A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

This work summarizes the HdHr group of Hermitian integration algorithms for dynamic structural analysis applications. It proposes a procedure for their use when nonlinear terms are present in the equilibrium equation. The simple pendulum problem is solved as a first example and the numerical results are discussed. Directions to be pursued in future research are also mentioned. Copyright (C) 2009 H.M. Bottura and A. C. Rigitano.

Algoritmos de alinhamento múltiplo e técnicas de otimização para esses algoritmos utilizando Ant Colony

Pós-graduação em Ciência da Computação - IBILCE

Utilização da técnica VxIAT para a determinação de volumes de precipitação na área central do Estado de São Paulo

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

Influence of Goertler vortices spanwise wavelength on heat transfer rates

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction—the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise–average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented

L'a(rche)tipico Brian O'Nolan. Comico e riso dalla tradizione al post-

This study aims at analysing Brian O'Nolans literary production in the light of a reconsideration of the role played by his two most famous pseudonyms ,Flann Brien and Myles na Gopaleen, behind which he was active both as a novelist and as a journalist. We tried to establish a new kind of relationship between them and their empirical author following recent cultural and scientific surveys in the field of Humour Studies, Psychology, and Sociology: taking as a starting point the appreciation of the comic attitude in nature and in cultural history, we progressed through a short history of laughter and derision, followed by an overview on humour theories. After having established such a frame, we considered an integration of scientific studies in the field of laughter and humour as a base for our study scheme, in order to come to a definition of the comic author as a recognised, powerful and authoritative social figure who acts as a critic of conventions. The history of laughter and comic we briefly summarized, based on the one related by the French scholar Georges Minois in his work (Minois 2004), has been taken into account in the view that humorous attitude is one of man’s characteristic traits always present and witnessed throughout the ages, though subject in most cases to repression by cultural and political conservative power. This sort of Super-Ego notwithstanding, or perhaps because of that, comic impulse proved irreducible exactly in its influence on the current cultural debates. Basing mainly on Robert R. Provine’s (Provine 2001), Fabio Ceccarelli’s (Ceccarelli 1988), Arthur Koestler’s (Koestler 1975) and Peter L. Berger’s (Berger 1995) scientific essays on the actual occurrence of laughter and smile in complex social situations, we underlined the many evidences for how the use of comic, humour and wit (in a Freudian sense) could be best comprehended if seen as a common mind process designed for the improvement of knowledge, in which we traced a strict relation with the play-element the Dutch historian Huizinga highlighted in his famous essay, Homo Ludens (Huizinga 1955). We considered comic and humour/wit as different sides of the same coin, and showed how the demonstrations scientists provided on this particular subject are not conclusive, given that the mental processes could not still be irrefutably shown to be separated as regards graduations in comic expression and reception: in fact, different outputs in expressions might lead back to one and the same production process, following the general ‘Economy Rule’ of evolution; man is the only animal who lies, meaning with this that one feeling is not necessarily biuniquely associated with one and the same outward display, so human expressions are not validation proofs for feelings. Considering societies, we found that in nature they are all organized in more or less the same way, that is, in élites who govern over a community who, in turn, recognizes them as legitimate delegates for that task; we inferred from this the epistemological possibility for the existence of an added ruling figure alongside those political and religious: this figure being the comic, who is the person in charge of expressing true feelings towards given subjects of contention. Any community owns one, and his very peculiar status is validated by the fact that his place is within the community, living in it and speaking to it, but at the same time is outside it in the sense that his action focuses mainly on shedding light on ideas and objects placed out-side the boundaries of social convention: taboos, fears, sacred objects and finally culture are the favourite targets of the comic person’s arrow. This is the reason for the word a(rche)typical as applied to the comic figure in society: atypical in a sense, because unconventional and disrespectful of traditions, critical and never at ease with unblinkered respect of canons; archetypical, because the “village fool”, buffoon, jester or anyone in any kind of society who plays such roles, is an archetype in the Jungian sense, i.e. a personification of an irreducible side of human nature that everybody instinctively knows: a beginner of a tradition, the perfect type, what is most conventional of all and therefore the exact opposite of an atypical. There is an intrinsic necessity, we think, of such figures in societies, just like politicians and priests, who should play an elitist role in order to guide and rule not for their own benefit but for the good of the community. We are not naïve and do know that actual owners of power always tend to keep it indefinitely: the ‘social comic’ as a role of power has nonetheless the distinctive feature of being the only job whose tension is not towards stability. It has got in itself the rewarding permission of contradiction, for the very reason we exposed before that the comic must cast an eye both inside and outside society and his vision may be perforce not consistent, then it is satisfactory for the popularity that gives amongst readers and audience. Finally, the difference between governors, priests and comic figures is the seriousness of the first two (fundamentally monologic) and the merry contradiction of the third (essentially dialogic). MPs, mayors, bishops and pastors should always console, comfort and soothe popular mood in respect of the public convention; the comic has the opposite task of provoking, urging and irritating, accomplishing at the same time a sort of control of the soothing powers of society, keepers of the righteousness. In this view, the comic person assumes a paramount importance in the counterbalancing of power administration, whether in form of acting in public places or in written pieces which could circulate for private reading. At this point comes into question our Irish writer Brian O'Nolan(1911-1966), real name that stood behind the more famous masks of Flann O'Brien, novelist, author of At Swim-Two-Birds (1939), The Hard Life (1961), The Dalkey Archive (1964) and, posthumously, The Third Policeman (1967); and of Myles na Gopaleen, journalist, keeper for more than 25 years of the Cruiskeen Lawn column on The Irish Times (1940-1966), and author of the famous book-parody in Irish An Béal Bocht (1941), later translated in English as The Poor Mouth (1973). Brian O'Nolan, professional senior civil servant of the Republic, has never seen recognized his authorship in literary studies, since all of them concentrated on his alter egos Flann, Myles and some others he used for minor contributions. So far as we are concerned, we think this is the first study which places the real name in the title, this way acknowledging him an unity of intents that no-one before did. And this choice in titling is not a mere mark of distinction for the sake of it, but also a wilful sign of how his opus should now be reconsidered. In effect, the aim of this study is exactly that of demonstrating how the empirical author Brian O'Nolan was the real Deus in machina, the master of puppets who skilfully directed all of his identities in planned directions, so as to completely fulfil the role of the comic figure we explained before. Flann O'Brien and Myles na Gopaleen were personae and not persons, but the impression one gets from the critical studies on them is the exact opposite. Literary consideration, that came only after O'Nolans death, began with Anne Clissmann’s work, Flann O'Brien: A Critical Introduction to His Writings (Clissmann 1975), while the most recent book is Keith Donohue’s The Irish Anatomist: A Study of Flann O'Brien (Donohue 2002); passing through M.Keith Booker’s Flann O'Brien, Bakhtin and Menippean Satire (Booker 1995), Keith Hopper’s Flann O'Brien: A Portrait of the Artist as a Young Post-Modernist (Hopper 1995) and Monique Gallagher’s Flann O'Brien, Myles et les autres (Gallagher 1998). There have also been a couple of biographies, which incidentally somehow try to explain critical points his literary production, while many critical studies do the same on the opposite side, trying to found critical points of view on the author’s restless life and habits. At this stage, we attempted to merge into O'Nolan's corpus the journalistic articles he wrote, more than 4,200, for roughly two million words in the 26-year-old running of the column. To justify this, we appealed to several considerations about the figure O'Nolan used as writer: Myles na Gopaleen (later simplified in na Gopaleen), who was the equivalent of the street artist or storyteller, speaking to his imaginary public and trying to involve it in his stories, quarrels and debates of all kinds. First of all, he relied much on language for the reactions he would obtain, playing on, and with, words so as to ironically unmask untrue relationships between words and things. Secondly, he pushed to the limit the convention of addressing to spectators and listeners usually employed in live performing, stretching its role in the written discourse to come to a greater effect of involvement of readers. Lastly, he profited much from what we labelled his “specific weight”, i.e. the potential influence in society given by his recognised authority in determined matters, a position from which he could launch deeper attacks on conventional beliefs, so complying with the duty of a comic we hypothesised before: that of criticising society even in threat of losing the benefits the post guarantees. That seemingly masochistic tendency has its rationale. Every representative has many privileges on the assumption that he, or she, has great responsibilities in administrating. The higher those responsibilities are, the higher is the reward but also the severer is the punishment for the misfits done while in charge. But we all know that not everybody accepts the rules and many try to use their power for their personal benefit and do not want to undergo law’s penalties. The comic, showing in this case more civic sense than others, helped very much in this by the non-accessibility to the use of public force, finds in the role of the scapegoat the right accomplishment of his task, accepting the punishment when his breaking of the conventions is too stark to be forgiven. As Ceccarelli demonstrated, the role of the object of laughter (comic, ridicule) has its very own positive side: there is freedom of expression for the person, and at the same time integration in the society, even though at low levels. Then the banishment of a ‘social’ comic can never get to total extirpation from society, revealing how the scope of the comic lies on an entirely fictional layer, bearing no relation with facts, nor real consequences in terms of physical health. Myles na Gopaleen, mastering these three characteristics we postulated in the highest way, can be considered an author worth noting; and the oeuvre he wrote, the whole collection of Cruiskeen Lawn articles, is rightfully a novel because respects the canons of it especially regarding the authorial figure and his relationship with the readers. In addition, his work can be studied even if we cannot conduct our research on the whole of it, this proceeding being justified exactly because of the resemblances to the real figure of the storyteller: its ‘chapters’ —the daily articles— had a format that even the distracted reader could follow, even one who did not read each and every article before. So we can critically consider also a good part of them, as collected in the seven volumes published so far, with the addition of some others outside the collections, because completeness in this case is not at all a guarantee of a better precision in the assessment; on the contrary: examination of the totality of articles might let us consider him as a person and not a persona. Once cleared these points, we proceeded further in considering tout court the works of Brian O'Nolan as the works of a unique author, rather than complicating the references with many names which are none other than well-wrought sides of the same personality. By putting O'Nolan as the correct object of our research, empirical author of the works of the personae Flann O'Brien and Myles na Gopaleen, there comes out a clearer literary landscape: the comic author Brian O'Nolan, self-conscious of his paramount role in society as both a guide and a scourge, in a word as an a(rche)typical, intentionally chose to differentiate his personalities so as to create different perspectives in different fields of knowledge by using, in addition, different means of communication: novels and journalism. We finally compared the newly assessed author Brian O'Nolan with other great Irish comic writers in English, such as James Joyce (the one everybody named as the master in the field), Samuel Beckett, and Jonathan Swift. This comparison showed once more how O'Nolan is in no way inferior to these authors who, greatly celebrated by critics, have nonetheless failed to achieve that great public recognition O’Nolan received alias Myles, awarded by the daily audience he reached and influenced with his Cruiskeen Lawn column. For this reason, we believe him to be representative of the comic figure’s function as a social regulator and as a builder of solidarity, such as that Raymond Williams spoke of in his work (Williams 1982), with in mind the aim of building a ‘culture in common’. There is no way for a ‘culture in common’ to be acquired if we do not accept the fact that even the most functional society rests on conventions, and in a world more and more ‘connected’ we need someone to help everybody negotiate with different cultures and persons. The comic gives us a worldly perspective which is at the same time comfortable and distressing but in the end not harmful as the one furnished by politicians could be: he lets us peep into parallel worlds without moving too far from our armchair and, as a consequence, is the one who does his best for the improvement of our understanding of things.

Untersuchungen zur Genauigkeit adaptiver unstetiger Galerkin-Simulationen mit Hilfe von Luftblasen-Testfällen

Allgemein erlaubt adaptive Gitterverfeinerung eine Steigerung der Effizienz numerischer Simulationen ohne dabei die Genauigkeit des Ergebnisses signifikant zu verschlechtern. Es ist jedoch noch nicht erforscht, in welchen Bereichen des Rechengebietes die räumliche Auflösung tatsächlich vergröbert werden kann, ohne die Genauigkeit des Ergebnisses signifikant zu beeinflussen. Diese Frage wird hier für ein konkretes Beispiel von trockener atmosphärischer Konvektion untersucht, nämlich der Simulation von warmen Luftblasen. Zu diesem Zweck wird ein neuartiges numerisches Modell entwickelt, das auf diese spezielle Anwendung ausgerichtet ist. Die kompressiblen Euler-Gleichungen werden mit einer unstetigen Galerkin Methode gelöst. Die Zeitintegration geschieht mit einer semi-implizite Methode und die dynamische Adaptivität verwendet raumfüllende Kurven mit Hilfe der Funktionsbibliothek AMATOS. Das numerische Modell wird validiert mit Hilfe einer Konvergenzstudie und fünf Standard-Testfällen. Eine Methode zum Vergleich der Genauigkeit von Simulationen mit verschiedenen Verfeinerungsgebieten wird eingeführt, die ohne das Vorhandensein einer exakten Lösung auskommt. Im Wesentlichen geschieht dies durch den Vergleich von Eigenschaften der Lösung, die stark von der verwendeten räumlichen Auflösung abhängen. Im Fall einer aufsteigenden Warmluftblase ist der zusätzliche numerische Fehler durch die Verwendung der Adaptivität kleiner als 1% des gesamten numerischen Fehlers, wenn die adaptive Simulation mehr als 50% der Elemente einer uniformen hoch-aufgelösten Simulation verwendet. Entsprechend ist die adaptive Simulation fast doppelt so schnell wie die uniforme Simulation.

Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Impact And Explosive Loads On Concrete Buildings Using Shell And Beam Type Elements

The threat of impact or explosive loads is regrettably a scenario to be taken into account in the design of lifeline or critical civilian buildings. These are often made of concrete and not specifically designed for military threats. Numerical simulation of such cases may be undertaken with the aid of state of the art explicit dynamic codes, however several difficult challenges are inherent to such models: the material modeling for the concrete anisotropic failure, consideration of reinforcement bars and important structural details, adequate modeling of pressure waves from explosions in complex geometries, and efficient solution to models of complete buildings which can realistically assess failure modes. In this work we employ LS-Dyna for calculation, with Lagrangian finite elements and explicit time integration. Reinforced concrete may be represented in a fairly accurate fashion with recent models such as CSCM model [1] and segregated rebars constrained within the continuum mesh. However, such models cannot be realistically employed for complete models of large buildings, due to limitations of time and computer resources. The use of structural beam and shell elements for this purpose would be the obvious solution, with much lower computational cost. However, this modeling requires careful calibration in order to reproduce adequately the highly nonlinear response of structural concrete members, including bending with and without compression, cracking or plastic crushing, plastic deformation of reinforcement, erosion of vanished elements etc. The main objective of this work is to provide a strategy for modeling such scenarios based on structural elements, using available material models for structural elements [2] and techniques to include the reinforcement in a realistic way. These models are calibrated against fully three-dimensional models and shown to be accurate enough. At the same time they provide the basis for realistic simulation of impact and explosion on full-scale buildings

Dynamic effect of high speed railway traffic loads on the ballast track settlement

The traditional ballast track structures are still being used in high speed railways lines with success, however technical problems or performance features have led to non-ballast track solution in some cases. A considerable maintenance work is needed for ballasted tracks due to the track deterioration. Therefore it is very important to understand the mechanism of track deterioration and to predict the track settlement or track irregularity growth rate in order to reduce track maintenance costs and enable new track structures to be designed. The objective of this work is to develop the most adequate and efficient models for calculation of dynamic traffic load effects on railways track infrastructure, and then evaluate the dynamic effect on the ballast track settlement, using a ballast track settlement prediction model, which consists of the vehicle/track dynamic model previously selected and a track settlement law. The calculations are based on dynamic finite element models with direct time integration, contact between wheel and rail and interaction with railway cars. A initial irregularity profile is used in the prediction model. The track settlement law is considered to be a function of number of loading cycles and the magnitude of the loading, which represents the long-term behavior of ballast settlement. The results obtained include the track irregularity growth and the contact force in the final interaction of numerical simulation

High fidelity simulations of failure in fiber-reinforced composites

Los ensayos virtuales de materiales compuestos han aparecido como un nuevo concepto dentro de la industria aeroespacial, y disponen de un vasto potencial para reducir los enormes costes de certificación y desarrollo asociados con las tediosas campañas experimentales, que incluyen un gran número de paneles, subcomponentes y componentes. El objetivo de los ensayos virtuales es sustituir algunos ensayos por simulaciones computacionales con alta fidelidad. Esta tesis es una contribución a la aproximación multiescala desarrollada en el Instituto IMDEA Materiales para predecir el comportamiento mecánico de un laminado de material compuesto dadas las propiedades de la lámina y la intercara. La mecánica de daño continuo (CDM) formula el daño intralaminar a nivel constitutivo de material. El modelo de daño intralaminar se combina con elementos cohesivos para representar daño interlaminar. Se desarrolló e implementó un modelo de daño continuo, y se aplicó a configuraciones simples de ensayos en laminados: impactos de baja y alta velocidad, ensayos de tracción, tests a cortadura. El análisis del método y la correlación con experimentos sugiere que los métodos son razonablemente adecuados para los test de impacto, pero insuficientes para el resto de ensayos. Para superar estas limitaciones de CDM, se ha mejorado la aproximación discreta de elementos finitos enriqueciendo la cinemática para incluir discontinuidades embebidas: el método extendido de los elementos finitos (X-FEM). Se adaptó X-FEM para un esquema explícito de integración temporal. El método es capaz de representar cualitativamente los mecanismos de fallo detallados en laminados. Sin embargo, los resultados muestran inconsistencias en la formulación que producen resultados cuantitativos erróneos. Por último, se ha revisado el método tradicional de X-FEM, y se ha desarrollado un nuevo método para superar sus limitaciones: el método cohesivo X-FEM estable. Las propiedades del nuevo método se estudiaron en detalle, y se concluyó que el método es robusto para implementación en códigos explícitos dinámicos escalables, resultando una nueva herramienta útil para la simulación de daño en composites. Virtual testing of composite materials has emerged as a new concept within the aerospace industry. It presents a very large potential to reduce the large certification costs and the long development times associated with the experimental campaigns, involving the testing of a large number of panels, sub-components and components. The aim of virtual testing is to replace some experimental tests by high-fidelity numerical simulations. This work is a contribution to the multiscale approach developed in Institute IMDEA Materials to predict the mechanical behavior of a composite laminate from the properties of the ply and the interply. Continuum Damage Mechanics (CDM) formulates intraply damage at the the material constitutive level. Intraply CDM is combined with cohesive elements to model interply damage. A CDM model was developed, implemented, and applied to simple mechanical tests of laminates: low and high velocity impact, tension of coupons, and shear deformation. The analysis of the results and the comparison with experiments indicated that the performance was reasonably good for the impact tests, but insuficient in the other cases. To overcome the limitations of CDM, the kinematics of the discrete finite element approximation was enhanced to include mesh embedded discontinuities, the eXtended Finite Element Method (X-FEM). The X-FEM was adapted to an explicit time integration scheme and was able to reproduce qualitatively the physical failure mechanisms in a composite laminate. However, the results revealed an inconsistency in the formulation that leads to erroneous quantitative results. Finally, the traditional X-FEM was reviewed, and a new method was developed to overcome its limitations, the stable cohesive X-FEM. The properties of the new method were studied in detail, and it was demonstrated that the new method was robust and can be implemented in a explicit finite element formulation, providing a new tool for damage simulation in composite materials.

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented