Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

Strength Predictions of Hat Stiffened Plate

Hat Stiffened Plates are used in composite ships and are gaining popularity in metallic ship construction due to its high strength-to-weight ratio. Light weight structures will result in greater payload, higher speeds, reduced fuel consumption and environmental emissions. Numerical Investigations have been carried out using the commercial Finite Element software ANSYS 12 to substantiate the high strength-to-weight ratio of Hat Stiffened Plates over other open section stiffeners which are commonly used in ship building. Analysis of stiffened plate has always been a matter of concern for the structural engineers since it has been rather difficult to quantify the actual load sharing between stiffeners and plating. Finite Element Method has been accepted as an efficient tool for the analysis of stiffened plated structure. Best results using the Finite Element Method for the analysis of thin plated structures are obtained when both the stiffeners and the plate are modeled using thin plate elements having six degrees of freedom per node. However, one serious problem encountered with this design and analysis process is that the generation of the finite element models for a complex configuration is time consuming and laborious. In order to overcome these difficulties two different methods viz., Orthotropic Plate Model and Superelement for Hat Stiffened Plate have been suggested in the present work. In the Orthotropic Plate Model geometric orthotropy is converted to material orthotropy i.e., the stiffeners are smeared and they vanish from the field of analysis and the structure can be analysed using any commercial Finite Element software which has orthotropic elements in its element library. The Orthotropic Plate Model developed has predicted deflection, stress and linear buckling load with sufficiently good accuracy in the case of all four edges simply supported boundary condition. Whereas, in the case of two edges fixed and other two edges simply supported boundary condition even though the stress has been predicted with good accuracy there has been large variation in the deflection predicted. This variation in the deflection predicted is because, for the Orthotropic Plate Model the rigidity is uniform throughout the plate whereas in the actual Hat Stiffened Plate the rigidity along the line of attachment of the stiffeners to the plate is large as compared to the unsupported portion of the plate. The Superelement technique is a method of treating a portion of the structure as if it were a single element even though it is made up of many individual elements. The Superelement has predicted the deflection and in-plane stress of Hat Stiffened Plate with sufficiently good accuracy for different boundary conditions. Formulation of Superelement for composite Hat Stiffened Plate has also been presented in the thesis. The capability of Orthotropic Plate Model and Superelement to handle typical boundary conditions and characteristic loads in a ship structure has been demonstrated through numerical investigations.

Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates

This paper presents a large amplitude vibration analysis of pre-stressed functionally graded material (FGM) laminated plates that are composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers. Nonlinear governing equations of motion are derived within the context of Reddy's higher-order shear deformation plate theory to account for transverse shear strain and rotary inertia. Due to the bending and stretching coupling effect, a nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to uniform temperature change, in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed FGM laminated plates are derived. A semi-analytical method that is based on one-dimensional differential quadrature and Galerkin technique is proposed to predict the large amplitude vibration behavior of the laminated rectangular plates with two opposite clamped edges. Linear vibration frequencies and nonlinear normalized frequencies are presented in both tabular and graphical forms, showing that the normalized frequency of the FGM laminated plate is very sensitive to vibration amplitude, out-of-plane boundary support, temperature change, in-plane compression and the side-to-thickness ratio. The CSCF and CFCF plates even change the inherent hard-spring characteristic to soft-spring behavior at large vibration amplitudes. (C) 2003 Elsevier B.V. All rights reserved.

Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Geochemical and nannofossil analyses of Cenomanian/Turonian sediments of DSDP Hole 75-530A

One of the key objectives of Deep Sea Drilling Project (DSDP) Leg 75 was to shed light on the underlying causes of Cretaceous oceanic anoxia in the South Atlantic by addressing two major hypotheses: productivity productivity-driven anoxia vs. enhanced ocean stratification leading to preservation of organic matter and black shale deposition. Here we present a detailed geochemical dataset from sediments deposited during the Cenomanian/Turonian (C/T) transition and the global oceanic anoxic event 2 (OAE 2) at DSDP Site 530A, located off-shore Namibia (southeast Angola Basin, north of Walvis Ridge). To characterise the succession of alternating black and green shales at this site and to reconstruct the evolution of their paleoenvironmental setting, we have combined data derived from investigations on bulk organic matter, biomarkers and the inorganic fraction. The location of the C/T boundary itself is biostratigraphically not well constrained due to the carbonate-poor (but organic matter-rich) facies of these sediments. The bulk d13Corg record and compound-specific d13C data, in combination with published as well as new biostratigraphic data, enabled us to locate more precisely the C/T boundary at DSDP Site 530A. The compound-specific d13C record is the first of this kind reported from C/T black shales in the South Atlantic. It is employed for paleoenvironmental reconstructions and chemostratigraphic correlation to other C/T sections in order to discuss the paleoceanographic aspects and implications of the observations at DSDP Site 530A in a broader context, e.g., with regard to the potential trigger mechanisms of OAE 2, global changes in black shale deposition and climate. On a stratigraphic level, an approximation and monitoring of the syndepositional degree of oxygen depletion within the sediments/bottom waters in comparison to the upper water column is achieved by comparing normalised concentrations of redox-sensitive trace elements with the abundance of highly source specific molecular compounds. These biomarkers are derived from photoautotrophic and simultaneously anoxygenic green sulphur bacteria (Chlorobiacea) and are interpreted as paleoindicators for events of photic zone euxinia. In contrast to a number of other OAE 2 sections that are characterised by continuous black shale sequences, DSDP Site 530A represents a highly dynamic setting where newly deposited black shales were repeatedly exposed to conditions of subtle bottom water re-oxidation, presumably leading to their progressive alteration into green shales. The frequent alternation between both facies and the related anoxic to slight oxygenated conditions can be best explained by variations in vertical extent of an oxygen minimum zone in response to changes in a highly productive western continental margin setting driven by upwelling.

Analysis of Combined Bending and Punching Tests of Reinforced Concrete Slabs within IMPACT III Project

The paper reports on a collaborative effort between the Swiss Federal Nuclear Safety Inspectorate (ENSI) and their consultants Principia and Stangenberg. As part of the IMPACT III project, reduced scale impact tests of reinforced concrete structures were carried out. The simulation of test X3 is presented here and the numerical results are compared with those obtained in the test, carried out in August 2013. The general object is to improve the safety of nuclear facilities and, more specifically, to demonstrate the capabilities of current simulation techniques to reproduce the behaviour of a reinforced concrete structure impacted by a soft missile. The missile is a steel tube with a mass of 50 kg and travelling at 140 m/s. The target is a 250 mm thick, 2,1 m by 2,1 m reinforced concrete wall, held in a stiff supporting frame. The reinforcement includes both longitudinal and transverse rebars. Calculations were carried out before and after the test with Abaqus (Principia) and SOFiSTiK (Stangenberg). In the Abaqus simulation the concrete is modelled using solid elements and a damaged plasticity formulation, the rebars with embedded beam elements, and the missile with shell elements. In SOFiSTiK the target is modelled with non-linear, layered shell elements for the reinforcement on both sides; non-linear shear deformations of shell/plate elements are approximately included. The results generally indicate a good agreement between calculations and measurements.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

Fatigue of curved steel bridge elements : design recommendations for fatigue of curved plate girder and box girder bridges /

Mode of access: Internet.

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

Hyaline tissue of thermally unaltered conodont elements and the enamel of vertebrates

Comparison of the ultrastructure of the hyaline tissue of conodont elements and the enamel of vertebrates provides little support for a close phylogenetic relationship between conodonts and vertebrates. Transmission and scanning electron microscopy shows that the mineralised component of the hyaline tissue of Panderodus and of Cordylodus elements consists of large, flat, oblong crystals, arranged in layers that run parallel to the long axis of the conodont. Enamel in the dentition of a living vertebrate, the lungfish Neoceratodus forsteri, has crystals of calcium hydroxyapatite, arranged in layers, and extending in groups from the dentine-enamel junction; the crystals are slender, elongate spicules perpendicular to the surface of the tooth plate, Similar crystal arrangements to those of lungfish are found in other vertebrates, but none resembles the organisation of the hyaline tissue of conodont elements, The crystals of hydroxyapatite in conodont hyaline tissue are exceptionally large, perpendicular or parallel to the surface of the element, with no trace of prisms, unlike the protoprismatic radial crystallite enamel of fish teeth and scales, or the highly organised prismatic enamel of mammals.

Flexural strengthening of RC beams using hybrid composite plate (HCP): experimental and analytical study

Hybrid Composite Plate (HCP) is a reliable recently proposed retrofitting solution for concrete structures, which is composed of a strain hardening cementitious composite (SHCC) plate reinforced with Carbon Fibre Reinforced Polymer (CFRP). This system benefits from the synergetic advantages of these two composites, namely the high ductility of SHCC and the high tensile strength of CFRPs. In the materialstructural of HCP, the ultra-ductile SHCC plate acts as a suitable medium for stress transfer between CFRP laminates (bonded into the pre-sawn grooves executed on the SHCC plate) and the concrete substrate by means of a connection system made by either chemical anchors, adhesive, or a combination thereof. In comparison with traditional applications of FRP systems, HCP is a retrofitting solution that (i) is less susceptible to the detrimental effect of the lack of strength and soundness of the concrete cover in the strengthening effectiveness; (ii) assures higher durability for the strengthened elements and higher protection to the FRP component in terms of high temperatures and vandalism; and (iii) delays, or even, prevents detachment of concrete substrate. This paper describes the experimental program carried out, and presents and discusses the relevant results obtained on the assessment of the performance of HCP strengthened reinforced concrete (RC) beams subjected to flexural loading. Moreover, an analytical approach to estimate the ultimate flexural capacity of these beams is presented, which was complemented with a numerical strategy for predicting their load-deflection behaviour. By attaching HCP to the beams’ soffit, a significant increase in the flexural capacity at service, at yield initiation of the tension steel bars and at failure of the beams can be achieved, while satisfactory deflection ductility is assured and a high tensile capacity of the CFRP laminates is mobilized. Both analytical and numerical approaches have predicted with satisfactory agreement, the load-deflection response of the reference beam and the strengthened ones tested experimentally.

GIS and geodatabases application to global scale plate tectonics modelling

Les reconstructions palinspastiques fournissent le cadre idéal à de nombreuses études géologiques, géographiques, océanographique ou climatiques. En tant qu?historiens de la terre, les "reconstructeurs" essayent d?en déchiffrer le passé. Depuis qu?ils savent que les continents bougent, les géologues essayent de retracer leur évolution à travers les âges. Si l?idée originale de Wegener était révolutionnaire au début du siècle passé, nous savons depuis le début des années « soixante » que les continents ne "dérivent" pas sans but au milieu des océans mais sont inclus dans un sur-ensemble associant croûte « continentale » et « océanique »: les plaques tectoniques. Malheureusement, pour des raisons historiques aussi bien que techniques, cette idée ne reçoit toujours pas l'écho suffisant parmi la communauté des reconstructeurs. Néanmoins, nous sommes intimement convaincus qu?en appliquant certaines méthodes et certains principes il est possible d?échapper à l?approche "Wégenerienne" traditionnelle pour enfin tendre vers la tectonique des plaques. Le but principal du présent travail est d?exposer, avec tous les détails nécessaires, nos outils et méthodes. Partant des données paléomagnétiques et paléogéographiques classiquement utilisées pour les reconstructions, nous avons développé une nouvelle méthodologie replaçant les plaques tectoniques et leur cinématique au coeur du problème. En utilisant des assemblages continentaux (aussi appelés "assemblées clés") comme des points d?ancrage répartis sur toute la durée de notre étude (allant de l?Eocène jusqu?au Cambrien), nous développons des scénarios géodynamiques permettant de passer de l?une à l?autre en allant du passé vers le présent. Entre deux étapes, les plaques lithosphériques sont peu à peu reconstruites en additionnant/ supprimant les matériels océaniques (symbolisés par des isochrones synthétiques) aux continents. Excepté lors des collisions, les plaques sont bougées comme des entités propres et rigides. A travers les âges, les seuls éléments évoluant sont les limites de plaques. Elles sont préservées aux cours du temps et suivent une évolution géodynamique consistante tout en formant toujours un réseau interconnecté à travers l?espace. Cette approche appelée "limites de plaques dynamiques" intègre de multiples facteurs parmi lesquels la flottabilité des plaques, les taux d'accrétions aux rides, les courbes de subsidence, les données stratigraphiques et paléobiogéographiques aussi bien que les évènements tectoniques et magmatiques majeurs. Cette méthode offre ainsi un bon contrôle sur la cinématique des plaques et fournit de sévères contraintes au modèle. Cette approche "multi-source" nécessite une organisation et une gestion des données efficaces. Avant le début de cette étude, les masses de données nécessaires était devenues un obstacle difficilement surmontable. Les SIG (Systèmes d?Information Géographiques) et les géo-databases sont des outils informatiques spécialement dédiés à la gestion, au stockage et à l?analyse des données spatialement référencées et de leurs attributs. Grâce au développement dans ArcGIS de la base de données PaleoDyn nous avons pu convertir cette masse de données discontinues en informations géodynamiques précieuses et facilement accessibles pour la création des reconstructions. Dans le même temps, grâce à des outils spécialement développés, nous avons, tout à la fois, facilité le travail de reconstruction (tâches automatisées) et amélioré le modèle en développant fortement le contrôle cinématique par la création de modèles de vitesses des plaques. Sur la base des 340 terranes nouvellement définis, nous avons ainsi développé un set de 35 reconstructions auxquelles est toujours associé un modèle de vitesse. Grâce à cet ensemble de données unique, nous pouvons maintenant aborder des problématiques majeurs de la géologie moderne telles que l?étude des variations du niveau marin et des changements climatiques. Nous avons commencé par aborder un autre problème majeur (et non définitivement élucidé!) de la tectonique moderne: les mécanismes contrôlant les mouvements des plaques. Nous avons pu observer que, tout au long de l?histoire de la terre, les pôles de rotation des plaques (décrivant les mouvements des plaques à la surface de la terre) tendent à se répartir le long d'une bande allant du Pacifique Nord au Nord de l'Amérique du Sud, l'Atlantique Central, l'Afrique du Nord, l'Asie Centrale jusqu'au Japon. Fondamentalement, cette répartition signifie que les plaques ont tendance à fuir ce plan médian. En l'absence d'un biais méthodologique que nous n'aurions pas identifié, nous avons interprété ce phénomène comme reflétant l'influence séculaire de la Lune sur le mouvement des plaques. La Lune sur le mouvement des plaques. Le domaine océanique est la clé de voute de notre modèle. Nous avons attaché un intérêt tout particulier à le reconstruire avec beaucoup de détails. Dans ce modèle, la croûte océanique est préservée d?une reconstruction à l?autre. Le matériel crustal y est symbolisé sous la forme d?isochrones synthétiques dont nous connaissons les âges. Nous avons également reconstruit les marges (actives ou passives), les rides médio-océaniques et les subductions intra-océaniques. En utilisant ce set de données très détaillé, nous avons pu développer des modèles bathymétriques 3-D unique offrant une précision bien supérieure aux précédents.<br/><br/>Palinspastic reconstructions offer an ideal framework for geological, geographical, oceanographic and climatology studies. As historians of the Earth, "reconstructers" try to decipher the past. Since they know that continents are moving, geologists a trying to retrieve the continents distributions through ages. If Wegener?s view of continent motions was revolutionary at the beginning of the 20th century, we know, since the Early 1960?s that continents are not drifting without goal in the oceanic realm but are included in a larger set including, all at once, the oceanic and the continental crust: the tectonic plates. Unfortunately, mainly due to technical and historical issues, this idea seems not to receive a sufficient echo among our particularly concerned community. However, we are intimately convinced that, by applying specific methods and principles we can escape the traditional "Wegenerian" point of view to, at last, reach real plate tectonics. This is the main aim of this study to defend this point of view by exposing, with all necessary details, our methods and tools. Starting with the paleomagnetic and paleogeographic data classically used in reconstruction studies, we developed a modern methodology placing the plates and their kinematics at the centre of the issue. Using assemblies of continents (referred as "key assemblies") as anchors distributed all along the scope of our study (ranging from Eocene time to Cambrian time) we develop geodynamic scenarios leading from one to the next, from the past to the present. In between, lithospheric plates are progressively reconstructed by adding/removing oceanic material (symbolized by synthetic isochrones) to major continents. Except during collisions, plates are moved as single rigid entities. The only evolving elements are the plate boundaries which are preserved and follow a consistent geodynamical evolution through time and form an interconnected network through space. This "dynamic plate boundaries" approach integrates plate buoyancy factors, oceans spreading rates, subsidence patterns, stratigraphic and paleobiogeographic data, as well as major tectonic and magmatic events. It offers a good control on plate kinematics and provides severe constraints for the model. This multi-sources approach requires an efficient data management. Prior to this study, the critical mass of necessary data became a sorely surmountable obstacle. GIS and geodatabases are modern informatics tools of specifically devoted to store, analyze and manage data and associated attributes spatially referenced on the Earth. By developing the PaleoDyn database in ArcGIS software we converted the mass of scattered data offered by the geological records into valuable geodynamical information easily accessible for reconstructions creation. In the same time, by programming specific tools we, all at once, facilitated the reconstruction work (tasks automation) and enhanced the model (by highly increasing the kinematic control of plate motions thanks to plate velocity models). Based on the 340 terranes properly defined, we developed a revised set of 35 reconstructions associated to their own velocity models. Using this unique dataset we are now able to tackle major issues of the geology (such as the global sea-level variations and climate changes). We started by studying one of the major unsolved issues of the modern plate tectonics: the driving mechanism of plate motions. We observed that, all along the Earth?s history, plates rotation poles (describing plate motions across the Earth?s surface) tend to follow a slight linear distribution along a band going from the Northern Pacific through Northern South-America, Central Atlantic, Northern Africa, Central Asia up to Japan. Basically, it sighifies that plates tend to escape this median plan. In the absence of a non-identified methodological bias, we interpreted it as the potential secular influence ot the Moon on plate motions. The oceanic realms are the cornerstone of our model and we attached a particular interest to reconstruct them with many details. In this model, the oceanic crust is preserved from one reconstruction to the next. The crustal material is symbolised by the synthetic isochrons from which we know the ages. We also reconstruct the margins (active or passive), ridges and intra-oceanic subductions. Using this detailed oceanic dataset, we developed unique 3-D bathymetric models offering a better precision than all the previously existing ones.

Using computational fluid dynamics to predict head losses in the auxiliary elements of a microirrigation sand filter

It is often assumed that total head losses in a sand filter are solely due to the filtration media and that there are analytical solutions, such as the Ergun equation, to compute them. However, total head losses are also due to auxiliary elements (inlet and outlet pipes and filter nozzles), which produce undesirable head losses because they increase energy requirements without contributing to the filtration process. In this study, ANSYS Fluent version 6.3, a commercial computational fluid dynamics (CFD) software program, was used to compute head losses in different parts of a sand filter. Six different numerical filter models of varying complexities were used to understand the hydraulic behavior of the several filter elements and their importance in total head losses. The simulation results show that 84.6% of these were caused by the sand bed and 15.4% were due to auxiliary elements (4.4% in the outlet and inlet pipes, and 11.0% in the perforated plate and nozzles). Simulation results with different models show the important role of the nozzles in the hydraulic behavior of the sand filter. The relationship between the passing area through the nozzles and the passing area through the perforated plate is an important design parameter for the reduction of total head losses. A reduced relationship caused by nozzle clogging would disproportionately increase the total head losses in the sand filter