the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a masonry arch subjected to its own weight (Heyman 1977). The note reports the results of an on-going research project at the University of Bergamo. First, analytical solutions are derived in the spirit of limit analysis, according to the classical three Heyman hypotheses and explicitly obtained in terms of the unknown angular position of the intrados hinge at the haunch, the minimum thickness to radius ratio and the non-dimensional
horizontal thrust (Colasante 2007, Cocchetti et al. 2010). Results are then compared to Heyman solution. Though only the first of these three characteristics is perceptibly influenced in engineering
terms, especially at increasing opening angle of the arch, the treatment settles an important conceptual difference on the use of the true line of thrust, along the line of Milankovitch work. Second, numerical simulations by the Discrete Element Method (DEM) in a Discontinuous Deformation Analysis (DDA) computational environment are provided, to further support the validity of the obtained solutions, with good overall matching of the obtained results (Rusconi 2008, Rizzi et al. 2010)
Strain-controlled Biaxial Tests of Coated-Fabric Membranes
No full textA better understanding of the mechanical behaviour of coated fabrics used for architectural membranes can lead to significant improvements in the design of tensile surface structures.
The plane biaxial test on a cruciform specimen is considered to be the most appropriate test to characterise the complex non-linear behaviour of such membrane material. The biaxial tests described in the literature are usually carried out under prescribed stress histories at various, constant stress ratios.
The present contribution describes some strain-controlled biaxial tests carried out at Politecnico di Milano, in which the strains in the central square of the specimen are prescribed. Such tests can be particularly meaningful in relation to installation and re-tensioning processes. Since they imply a variable stress ratio, the results obtained by these non-traditional tests complement the ones of stress-controlled experiments.
It appears that these two types of biaxial tests can be exploited jointly in order to select and calibrate constitutive models for coated fabrics; these are needed for the overall modelling of tensile structures, with the aim of simulating both the response under external loadings and the installation process
Analytical and numerical analysis on the collapse mode of circular masonry arches
No full textIn this paper, an analytical and numerical analysis on the collapse mode of circular masonry arches is presented. Specific reference is made to the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a masonry arch subjected to its own weight (Heyman 1977). The note reports the results of an on-going research project at the University of Bergamo. First, analytical solutions are derived in the spirit of limit analysis, according to the classical three Heyman hypotheses and explicitly obtained in terms of the unknown angular position of the intrados hinge at the haunch, the minimum thickness to radius ratio and the non-dimensional horizontal thrust (Colasante 2007, Cocchetti et al. 2010). Results are then compared to Heyman solution. Though only the first of these three characteristics is perceptibly influenced in engineering terms, especially at increasing opening angle of the arch, the treatment settles an important conceptual difference on the use of the true line of thrust, along the line of Milankovitch work. Second, numerical simulations by the Discrete Element Method (DEM) in a Discontinuous Deformation Analysis (DDA) computational environment are provided, to further support the validity of the obtained solutions, with good overall matching of the obtained results (Rusconi 2008, Rizzi et al. 2010)
Tensile structures: biaxial testing and constitutive modelling of coated fabrics at finite strains
Get PDFLa presente tesi riguarda la caratterizzazione meccanica e la modellazione costitutiva dei tessuti rivestiti impiegati nelle tensostrutture a membrana. Tali strutture sono costitutite da superfici sottili soggette esclusivamente a tensione, nelle quali sono assenti compressioni e momenti flettenti; si tratta quindi ti forme strutturali altamente efficienti, che richiedono conoscenze specifiche per essere progettate. La rapida diffusione di questa tipologia strutturale ha causato eterogeneità nelle procedure di progettazione impiegate attualmente, oltre alla frammentazione della conoscenza tecnica a disposizione dei produttori di membrane. Questi aspetti sono parzialmente legati all’assenza di normative europee sulle strutture a membrana.
In questo lavoro vengono forniti una serie di contributi in linea con gli obiettivi del Cluster di Ricerca sui “Tessili Innovativi” (ClusTEX), che è stato creato nel 2008 al Politecnico di Milano con lo scopo di sistematizzare ed incrementare il know-how sui compositi avanzati posseduto da diversi gruppi di ricerca.
In primis viene presentata una revisione delle informazioni sulle attuali procedure di analisi e progettazione presenti in letteratura. In particolare, viene fatto un tentativo di riorganizzare e descrivere in un quadro unificato i molteplici metodi impiegati per la ricerca della forma e per la generazione dei modelli di taglio. La scarsità di fonti riguardanti i modelli di taglio mette in luce la necessità di ulteriore ricerca e può essere parzialmente attribuita all’assenza di leggi costitutive affidabili per la descrizione del compotamento di primo carico cui sono soggetti i tessuti rivestiti durante l’installazione.
Successivamente la tesi si focalizza sui materiali utilizzati per le membrane delle tensostrutture, che sono principalmente materiali compositi, realizzati con una matrice polimerica rinforzata da fili tessuti. Vengono descritti il processo di produzione e le principali caratteristiche tecniche di tali tessuti rivestiti. Ne viene inoltre indagato in modo estensivo il comportamento meccanico, sia per mezzo di dati raccolti dalla letteratura, sia tramite i risultati commentati di test uniassiali e biassiali eseguiti direttamente dall’autore.
La complessa risposta dei tessuti tecnici, caratterizzata da elevati livelli di nonlinearità ed anisotropia, non è modellata adeguatamente nella attuale pratica progettuale, che impiega spesso la legge costitutiva ortotropa lineare elastica. Dall’altro lato, i modelli costitutivi utilizzati per scopi di ricerca sono spesso troppo complessi e computazionalmente dispendiosi. In questo contesto, la modellazione iperelastica in grandi deformazioni sembra essere una soluzione promettente per riprodurre in modo efficiente la risposta di tali materiali.
In questa tesi viene proposto un nuovo modello costitutivo, che è stato creato aggiungendo un termine all’energia libera del modello di Holzapfel-Gasser-Ogden per tessuti biologici. Il nuovo contributo energetico è stato pensato per catturare la forte interazione fra trama e ordito che nasce dalla tessitura (il cosidetto “crimp interchange”). Il modello proposto è calibrato per diversi materiali, sulla base dei risultati dei test biassiali descritti in precedenza. Viene presentata una validazione dello stesso, eseguita tramite alcuni semplici problemi di riferimento, dei quali la soluzione analitica è stata calcolata con un codice indipendente, sviluppato dall’autore con il software Mathematica. Il confronto con i risultati sperimentali di test di trazione uniassiali, bias e biassiali mostrano la capacità del modello di riprodurre il comportamento sforzo-deformazione dei tessuti rivestiti.
Infine, la nuova legge costitutiva è implementata in una user subroutine per ABAQUS ed i medesimi esempi di validazione sono risolti numericamente, con risultati vicini a quelli analitici. L’implementazione in un software agli elementi finiti apre la strada alla applicazione del modello nell’analisi strutturale globale delle tensostrutture. Ciò nonostante, alcuni problemi numerici devono ancora essere risolti: valori molto grandi di sforzo oltre una certa soglia di deformazione, difficoltà del metodo di Newton nel predire valori ragionevoli di incremento dello spostamento quando la rigidezza è piccola, derivate discontinue dell’energia dovute alla disattivazione di alcuni termini quando le fibre subiscono accorciamenti. Si tratta di aspetti che meriterebbero maggiore approfondimento, col fine di migliorare l’efficienza dell’algoritmo risolutivo.This thesis deals with the mechanical characterisation and constitutive modelling of coated fabrics that are employed in tensile membrane structures. These are made of thin surfaces that can carry only tension and no compression or bending; therefore they represent highly efficient structural forms, which require specific knowledge to be designed. The rapid growth of this structural typology has led to heterogeneity of the current design procedures and to fragmentation of the technical knowledge that membrane producers have at their disposal. These two aspects are partially linked to the absence of European standards on membrane structures.
A series of contributions are provided in this work, which are in line with the objectives of the Research Cluster on “Innovative Textiles” (ClusTEX) that has been created in 2008 at Politecnico di Milano, with the aim of systematising and enhancing the expertise currently possessed by several research units on the subject of advanced composites.
First, an extensive literature review is carried out, to assess the current state of the art about the analysis and design of tensile structures. The multiplicity of methods employed in the form-finding and cutting pattern generation stages is described within a unified framework. The scarcity of references about cutting pattern highlights the need of further research and may be partially attributed to the absence of reliable constitutive laws for the description of the first-loading behaviour that coated fabrics undergo during installation.
Then, the thesis focus is put on membrane materials for tensile structures. These are mainly composite materials made of a polymeric matrix, reinforced by means of woven yarns. The production process and the main technical characteristics of these composites are described. The mechanical behaviour of coated woven fabrics, which turns out to be extremely dependent on their internal meso-structure, is deeply explored. The experimental results obtained from uniaxial and biaxial tests, which have been performed directly by the author, are also commented.
The complex anisotropic nonlinear behaviour of coated woven fabrics is not adequately modelled in the current design practice, which often employs the orthotropic linear elastic constitutive law. On the other hand, the constitutive models used for research purposes are often too complex and computationally expensive. Within this framework, hyperelastic modelling at finite strains seems to be promising to efficiently reproduce the response of such materials.
A new model is proposed in this thesis, which has been created by adding a term to the free-energy of the existing Holzapfel-Gasser-Ogden model for biological tissues. This new energy component has been thought to capture the strong interaction between the warp and fill yarns which is due to the weaving (crimp interchange). The proposed model is calibrated for different materials, by employing the biaxial test data previously presented. A validation of the new model is performed through some simple benchmark problems, of which the analytical solution is evaluated with a code developed by the author with Mathematica software. The comparison of the results with experimental data shows that the model can reproduce well the stress-strain behaviour of coated woven fabrics for uniaxial and bias extension tests, as well as for biaxial tests.
Finally, the new constitutive law is implemented into a user subroutine for ABAQUS, and the same validation examples are solved numerically, with results that are close to the analytical solution. This implementation into a general purpose finite element software opens the doors to the application of this model to structural design. However, some numerical issues have still to be solved: extremely large stresses at very large strains, difficulty of Newton’s method in predicting a reasonable displacement correction when the stiffness is law, discontinuous derivatives of the strain energy due to deactivation of the some terms when fibres are shortened. These are all aspects that would deserve further studies, aimed at improving the efficiency of the solution algorithm.DIPARTIMENTO DI INGEGNERIA CIVILE E AMBIENTALE26NOVATI, GIORGIOPAOLUCCI, ROBERT
On the analysis of minimum thickness in circular masonry arches
No full textIn this paper, the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general opening angle, subjected only to its own weight is re-examined. Classical analytical solutions provided by J. Heyman are first re-derived and explored in details. Such derivations make obviously use of equilibrium relations. These are complemented by a tangency condition of the resultant thrust at the haunches’ intrados. Later, given the same basic equilibrium conditions, the tangency condition is more correctly re-stated in terms of the true line of thrust, i.e. the locus of the centers of pressure of the resultant internal forces at each theoretical joint of the arch. Explicit solutions are obtained for the unknown position of the intrados hinge at the haunches, the minimum thickness to radius ratio and the non-dimensional horizontal thrust. As expected from quoted Coulomb’s observations, only the first of these three characteristics is perceptibly influenced, in engineering terms, by the analysis. This occurs more evidently at increasing opening angle of the arch, especially for over-complete arches. On the other hand, the treatment presented here sets an important conceptual difference, which appears to be relevant, in the analysis of the statics of masonry arches. Finally, similar trends are confirmed as well for a Milankovitch-type solution that accounts for the true self-weight distribution along the arch
On the analysis of minimum thickness in circular masonry arches
No full textIn this paper, the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general opening angle, subjected only to its own weight is reexamined. Classical analytical solutions provided by J. Heyman are first rederived and explored in details. Such derivations make obviously use of equilibrium relations. These are complemented by a tangency condition of the resultant thrust force at the haunches' intrados. Later, given the same basic equilibrium conditions, the tangency condition is more correctly restated explicitly in terms of the true line of thrust, i.e., the locus of the centers of pressure of the resultant internal forces at each theoretical joint of the arch. Explicit solutions are obtained for the unknown position of the intrados hinge at the haunches, the minimum thickness to radius ratio and the nondimensional horizontal thrust. As expected from quoted Coulomb's observations, only the first of these three characteristics is perceptibly influenced, in engineering terms, by the analysis. This occurs more evidently at increasing opening angle of the arch, especially for over-complete arches. On the other hand, the systematic treatment presented here reveals the implications of an important conceptual difference, which appears to be relevant in the statics of masonry arches. Finally, similar trends are confirmed as well for a Milankovitch-type solution that accounts for the true self-weight distribution along the arch
On the mixed collapse mechanism of semi-circular masonry arches
No full textStarting from classical Heyman’s studies on the purely-rotational collapse mode of circular masonry arches, the hypothesis that friction is high enough to prevent sliding among the blocks, implying no sliding failure, is released. The onset of sliding is ruled by a classical Coulomb’s static friction law. The influence of the friction coefficient on the collapse mechanism is analysed, both analytically and numerically, by locating instances of purely-rotational, mixed sliding-rotational and purely-sliding mechanisms. A doubly built-in, symmetric, complete semi-circular masonry arch subjected only to its own weight is considered. The characteristic values of the friction coefficient that limit the ranges associated to each collapse mode are identified. Analytical formulas are provided to estimate the geometrical parameters that define the limit equilibrium states of the arch, in primis the minimum thickness to radius ratio. These formulas, starting from the analysis of the classical instance of purely-rotational collapse, make new explicit reference to the mixed sliding-rotational collapse mechanism. The obtained results are compared consistently to those available in the literature
Promote Community Engagement in Participatory Research for Improving Breast Cancer Prevention: The P.I.N.K. Study Framework
No full textBreast cancer (BC) has overtaken lung cancer as the most common cancer in the world and the projected incidence rates show a further increase. Early detection through population screening remains the cornerstone of BC control, but a progressive change from early diagnosis only-based to a personalized preventive and risk-reducing approach is widely debated. Risk-stratification models, which also include personal lifestyle risk factors, are under evaluation, although the documentation burden to gather population-based data is relevant and traditional data collection methods show some limitations. This paper provides the preliminary results from the analysis of clinical data provided by radiologists and lifestyle data collected using self-administered questionnaires from 5601 post-menopausal women. The weight of the combinations of women’s personal features and lifestyle habits on the BC risk were estimated by combining a model-driven and a data-driven approach to analysis. The weight of each factor on cancer occurrence was assessed using a logistic model. Additionally, communities of women sharing common features were identified and combined in risk profiles using social network analysis techniques. Our results suggest that preventive programs focused on increasing physical activity should be widely promoted, in particular among the oldest women. Additionally, current findings suggest that pregnancy, breast-feeding, salt limitation, and oral contraception use could have different effects on cancer risk, based on the overall woman’s risk profile. To overcome the limitations of our data, this work also introduces a mobile health tool, the Dress-PINK, designed to collect real patients’ data in an innovative way for improving women’s response rate, data accuracy, and completeness as well as the timeliness of data availability. Finally, the tool provides tailored prevention messages to promote critical consciousness, critical thinking, and increased health literacy among the general population
