Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Higher grade steels are being rolled in South Africa by suppliers and results in structural members having an increased axial and bending moment capacity due to an increased yield stress. Structural elements used in designs are stronger and therefore lighter sections with sufficient axial and bending moment capacity are used. Displacements of structural elements are calculated using the stiffness and Young’s modulus of a profile. These values are not affected by the increased yield stress in higher steel grades and therefore have a negative effect on the displacements of the structure. The potential of these higher grade structural elements are not utilized through serviceability limit state criteria, since the displacement determination does not account for the increased capacities of higher grade steels, but only stiffness and elasticity of the members. Structural analysis of portal frames does not account for the real behaviour of steel connections and column bases. It is assumed that connections and bases are either fully rigid or perfectly pinned. This assumption is used in the analysis and design of the structure. Although it is assumed that connections and bases are either rigid or pinned, the real behaviour is in between these two extremes. Rigid connections exhibit a certain flexibility under loading whereas pinned bases provide a certain restraint under loading. The real behaviour of connections and bases are referred to as the moment-rotation behaviour of the connection. For a certain applied moment to the connection or base, the connection exhibits a certain rotation. The focus of this study is placed on the accuracy and feasibility of modelling the real behaviour of connections and bases in a structural analysis of a portal frame. A connection stiffness is determined from the connection’s moment-rotation behaviour, and is assigned to a rotational spring of zero length in a structural analysis. An experimental investigation was conducted to obtain the real displacement data of a portal frame subject to loads for two different support conditions, i.e. a perfect hinge and grouted-support. A perfect hinge support was used to isolate the moment-rotation response of the ridge and eaves connection. The experimental results were used to compared to the results obtained from a structural analysis to determine the accuracy of the numerical results. A real design case was investigated with load combinations imposed on the frame in accordance with SANS 10160:2011. Three methods of modelling connections and bases in an analysis were considered. Firstly modelling connections as rigid and bases as pinned, secondly modelling connections as linear rotational springs and bases as pinned. Lastly was to model connections as linear rotational springs and bases as non-linear rotational springs. The outcome of the research was that more accurate displacements of a portal frame could be obtained by modelling the real behaviour of rigid connections as rotational springs, but this is not the case with grouted column bases. It is thus not feasible to model the real behaviour of connections and bases in a structural analysis as the current method of modelling connections as rigid and bases as pinned provides reliable and accurate displacement results. / AFRIKAANSE OPSOMMING: Hoë graad staal word tans in Suid Afrika gerol deur verskaffers en lei daartoe dat strukturele elemente oor ’n groter aksiale- en buigmomentkapasiteit het as gevolg van ’n groter vloeispanning. Strukturele elemente in ontwerpe is sterker en gevolglik het ligter elemente die benodigde aksiale- en buigmoment-kapasiteit. Verplasings van strukturele elemente word bepaal vanaf die styfheid en Young modulus van die element. Hierdie waardes word nie beïnvloed deur die groter vloeispanning van hoë graad staal nie, en het dus ’n negatiewe uitwerking op die verplasings van die struktuur. Die potensiaal van die gebruik van hoë graad staal word nie benut in die geval van voldoening aan diensbaarheids kriterium nie, aangesien verplasings bepaal word vanaf die styfheid en elastisiteit van die elemente, en nie vloeispanning nie. Strukturele analise van portaalrame neem nie die ware gedrag van konneksies en kolomvoetstukke in ag nie. Die aanname word gemaak in analises en ontwerpe dat konneksies en voetstukke óf rigied óf geskarnierd is. Hierdie is slegs ’n aanname en in die werklikheid lê die ware gedrag van konneksies en voetstukke tussen hierdie grense. Rigiede konneksies toon ’n sekere buigbaarheid tydens belasting en geskarnierde voetstukke toon ’n sekere beperking teen rotasies. Die ware gedrag van konneksies en voetstukke word gedefinieer as moment-rotasie gedrag. Vir ’n spesifieke aangewende moment, ondergaan die konneksie of voetstuk ’n sekere rotasie. Hierdie studie fokus op die akkuraatheid en uitvoerbaarheid van die modellering van die ware gedrag van konneksies en voetstukke in ’n strukturele analise van portaalrame. Die styfheid van ’n konneksie word bepaal vanaf sy unieke moment-rotasie gedrag, en word ingevoer as ’n styfheid van ’n rotasieveer in ’n strukturele analise. ’n Eksperimentele ondersoek was gedoen om verplasingswaardes van ’n portaalraam onder belastings te bepaal. Twee ondersteunings is ondersoek in die eksperimentele program, naamlik ’n geskarnierde ondersteuning asook ’n breivul ondersteuning. Die gebruik van die geskarnierde ondersteuning isoleer die moment-rotasie gedrag van die nok en dakrand konneksies. Die eksperimentele resultate was gebruik om die akkuraatheid van die resultate vanaf die strukturele analise te ondersoek. Laastens was ’n ontwerpsprobleem ondersoek deur laskombinasies, soos bepaal volgens die riglyne van SANS 10160:2011, op ’n portaalraam aan te wend. Drie gevalle van modellering van konneksies in ’n strukturele analise is ondersoek. Eerstens om konneksies as rigied en voetstukke as geskarnierd te beskou. Tweedens was die konneksies as linieêre rotasievere gemodelleer en voetstukke as geskarnierd te beskou. Laastens was om konneksies as linieêre rotasievere te modeleer en voetstukke as nie-linieêre rotasievere. Die navorsing het getoon dat meer akkurate verplasings van portaalrame bepaal kan word deur rigiede konneksies te modelleer as rotasievere, maar dit is nie die geval met breivul ondersteunings nie. Die gevolg is dat die uitvoerbaarheid van die modellering van konneksies en voetstukke as rotasievere nie effektief is nie, aangesien die huidige metode van die modellering van konneksies as rigied en voetstukke as geskarnierd akkurate en betroubare resultate lewer.

Σε αυτή τη Διπλωματική εργασία μελετάται η ταλαντωτική συμπεριφορά μιας κυκλικής πλάκας γραφενίου προκειμένου να διαπιστωθεί αν μπορεί να λειτουργήσει σαν νανομηχανική συσκευή ανίχνευσης μάζας. Για το λόγο αυτό δημιουργήθηκε και χρησιμοποιήθηκε ένα μοντέλο πεπερασμένων στοιχείων. Σε αυτό το μοντέλο οι αλληλεπιδράσεις μεταξύ των ατόμων και οι σχετικές κινήσεις αυτών προσομοιώθηκαν με κατάλληλα ελατήρια των οποίων η δυσκαμψία έχει υπολογιστεί χρησιμοποιώντας την ενέργεια δεσμού από τη θεωρία των μορίων. Ακόμη, τα άτομα του άνθρακα προσομοιώνονται με μάζες στη θέση των ατόμων άνθρακα. Το αναπτυχθέν μοντέλο αναπαριστά το δίσκο του γραφενίου σαν ορθότροπο υλικό. Προκείμενου να αποκτηθεί μια καλή εικόνα της συμπεριφοράς του κυκλικού γραφενίου γίνεται αρχικά διερεύνηση της ελεύθερης ταλάντωσης για διάφορες διαμέτρους αυτού. Επιπλέον, εξετάζεται η ταλαντωτική συμπεριφορά του γραφενίου με την προσκόλληση μάζας διαφόρων μεγεθών και σε διάφορες θέσεις πάνω στο γραφένιο κατά μήκος της ακτίνας του. Η επεξεργασία των μοντέλων έχει ως αποτέλεσμα τις φυσικές συχνότητες ταλάντωσης του γραφενίου και τις αντίστοιχες ιδιομορφές των φύλλων γραφενίου με ή χωρίς την προσκολλημένη μάζα παρέχοντας τα ταλαντωτικά τους χαρακτηριστικά. Επομένως, έχοντας δημιουργήσει μοντέλα για διάφορες διαμέτρους και μάζες μπορεί να εξεταστεί και να αποκτηθεί μια πλήρης εικόνα για την ενδεχόμενη ταλαντωτική συμπεριφορά του κυκλικού μονοστρωματικού δίσκου γραφενίου σαν αισθητήριο μάζας. / In this Diploma thesis is studied the vibrational behavior of a circular graphene sheet so as to investigate if this can operate as a nanomechanical system of mass sensing. For this purpose a finite elements’ model was created and being used. In this model the interatomic interactions and their relative positions are simulated by equivalent spring elements whose stiffness derived by corresponding potential energies provided by molecular theory and expressing the resistance in relative movements between carbon atoms under deformation. Moreover, the inertial effects of the system are simulated by using appropriate lumped masses in atomic positions. The model created represents the graphene plate as an orthotropic material. In order to obtain a full view of the behavior of circular graphene, firstly is been done investigation of its free vibration for different diameters of the plate. After that, is studied the Vibrational behavior with a mass lying on it. The solution gives the natural frequencies and corresponding mode shapes of vibration of individual graphene sheets and graphene-attached mass systems providing their vibrational characteristics. Subsequently, assuming the geometric characteristics of graphene as well as the weight and position of the attached mass as the global design parameters, a parametric study on mass sensing characteristics is presented in order to examine the potential behavior of a circular graphene monolayer as mass sensor.

Le terme gridshell désigne une coque discrète qui est obtenue par déformation élastique d'une grille bidirectionnelle continue plane sans rigidité en cisaillement puis rigidifiée par une troisième direction de barres. Ainsi défini, un gridshell a un potentiel structural intéressant et peut répondre à des exigences architecturales complexes. La recherche de forme de ces structures a été menée à travers l'histoire principalement par deux méthodes, la méthode du filet inversé et la relaxation dynamique. Ces deux méthodes permettent d'obtenir une forme approchée de celle proposée par l'architecte, dérivant d'une grille à plat et de conditions aux limites partiellement ou complètement imposées. Dans le cadre de cette thèse, nous nous sommes intéressés à générer un gridshell sur une surface à forme et contours imposés. Un outil numérique se basant sur la méthode du compas a été développé. Il permet de mailler un réseau de Tchebychev sur une surface connaissant son équation cartésienne. Un autre outil permettant le maillage se basant sur un calcul en éléments finis explicite a été mis en œuvre. La particularité de cette technique est de pouvoir tenir en compte des propriétés mécaniques de la structure et de simuler le comportement du gridshell. Des applications des deux méthodes sur des formes architecturalement intéressantes ont permis de voir les limitations de la possibilité de mailler une forme avec un réseau de Tchebychev. La méthode du compas a ensuite été couplée à des algorithmes métaheuristiques types génétiques. L'algorithme résultant permet d'optimiser un gridshell en minimisant la courbure dans les barres et donc les contraintes dans la structure introduites lors de la mise en forme. Il a été mis en œuvre et testé pour plusieurs surfaces / Gridshells are often defined as structures that have the shape and rigidity of a double curvature shell but they consist of a grid and not a continuous surface. They are obtained by elastic deformation of a two-way grid initially flat. The deformed grid is then rigidified using a third direction of bars. Thus, a gridshell has an interesting structural potential and can respond to complex architectural requirements. Two methods have been used through out history for the form finding of gridshells, the inversion method and the dynamic relaxation method. Both techniques lead to a deformed grid which is a result of calculations. The form obtained is closed to the one proposed by the architect. A numerical tool based on the compass method is developed in this thesis. It allows mapping aTchebychev net on an imposed form and imposed boundary conditions.Another tool based on an explicit dynamic finite element calculationis proposed. The particularity of this technique is to be able to take into account the mechanical properties of the structure and to simulate the gridshell behavior. Applications of both methods on differents forms show the limitations of mapping a Tchebychev net on an imposed form. The compass method has been coupled with geneticalgorithms. The algorithm optimizes the gridshell by minimizing the curvature in bars in order not to break the bars during the construction. It has been implemented and tested on several surfaces

In this paper we present novel analytic and finite element solutions to 1-D straight rods made of Ramberg-Osgood and Hollomon type materials. These material models are studied because they are a more accurate representation of the material properties of certain metals used often in manufacturing than the simpler composite linear types of stress/strain models. Here, various types of loads are considered and solutions are compared against some linear models. It is shown that the nonlinear models do have manageable solutions, which produce important differences in the results - attributes which suggest that these models should take a more prominent place in engineering analysis.

Les chaussées subissent des sollicitations liées au trafic et au climat conduisant à leur dégradation, par fissuration notamment. Il est nécessaire dans le contexte actuel de pouvoir modéliser le comportement de ces structures multicouches endommagées afin de prévoir leur durée de vie résiduelle ou dimensionner des solutions de renforcement. L’objectif de la thèse est ainsi de proposer un outil de calcul dédié à l'analyse 3D des chaussées fissurées ou comportant des discontinuités. L’approche retenue repose sur la modélisation simplifiée d’une chaussée par un empilement de plaques du Modèle Multi-particulaire des Matériaux Multicouches à 5n équations d’équilibre (M4-5n). Un outil de calcul rapide de référence de chaussées 2D fissurées et une méthode de résolution générale du M4-5n par Eléments Finis mixtes sont développés. Le point de départ de la méthode de résolution est l’écriture, pour le M4-5n, du principe variationnel basé sur le théorème de l'énergie complémentaire où la condition de contraintes statiquement admissibles est assurée à partir de multiplicateurs de Lagrange. La discrétisation des efforts généralisés utilise des espaces d’interpolation permettant le bon conditionnement du système d’équations algébriques à résoudre et garantissant la stabilité de la solution. La méthode est implémentée dans FreeFem++. Elle ramène le problème 3D initial à une modélisation EF 2D et conduit à des valeurs finies des efforts généralisés au niveau des fissures ou décollement d’interface. L’outil de calcul final ainsi développé est validé et appliqué à l’étude de la réponse d’une structure fissurée,représentative d’une chaussée testée en vraie grandeur sur le site de l’IFSTTAR. / Pavements are multilayer structures which undergo cracking distress due to traffic and climatic factors. It is important nowadays to be able to model the mechanical response of such damaged pavements in order to assess their residual lifetime or to design reinforcement solutions. In this context, the present thesis aims at developing a numerical tool dedicated to the analysis of pavements incorporating cracks or discontinuities. In the developed approach, the pavement structure is modeled as a stacking of “plate” elements of typeM4-5n (Multi-Particle Models of Multilayer Materials) which considers 5n equilibrium equations. A reference quick 2D calculation tool for cracked pavements and a general solving of M4-5n by the mixed Finite Element (FE) method was developed. The starting point for this method is the derivation for M4-5n of the variational principle based on the complementary energy theorem whose condition of statically admissible stress is taken into account using Lagrange multipliers. Discretization of the generalized stresses involves interpolation spaces, proposed to avoid ill-conditioned system of algebraic equations after discretization and to insure stability of the solution. The developed method is implemented in a FreeFem++ script. In this method, the initial 3D problem can be handled through FE simulations in 2D and finite values of the generalized stresses are obtained at crack and interlayer debonding locations. The developed numerical tool was validated and applied to the study of the mechanical response of a structure with cracks representative of a pavement tested underfull-scale conditions during an accelerated fatigue test performed at IFSTTAR.

La macroségrégation est un défaut connu dans les procédés de coulées industrielles. La genèse de ce défaut est la conséquence de l'interaction complexe entre la microségrégation ou la distribution des espèces chimiques à l'échelle de la microstructure et les mouvements des phases liquide et solides. Les hétérogéneités de concentration en solutés à l'échelle de la pièce peuvent être rédhibitoires vis-à-vis de la qualité du produit.Dans ce travail, on propose un modèle numérique pour simuler et prédire la formation des macroségrégations en coeur des pièces d'alliages multi-constitués, induites par des variations thermiques et solutales dans la phase liquide. Dans un premier temps, on considère que le métal solidifie à volume constant. Dans ce contexte, la convection thermosolutale est étudiée ainsi que son influence sur la formation des canaux ségrégées à différentes échelles de modélisation. Dans un deuxième temps, le modèle vise à prédire les macroségrégations en présence de changement de volume du métal, dont la cause principale est le retrait à la solidification, pouvant être à l'origine du phénomène de ségrégation inverse. La surface entre le métal et le gaz environnant au cours du retrait évolue pendant le retrait en fonction du chemin de solidification qui varie avec la macroségrégation. Cette évolution d'interface est suivi par la méthode level set. Des prédictions de concentration moyenne, couplées aux bases de données thermodynamiques pour mieux prédire les chemins de solidification des alliages multi-constitués, sont analysées et comparées avec des résultats expérimentaux. Finalement, des calculs de solidification en microgravité sont présentées, simulant un essai expérimental dans le contexte du projet CCEMLCC lancé par l'Agence Spatiale Européenne. Les résultats en fin de solidification montrent un accord acceptable quant à la forme et l'élongation des échantillons solidifiés. Ces calculs sont faits avec des approximations binaire, ternaire et quaternaire d'une même nuance d'acier utilisée dans les essais en microgravité. / Macrosegregation is key defect in industrial casting processes. During solidification, solute redistribution at the scale of microstructure, also known as microsegregation, take place with complex interactions, in order to form one or more solid phases. These interactions between microsegregation and movements of liquid and solid phases may lead to macrosegregations. These solute heterogeneities spanning on a larger scale, may result in a bad casting quality. In this thesis, we propose a numerical model to simulate and predict macrosegregations occurring in the centre of multicomponent alloys, caused by thermal and solutal variations in the liquid phase. First, we assume that the metallic alloy solidifies with a constant volume. In this context, we study the influence of thermosolutal convection on the formation of channel segregations, at different modelling scales. The second part of this modelling work consider solidification while the metallic alloy's volume is decreasing, mainly due to overall density variation, also known as solidification shrinkage, possibly leading to the so-called inverse segregation phenomenon, appearing on the alloy's skin. In the context of solidification shrinkage, the shape of the metal's boundary with surrounding gases varies according to a constantly changing solidification path due to macrosegregation. The level set method is therefore used to track its evolution with time. Composition predictions, coupled with thermodynamic database mappings for more accurate multicomponent solidification paths, are analysed and compared to existing experimental setups. Finally, simulations of a reduced-gravity solidification cases are performed, mocking an experimental benchmark from the CCEMLCC project launched by the European Space Agency. The results after complete solidification show acceptable agreement for the final shape, compared to experimental results. These computations were performed with binary, ternary and quaternary approximations of the same steel grade which was used in reduced-gravity experiments.

Dans l'étude des éléments combustibles des réacteurs à eau pressurisée, cette thèse s'inscrit dans la compréhension et la modélisation du comportement viscoplastique du dioxyde d'uranium (UO2) à l'échelle du polycristal. Lors de fonctionnement de type incidentel du réacteur, le combustible subit une forte élévation de la température avec un gradient thermique de la pastille engendrant des déformations viscoplastiques contrôlées par des mouvements de dislocations. D'abord, un modèle de plasticité cristalline a été développé de manière à décrire l’anisotropie viscoplastique du matériau en fonction de la température et de la vitesse de sollicitation. Des simulations par éléments finis (EF) sur monocristaux ont permis d’identifier que les trois modes de glissement généralement observés dans l'UO2 sont importants pour décrire le comportement anisotrope du matériau. Dans un second temps, les coefficients de la matrice d'interactions entre dislocations ont été déterminés spécifiquement pour l’UO2 afin d’améliorer la modélisation des polycristaux. En effet, en calculant par EF les dislocations géométriquement nécessaires, qui sont responsables d’une forte augmentation de la densité de dislocations stockées dans les polycristaux, les interactions entre dislocations permettent de simuler l’effet dé taille de grain et l’écrouissage des pastilles. Finalement, le modèle, adapté pour les polycristaux, a été validé par comparaison avec les essais expérimentaux sur pastille et par comparaison du comportement intra-granulaire simulé avec des mesures EBSD. Grâce à cette dernière comparaison, il est possible de remonter indirectement aux hétérogénéités de déformation dans les grains / This thesis is part of the study of fuel elements of pressurized water reactors and, more specifically, focus on the understanding and modelling of the viscoplastic behavior of uranium dioxide (UO$_2$) at polycrystalline scale. During the incidental operation of the reactor, the fuel undergoes a strong increase of temperature and thermal gradient between the center and the periphery of the pellet leading to viscoplastic strains due to dislocation movement mechanisms. First, a crystal plasticity model was developed in order to describe the viscoplastic anisotropy of the material considering the temperature and the loading rate. Finite element (FE) simulations on single crystals enabled to highlight that the three slip modes generally observed in UO$_2$ are crucial to describe the anisotropic behavior of the material. Secondly, coefficients of the interaction matrix have been identified specifically for UO$_2$ in order to improve the polycrystal modelling. Indeed, by calculating geometrically necessary dislocations (GNDs), which are responsible of the great increase of the stored dislocation density in polycrystals, the interactions between dislocations enable to simulate de grain size sensitivity and hardening of the fuel pellet. Finally, the model adapted for polycrystals, have been validated by comparing FE simulations with pellet compression tests and by comparing the simulated intra-granular behavior with EBSD measurements. Thanks to the latter comparison, it is possible to indirectly compare the strain heterogeneities in the grains

[pt] Este trabalho apresenta uma metodologia para geração de malhas adaptativas de elementos finitos 2D e 3D usando modeladores geométricos com multi-regiões e superfícies paramétricas. A estratégia adaptativa adotada é fundamentada no refinamento independente das curvas, superfícies e sólidos. Inicialmente as curvas são refinadas, no seu espaço paramétrico, usando uma técnica de partição binária da curva (binary-tree). A discretização das curvas é usada como dado de entrada para o refinamento das superfícies. A discretização destas é realizada no seu espaço paramétrico e utiliza uma técnica de avanço de fronteira combinada com uma estrutura de dados do tipo quadtree para gerar uma malha não estruturada de superfície. Essas malhas de superfícies são usadas como dado de entrada para o refinamento dos domínios volumétricos. A discretização volumétrica combina uma estrutura de dados do tipo octree juntamente com a técnica de avanço de fronteira para gerar uma malha sólida não estruturada de elementos tetraédricos. As estruturas de dados auxiliares dos tipos binary-tree, quadtree e octree são utilizadas para armazenar os tamanhos característicos dos elementos gerados no refinamento das curvas, superfícies e regiões volumétricas. Estes tamanhos característicos são definidos pela estimativa de erro numérico associado à malha global do passo anterior do processo adaptativo. A estratégia adaptativa é implementada em dois modeladores: o MTOOL (2D) e o MG (3D), que são responsáveis pela criação de um modelo geométrico, podendo ter, multi-regiões, onde no caso 3D as curvas e superfícies são representadas por NURBS. / [en] This work presents a methodology for adaptive generation of 2D and 3D finite-element meshes using geometric modeling with multi- regions and parametric surfaces. The adaptive strategy adopted in this methodology is based on independent refinements of curves, surfaces and solids. Initially, the model´s curves are refined using a binary-partition algorithm in parametric space. The discratizetion of these curves is used as input for the refinement of adjacent surfaces. Surface discretization is also performed in parametric space and employs a quadtree-based refinement coupled to an advancing-front technique for the generation of an unstructured triangulation. These surface meshes are used as input for the refinement adjacent volumetric domains. Volume discretization combines an octree refinement with an advancing-front technique to generate an unstructural mesh of tetrahedral elements. In all stages of the adaptive strategy, the refinement of curves, surface meshes and solid meshes is based on estimated numerical errors associated to the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes into account metric distortions between parametric and Cartesian spaces and high curvatures of the model´s geometric entities. The adaptive strategies are implemented in two different modelers: MTOOL (2D) and MG (3D), which are responsible for the creation of a geometric model with multi-regions, where for case 3D the curves and surfaces are represented by NURBS, and for the interactive and automatic finite-element mesh generation associated to surfaces and solid regions. Numerical examples of the simulation of engineering problems are presented in order to validate the methodology proposed in this work.

[pt] O presente trabalho avalia a utilização de elementos enriquecidos para obtenção de cargas críticas, freqüências de vibração e seus respectivos modos de peças estruturais bidimensionais (flexão de placas retangulares sujeitas a compressão em seu plano). O método de aproximação empregado foi o de Rayleigh-Ritz voltado para o uso de elementos finitos convencionais enriquecidos com funções de deslocamentos adicionais internas e de contorno. As funções ditas internas são desenvolvidas de forma a não envolver deslocamentos e rotações nodais e no contorno. Já as funções ditas de contorno são concebidas de forma a envolver apenas deslocamentos internos e ao longo de um lado apenas, sem deslocamentos generalizados nodais. Para este estudo foram desenvolvidas duas famílias de funções, uma com termos adicionais trigonométricos e outra com termos adicionais polinomiais. Para o cálculo de cargas críticas e freqüências são utilizadas as matrizes de rigidez elástica, rigidez geométrica e de massa, introduzidas em problemas generalizados de autovalores. Resultados numéricos são obtidos através de procedimentos computacionais utilizando o software Maple. Verifica-se que as funções adicionais trigonométricas, embora mais satisfatórias que as polinomiais quanto à convergência, exigem maior esforço computacional. São comparados resultados de elementos para placas esbeltas (teoria de Kirchhoff), com três e quatro graus de liberdade por nó, onde o quarto grau de liberdade corresponde à derivada mista (torção). Mostra-se que as funções adicionais, não-nodais, requerem o uso do elemento com quatro graus de liberdade por nó, para se ter convergência no cálculo das cargas críticas e freqüências em situações gerais. Outros exemplos abordam preliminarmente a inclusão de efeitos de dano e ortotropia no material, visando a modelagem de lajes comprimidas e pilares com seções retangulares alongadas. Esta modelagem envolvendo combinação de funções adicionais gerais e elementos convencionais representa um passo no desenvolvimento de uma técnica aplicável à combinação de modos globais e localizados de instabilidade / [en] The focus of the present work is to developand evaluate enriched elements used to obtain critical loads, frequencies of vibration and respective modes for two-dimensional structural components (rectangular plates in bending under inplane compressive loading). The Rayleigh-Ritz approximation method has been employed, directed to the use of conventional finite elements enriched by internal and boundary additional displacements functions. The socalled internal functions are do not involve nodal and boundary displacements and rotations. The boundary functions are conceived to include displacements within the element and along one side, without involving any generalized nodal displacements. Two displacement function families were developed, the first with trigonometric additional terms and the second with polynomial additional terms. Critical loads and frequencies, and respective modes, are obtained by the use of elastic stifiness, geometric, and mass matrices, introduced in generalized eigenvalue problems. Numerical results are obtained by computational procedures using Maple software. The trigonometric additional functions, in spite of better convergence properties, demand greater computational effort. The basic elements are classical thin plate elements (Kirchhoff's theory) with three or four degrees of freedom per node, where the fourth degree of freedom corresponds to the mixed derivative (torsion). The results indicate that non- nodal additional functions require the use of elements with four freedom degrees by node to obtain convergence of critical loads and frequencies convergence in general situations. Other examples consist of preliminary approaches to include damage effects, in reinforced orthotropic plates, as modeling columns with wide rectangular sections and compressed slabs. The use of general additional functions combined with conventional elements represents a step on the development of a technique applicable to global and localized instability modes.

[pt] A relação entre os processos hidrológicos de escoamento superficial e subterrâneo apresenta uma grande variabilidade espacial e temporal. Podendo ser representado de forma qualitativa como parte sequêncial do ciclo hidrológico, estes processos, demostram sua grande dependência e importância nos estudos de balanços hídricos. Visando uma representação quantitativa, este trabalho faz o acoplamento, entre os modelos numéricos de escoamento superficial e de fluxo em meios porosos. Para o meio poroso adotou-se o modelo numérico SWMS_3D (Simunek et al, 1995), o qual resolve a equação de Richards, para fluxo em meios porosos saturados e não saturados nas três dimensões. Na simulação da dinâmica superficial, foram desenvolvidos dois modelos derivados das equações de Saint- Venant: o modelo da Onda Cinemática e o modelo de Difusão. Para a solução numérica foi empregado o método dos elementos finitos através da formulaçao de Galerkin, adotando uma malha tridimensional de elementos tetraédricos, formando uma sub-malha de elementos triangulares na superfície. O modelo de escoamento superficial emprega a malha triangular e interage com o programa SWMS_3D modificado (que utiliza a malha de tetraédros) através das imposições das condições de contorno transientes. Este, responderá com uma parcela de fluxo correspondente à recarga ou descarga no contorno a cada passo de tempo. Com isso, o modelo gerado é capaz de quantificar espacialmente e temporalmente as cargas de pressão em todos os pontos do domínio de estudo. / [en] While analyzing the interaction between the hydrological processes of surface and groundwater flow, it is seen that there is a big difference in its interaction in the space and time. These processes can be represented in a qualitative form as part of the hydrological cycle, demonstrating its dependences and importance in the hydrological balance. This work does the numerical coupling of the surface and groundwater flow. This work adopted the SWMS_3D numerical model (Simunek et. al., 1995), which resolves the Richards equation for saturated and non saturated porous media flow in 3D. In order to simulate the superficial dynamic flow, two models from Saint-Vennat equation were developed, these models are: the cinematic wave model and the diffusion model. These two models consider the average outflow in sections in a 2D scenario. For the numerical solution the finite element method was adopted through the Galerkin formulation. Adopting a 3D domain mesh of tetrahedral elements, seen from above, in 2D, we can see a triangular element mesh. The superficial flow model uses the triangular mesh and iterates with the SWMS_3D modified software, which uses the tetrahedral elements mesh. This was done by changes in the boundary conditions to the models. The SWMS_3D will answer with a flow portion corresponding to a sink or source action in the surface, in each time step. Finally the generated model is able to quantify in space and in time the pressure head in the study domain.