Tesis sobre el tema "Linear elasticty"
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1
Mou, Guangjin. "Design of exotic architectured materials in linear elasticity". Electronic Thesis or Diss., Sorbonne université, 2023. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2023SORUS519.pdf.
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Les classes de symétrie d'un comportement linéaire définissent les différents types d'anisotropie qui peuvent être modélisés par les tenseurs constitutifs associés. Cependant, les espaces des matériaux linéaires sont très riches et toute une gamme de possibilités intermédiaires peut exister au-delà des classes de symétrie. Les matériaux présentant des propriétés anisotropes non-standard associées à ces possibilités intermédiaires sont appelés matériaux exotiques. Par exemple, le matériau 2D R0-orthotrope est un cas bien connu de matériau exotique.L'objectif principal de cette recherche est de développer des outils géométriques pour caractériser les espaces linéaires des matériaux de manière très fine, ce qui permet de détecter ces possibilités intermédiaires. L'ensemble exotique obtenu est intrinsèquement caractérisé par une relation polynomiale entre les invariants du tenseur d'élasticité. En conséquence, nous prouvons que la R0-orthotropie est le seul type de matériau élastique exotique en 2D. Cependant, lorsque l'on généralise à l'élasticité linéaire 3D, ce nombre s'élève à 163.Le deuxième objectif de cette étude est d'obtenir une mésostructure présentant à grande échelle le comportement exotique décrit précédemment. Un algorithme d'optimisation basé sur la dérivée topologique est implémenté dans Python/FEniCS pour réaliser la design de mésostructure périodiques. Le matériau 2D R0-orthotrope et plusieurs cas de matériaux exotiques 3D sont étudiés. La fonction objective du problème d'optimisation est formulée en termes d'invariants du tenseur d'élasticité effectif cibleThe symmetry classes of a linear constitutive law define the different types of anisotropy that can be modelled by the associated constitutive tensors. However, the spaces of linear materials are very rich and a whole range of intermediate possibilities can exist beyond symmetry classes. Materials with non-standard anisotropic properties associated with such intermediate possibilities are called exotic materials. For instance, 2D R0-orthotropic material is a well-known case of exotic material.The primary objective of this research is to develop geometrical tools to characterise the linear material spaces in a very fine way, which allow these intermediate possibilities to be detected. The exotic set obtained is intrinsically characterised by a polynomial relation between elasticity tensor invariants. As a result, we prove that R0-orthotropy is the only type of 2D exotic elastic material. However, when generalised to 3D linear elasticity, this number is up to 163.The second objective of this study is to obtain a mesostructure exhibiting at macroscale the exotic behaviour described previously. A topological derivative-based optimisation algorithm is implemented in Python/FEniCS to realise the design of periodic metamaterials. The 2D R0-orthotropic material and several cases of 3D exotic materials are studied. The objective function of the optimisation problem is formulated in terms of the invariants of the target effective elasticity tensor
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Bosher, Simon Henry Bruce. "Non-linear elasticity theory". Thesis, Queen Mary, University of London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407883.
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Ang, W. T. "Some crack problems in linear elasticity /". Title page, table of contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09PH/09pha581.pdf.
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Austin, D. M. "On two problems in linear elasticity". Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378026.
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Johnson, Fen Rui. "A study of finite and linear elasticity". CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1096.
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Domino, Lucie. "Contrôle et manipulation d'ondes hydroélastiques". Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLET020.
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Cette thèse porte sur la physique des ondes, dans le but de contrôler leur propagation. Nous cherchons à mettre en évidence des phénomènes communs à toutes les ondes grâce à un système expérimental modèle utilisant les ondes à la surface d’un liquide. Plus précisément, nous choisissons de travailler avec des ondes hydroélastiques en couvrant la surface du liquide avec un film élastique. Les déformations élastiques de cette membrane sont couplées aux mouvements du fluide, de sorte qu’en modifiant les propriétés de la membrane nous pouvons agir sur la propagation des ondes. Ainsi, en changeant localement l’épaisseur du film élastique nous montrons qu’il est possible de dévier, réfléchir ou encore focaliser les ondes. Ensuite, en structurant périodiquement la membrane nous mettons en évidence des effets liés à la périodicité et/ou à la nature des objets formant le réseau régulier. Nous utilisons des perforations circulaires dont nous varions le diamètre, l’espacement et l’arrangement dans l’espace, ce qui nous permet de contrôler très finement le comportement des ondes dans le cristal artificiel ainsi formé. Nous mettons notamment en évidence l’existence de bandes interdites de propagation. Enfin, nous re-visitons l’instabilité de Faraday, connue en hydrodynamique, en vibrant verticalement un bain liquide recouvert d’une membrane élastique, et nous montrons que cette instabilité existe également pour les ondes hydroélastiquesThis thesis deals with waves at the surface of a liquid, and aims at controlling their propagation. We want to show universal results, valid for all waves, using model experiments. We work with hydroelastic waves, obtained with an elastic membrane that covers the liquid surface. The elastic deformation of this membrane couples with the motion of the fluid, so that we can change the propagation of the waves by modifying the properties of the elastic cover. We show that if we locally change the thickness of the elastic cover, we can deviate, reflect or focus the waves. We then periodically structure the membrane and thus unveil effects due to he periodicity and/or the nature of the objects that form the regular array. We use an ensemble of circular perforations of which we vary the diameter, the spacing and the pattern, in order to accurately control the propagation of the waves in this artificial crystal. In particular, we show that there exist band gaps for the waves. Lastly, we re-visit the Faraday instability, known in hydrodynamics, by vertically vibrating a fluid layer covered with an elastic membrane, and we show that this instability also exist for hydroelastic waves
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Laing, Kara Louise. "Non-linear deformation of a helical spring". Thesis, University of East Anglia, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323220.
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Chinviriyasit, Settapat. "Numerical methods for treating quasistatic linear viscoelastic problems". Thesis, Brunel University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367443.
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Harursampath, Dineshkumar. "Non-classical non-linear effects in thin-walled composite beams". Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/12501.
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DeFigueiredo, Tania Glacy do Brasil. "A new boundary element formation and its application in engineering". Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278110.
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Browne, Philip. "Topology optimization of linear elastic structures". Thesis, University of Bath, 2013. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.577747.
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Topology optimization is a tool for finding a domain in which material is placed that optimizes a certain objective function subject to constraints. This thesis considers topology optimization for structural mechanics problems, where the underlying PDE is derived from linear elasticity. There are two main approaches for solving topology optimization: Solid Isotropic Material with Penalisation (SIMP) and Evolutionary Structural Optimization (ESO). SIMP is a continuous relaxation of the problem solved using a mathematical programming technique and so inherits the convergence properties of the optimization method. By contrast, ESO is based on engineering heuristics and has no proof of optimality. This thesis considers the formulation of the SIMP method as a mathematical optimization problem. Including the linear elasticity state equations is considered and found to be substantially less reliable and less efficient than excluding them from the formulation and solving the state equations separately. The convergence of the SIMP method under a regularising filter is investigated and shown to impede convergence. A robust criterion to stop filtering is proposed and demonstrated to work well in high-resolution problems (O(10^6)). The ESO method is investigated to fully explain its non-monotonic convergence behaviour. Through a series of analytic examples, the steps taken by the ESO algorithm are shown to differ arbitrarily from a linear approximation. It is this difference between the linear approximation and the actual value taken which causes ESO to occasionally take non-descent steps. A mesh refinement technique has been introduced with the sole intention of reducing the ESO step size and thereby ensuring descent of the algorithm. This is shown to work on numerous examples. Extending the classical topology optimization problem to included a global buckling constraint is considered. This poses multiple computational challenges, including the introduction of numerically driven spurious localised buckling modes and ill-defined gradients in the case of non-simple eigenvalues. To counter such issues that arise in a continuous relaxation approach, a method for solving the problem that enforces the binary constraints is proposed. The method is designed specifically to reduce the number of derivative calculations made, which is by far the most computationally expensive step in optimization involving buckling. This method is tested on multiple problems and shown to work on problems of size O(10^5).
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Wang, Yanqiu. "Preconditioning for the mixed formulation of linear plane elasticity". Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/2781.
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In this dissertation, we study the mixed finite element method for the linear plane elasticity problem and iterative solvers for the resulting discrete system. We use the Arnold-Winther Element in the mixed finite element discretization. An overlapping Schwarz preconditioner and a multigrid preconditioner for the discrete system are developed and analyzed. We start by introducing the mixed formulation (stress-displacement formulation) for the linear plane elasticity problem and its discretization. A detailed analysis of the Arnold-Winther Element is given. The finite element discretization of the mixed formulation leads to a symmetric indefinite linear system. Next, we study efficient iterative solvers for the symmetric indefinite linear system which arises from the mixed finite element discretization of the linear plane elasticity problem. The preconditioned Minimum Residual Method is considered. It is shown that the problem of constructing a preconditioner for the indefinite linear system can be reduced to the problem of constructing a preconditioner for the H(div) problem in the Arnold-Winther finite element space. Our main work involves developing an overlapping Schwarz preconditioner and a multigrid preconditioner for the H(div) problem. We give condition number estimates for the preconditioned systems together with supporting numerical results.
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Bala, Chandran Ram. "Development of discontinuous Galerkin method for nonlocal linear elasticity". Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/41730.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 75-81).
A number of constitutive theories have arisen describing materials which, by nature, exhibit a non-local response. The formulation of boundary value problems, in this case, leads to a system of equations involving higher-order derivatives which, in turn, results in requirements of continuity of the solution of higher order. Discontinuous Galerkin methods are particularly attractive toward this end, as they provide a means to naturally enforce higher interelement continuity in a weak manner without the need of modifying the finite element interpolation. In this work, a discontinuous Galerkin formulation for boundary value problems in small strain, non-local linear elasticity is proposed. The underlying theory corresponds to the phenomenological strain-gradient theory developed by Fleck and Hutchinson within the Toupin-Mindlin framework. The single-field displacement method obtained enables the discretization of the boundary value problem with a conventional continuous interpolation inside each finite element, whereas the higher-order interelement continuity is enforced in a weak manner. The proposed method is shown to be consistent and stable both theoretically and with suitable numerical examples.
by Ram Bala Chandran.
S.M.
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McKay, Barry. "Wrinkling problems for non-linear elastic membranes". Thesis, University of Glasgow, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307187.
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Schenck, David Robert. "Some Formation Problems for Linear Elastic Materials". Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/28608.
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Some equations of linear elasticity are developed, including those
specific to certain actuator structures considered in formation
theory. The invariance of the strain-energy under the transformation
from rectangular to spherical coordinates is then established for use
in two specific formation problems. The first problem, involving an
elastic structure with a cylindrical equilibrium configuration, is
formulated in two dimensions using polar coordinates. It is shown
that $L^2$ controls suffice to obtain boundary displacements in
$H^{1/2}$. The second problem has a spherical equilibrium
configuration and utilizes the elastic equations in spherical
coordinates. Results similar to those obtained in the two dimensional
case are indicated for the three dimensional problem.Ph. D.
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Hein, Torsten y Marcus Meyer. "Identification of material parameters in linear elasticity - some numerical results". Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200702040.
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In this paper we present some numerical results concerning the identification of material parameters in linear elasticity by dealing with small deformations. On the basis of a precise example different aspects of the parameter estimation problem are considered. We deal with practical questions such as the experimental design for obtaining sufficient data for recovering the unknown parameters as well as questions of treating the corresponding inverse problems numerically. Two algorithms for solving these problems can be introduced and extensive numerical case studies are presented and discussed.
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Ren, Xiaoan. "The method of arbitrary lines in non-linear visco-elasticity". Thesis, University of Westminster, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240413.
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Álvarez, Inostroza Catalina Paz. "Virtual element method for linear elasticity problems in modifiable meshes". Tesis, Universidad de Chile, 2017. http://repositorio.uchile.cl/handle/2250/149576.
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Magíster en Ciencias, Mención Computación.
Ingeniera Civil en Computación.
Ingeniera Civil Mecánica.Los métodos numéricos son una valiosa herramienta en las ciencias y la ingeniería, ya que permiten obtener soluciones a muchos problemas difíciles. La elasticidad lineal, el estudio de como los objetos se deforman y cargan dado a cargas, es un problema en que los métodos numéricos tienden a usarse. El Método de Elemento Finito (FEM) es el método más usado para resolver problemas de elasticidad lineal; tiene muchas ventajas: es estable, es fácil aumentar el orden de los elementos para mejorar las aproximaciones, entre otros. Tiene, sin embargo, un buen número de desventajas: en general se debe usar con mallas de triángulos o cuadriláteros, menos flexibles que las de polígonos, y la precisión de la solución depende de la calidad de la malla. Estas dos desventajas hacen que FEM no sea la mejor opción para aplicaciones en que la calidad de la malla no está asegurada dado que cambia en el momento, como por ejemplo mecánica de fractura o análisis con mallas adaptivas. Nosotros teorizamos que una técnica novedosa, el Método de Elemento Virtual (VEM), es mejor para esta clase de aplicaciones; sin embargo, esta idea debe ser probada. Considerando los problemas anteriores, este trabajo presenta un estudio del uso de VEM para aplicaciones en que las mallas cambian en tiempo real. Para testear la hipótesis presentada, se implementa: una librería para la generación eficiente de mallas poligonales, basadas en el diagrama de Voronoi restringido; una extensión a dicha librería, incluyendo operaciones para modificar las mallas; y una librería final, que implementa VEM y FEM para elasticidad lineal. Hacemos énfasis en que nuestra implementación de VEM es la primera de código abierto disponible. Usando las herramientas implementadas, presentamos experimentos validando la convergencia numérica de los dos métodos; los resultados son satisfactorios, por lo que se procede con las pruebas para validar la hipótesis principal de esta tesis. Presentamos una comparación de los errores nodales para VEM y FEM cuando las mallas son sometidas a distintos cambios y concluimos que VEM se comporta mejor cuando las mallas cambian, incluso logrando tasas de error similares a las obtenidas cuando no se aplica ningún cambio. De esta forma, concluimos que VEM es una herramienta valida para la resolución de problemas de elasticidad lineal, en particular cuando las mallas presentan cambios imprevistos. Analizándo geométricamente las mismas pruebas, concluimos que las mallas de polígonos dan elementos de mejor calidad, para las operaciones probadas, en comparación con triangulaciones. Finalmente, se presenta la complejidad teórica de los algoritmos, y se compara contra resultados experimentales; también se presentan ejemplos mostrando las funcionalidades logradas, concluyendo con los aspectos relacionados al trabajo futuro.
Este trabajo ha sido parcialmente financiado por CONICYT
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Orekhov, Viktor Leonidovich. "Series Elasticity in Linearly Actuated Humanoids". Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/71788.
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Recent advancements in actuator technologies, computation, and control have led to major leaps in capability and have brought humanoids ever closer to being feasible solutions for real-world applications. As the capabilities of humanoids increase, they will be called on to operate in unstructured real world environments. This realization has driven researchers to develop more dynamic, robust, and adaptable robots.
Compared to state-of-the-art robots, biological systems demonstrate remarkably better efficiency, agility, adaptability, and robustness. Many recent studies suggest that a core principle behind these advantages is compliance, yet there are very few compliant humanoids that have demonstrated successful walking.
The work presented in this dissertation is based on several years of developing novel actuators for two full-scale linearly actuated compliant humanoid robots, SAFFiR and THOR. Both are state-of-the-art robots intended to operate in the extremely challenging real world scenarios of shipboard firefighting and disaster response.
The design, modeling, and control of actuators in robotics application is critical because the rest of the robot is often designed around the actuators. This dissertation seeks to address two goals: 1) advancing the design of compliant linear actuators that are well suited for humanoid applications, and 2) developing a better understanding of how to design and model compliant linear actuators for use in humanoids.
Beyond just applications for compliant humanoids, this research tackles many of the same design and application challenges as biomechanics research so it has many potential applications in prosthetics, exoskeletons, and rehabilitation devices.Ph. D.
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Hall, R. W. "Two dimensional isoviscous EHL and associated contact problems in linear elasticity". Thesis, University of Leeds, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374172.
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Blacker, David James. "Robust non-conforming finite element approximation in nearly incompressible linear elasticity". Thesis, University of Strathclyde, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269972.
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Lejri, Mostfa. "Subsurface stress inversion modeling using linear elasticity : sensitivity analysis and applications". Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS212/document.
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Aujourd’hui, l’un des principaux défis dans l’industrie pétrolière, et particulièrement dans le domaine de l’exploration, est l’exploitation des nouvelles ressources dans des zones structuralement complexes.Nous savons que la géométrie et le glissement le long des failles actives modifie la distribution locale des contraintes. La connaissance du champ de contrainte perturbé actuel est importante pour l’étude des tremblements de Terre, pour la planification de forages ainsi que pour la prédiction de la fracturation induite par l’hydro-fracturation et la prédiction de la réactivation des fractures. Les contraintes perturbées passées, quant à elles sont responsables du développement des fractures naturelles (préexistantes). La détection et la modélisation de celles-ci sont essentielles tant dans le domaine pétrolier (migration et piégeage des fluides) pour une exploitation efficace et à moindre coût des réserves naturelles.Comprendre et quantifier le développement spatial et temporel de ces contraintes a un impact économique non négligeable. L'analyse des paléo-contraintes a été introduite dans un premier temps par Anderson (1905 & 1942) de manière intuitive, puis dans le milieu du siècle dernier, Wallace (1951) et Bott ( 1959) proposèrent les simples postulats que le champ de contrainte est homogène et que la direction du rejet est parallèle à la traction projetée sur le plan de faille. Beaucoup de méthodes d’inversion de contraintes reposent aujourd’hui sur ce principe.Afin d’étudier la validité de l’hypothèse Wallace et Bott, une comparaison avec les vecteurs de glissement générés à partir de modèles numériques (BEM) est effectuée. En testant l’influence de multiples paramètres (géométrie, contraintes au limites du modèle, friction, coefficient de poisson, demi-espace, pression de fluide dans la faille), il est montré que les failles à géométries complexes soumises à certaines contraintes aux limites peuvent engendrer des vecteurs glissements présentant des écarts important avec les la plus grande contraintes cisaillantes résolue sur le plan de faille. A l’inverse, la présence d’une forte friction de glissement permet, dans certaines conditions, de valider l’hypothèse de Wallace et Bott. On s’attache ensuite à comparer les résultats des inversions de contraintes basées sur l’hypothèse de Wallace et Bott (appelé méthode d’inversion classique de contraintes) avec une méthode géomécanique. Pour cela, une faille à géométrie complexe est utilisée dans une étude de sensibilité (contraintes aux limites, friction, échantillonnage) permettant d’analyser l’incertitude des résultats des deux méthodes d’inversion. Cette analyse est ensuite confrontée à l’étude d’un cas de terrain, montrant les avantages et inconvénients des méthodes d’inversions classiques de contraintes.Un des principaux défis de l’industrie pétrolière est l’exploitation des ressources des zones structuralement complexes telles que les réservoirs naturellement fracturés. Connaitre l’état de contraintes hétérogène passé permet d’optimiser la modélisation de ces fractures naturelles. Etant donné que les glissements sur les failles sont difficiles à observer dans les réservoirs pétroliers, les données de d’orientation de fractures (joints, failles, stylolites) sont naturellement prises en compte lors de l’inversion des contraintes. On montre, en utilisant divers exemples de terrain et d’industrie, que dans de tels cas, l’utilisation d’inversions basée sur la mécanique est beaucoup plus appropriée. Cependant, il est parfois difficile de déterminer le type cinématique de fracture observée le long des puits, et très souvent, les zones étudiées ont subi une tectonique polyphasée. La dernière partie vise donc à résoudre le problème des données de types cinématiques non identifiables (joints, failles, stylolites…) et étend parallèlement l’inversion mécanique des contraintes à la séparation de phases tectoniquesToday, one of the main challenges in the oil industry, especially during the exploration phase, is the exploitation of new resources in structurally complex areas such as naturally fractured reservoirs, salt diapirs, mountain ranges, and unconventional reservoirs.We know that the geometry and sliding along active faults modifies the local stress distribution. Knowing the present day perturbed stress field is important for the study of earthquakes, for the planning of the borehole drilling and stability as well as for the prediction of fractures induced by hydro-fracturing and reactivation of natural fractures. In the other side, perturbed paleostress are responsible for the development of (pre-existing) natural fractures. The detection and modeling of the latter, are essential both in the oil industry (migration and trapping of fluids) for a cost efficient recovery of natural reserves.Understanding and quantifying the spatial and temporal development of the stress distribution has a significant economic and environmental impact. The analysis of paleo-constraints was intuitively introduced first by Anderson (1905 & 1942), then in the middle of the last century, Wallace (1951) and Bott (1959) proposed the simple hypothesis that (i) The stress field is homogeneous in space and constant in time, and that (ii) the slip direction is parallel to the traction projected on the fault plane which gives the direction of the shear stress. Many stress inversion methods are based on this hypothesis while recent studies raise doubts as to their compatibility with rock mechanics.In order to investigate the validity of the Wallace and Bott hypothesis, a comparison with vectors of slip generated with numerical models (BEM) is performed. By testing the influence of multiple parameters (geometry, boundary conditions, friction, Poisson’s coefficient , half-space, fault fluid pressure), it is shown that the complex geometry faults subject to specific boundary conditions can yield slip vectors with significant discrepancies with the maximum shear stress resolved on the fault plane. Conversely, the presence of a high sliding friction, allows under certain conditions, to validate the hypothesis of Wallace and Bott.We then focus on the task to compare the results of stress inversions based on the assumption of Wallace and Bott (called classical stress inversion methods) to a geomechanical method. For this, a complex fault geometry is used in a sensitivity analysis (boundary conditions, friction, sampling) to evaluate the uncertainty of the results of the two inversion methods. This analysis is then compared to a case study, Chimney Rock (Utah, USA), showing the advantages and disadvantages of the classical stress inversion methods.One of the main challenges of the oil industry is the exploitation of resource in structurally complex oil fields such as naturally fractured reservoirs. Knowing the heterogeneous paleostress allows to optimize the modeling of these natural fractures. Since slip on faults is hardly observed in petroleum reservoirs, fracture orientation data (joints, faults, stylolites) are naturally taken into account during the inversion of stresses. It is shown, using various field and industry examples, that in such cases the use of mechanical stress inversions is much more appropriate.However, it is sometimes difficult to determine the fracture kinematics observed along wellbores, and very often the studied regions underwent multiple tectonic phases. The final section aims to address the problem of data with unknown kinematic (joints, faults, stylolites ...) and expends the mechanical stress inversion to the separation of tectonic phases
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Leurent, Thomas B. (Thomas Bruno) 1975. "Reduced basis output bounds for linear elasticity : application to microtruss structures". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/89325.
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Mukhopadhyay, S., R. Picard, S. Trostorff y M. Waurick. "On some models in linear thermo-elasticity with rational material laws". Sage, 2016. https://tud.qucosa.de/id/qucosa%3A35516.
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In the present work, we shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models allowing for more general material properties such as anisotropies, inhomogeneities, etc.
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Hall, Anthony R. "The Pseudo-Rigid-Body Model for Fast, Accurate, Non-Linear Elasticity". BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3869.
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We introduce to computer graphics the Pseudo-Rigid-Body Mechanism (PRBM) and the chain algorithm from mechanical engineering, with a unified tutorial from disparate source materials. The PRBM has been used successfully to simplify the simulation of non-linearly elastic beams, using deflections of an analogous spring and rigid-body linkage. It offers computational efficiency as well as an automatic parameterization in terms of physically measurable, intuitive inputs which fit naturally into existing animation work flows for character articulation. The chain algorithm is a technique for simulating the deflection of complicated elastic bodies in terms of straight elastic elements, which has recently been extended to incorporate PRBM beam-elements in three dimensions. We present a new, mathematically equivalent optimization of the 3D PRBM chain algorithm, from its former asymptotic complexity of O(n^2) in the number of elements n, to O(n). We also extend an existing PRBM for combined moment-force loads to 3D, where the existing 3D PRBM chain algorithm was limited to 3D PRBM elements for a moment-only load. This optimization and extension are validated by duplicating prior experimental results, but substituting the new optimization and combined-load elements. Finally, a loose road-map is provided with several key considerations for future extension of the techniques to dynamic simulations.
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Cáncer, Castillo Víctor. "Non-linear elastic response of scale invariant solids". Doctoral thesis, Universitat Autònoma de Barcelona, 2020. http://hdl.handle.net/10803/671059.
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L’objectiu d’aquesta tesis és aplicar mètodes de teoria de camps per entendre la resposta elàstica no-lineal (ENL) dels sòlids. La resposta ENL conté un gran número de quantitats observables, que no sempre són fàcils de derivar de la composició microscòpica del material. Un actor esencial en la resposta elàstica dels sòlids són els fonons, que poden ser descrits com els bosons de Goldstone d’una ruptura espontània de les simetries de l’espai-temps. Com a tals, la seva dinàmica a baixes energies (incloent no-linealitats) pot ser capturada sistemàticament per mètodes estàndard de Teoria de Camps Efectiva (TCE). Això ofereix naturalment una manera nova de lidiar amb la fenomenologia ENL. Una conclusió principal es que, efectivament, aquests mètodes de baixes energies donen informació no trivial, com relacions entre differents observables ENL. Il·lustrem aquest fet obtenint límits en la màxima deformació que un material pot tolerar, que pot ser expressat en funció d’altres observables ENL.
Un cas especial són els sòlids invariants d’escala (IE). Això inclou dos sub-casos diferents, ja que l’EI pot realitzar-se de manera manifesta o com una simetria trencada espontàniament. El primer cas correspon a un punt fix no trivial i requereix l’ús de metodes hologràfics (AdS/CFT). El segon cas pot ser descrit utilitzant mètodes TCE. Comparem els resultats obtinguts als dos casos i trobem que els límits difereixen significativament als dos sub-casos.El objetivo de esta tesis es aplicar métodos de teoría de campos para entender la respuesta elástica no-lineal (ENL) de los sólidos. La respuesta ENL contiene un gran número de cantidades observables, que no siempre son fáciles de derivar de la composición microscópica del material. Un actor esencial en la respuesta elástica de los solidos son los fonones, que pueden ser descritos como bosones de Goldstone de una ruptura espontánea de las simetrías del espacio-tiempo. Como tales, su dinàmica a bajas energías (incluyendo no linealidades) puede ser capturado sistemáticamente con métodos estándar de Teoría de Campos Efectiva (TCE) a bajas energías. Esto ofrece naturalmente una manera nueva de tratar la fenomenología ENL. Una conclusión principal es que, efectivamente, los métodos de baja energía TCE ofrecen información no trivial, como relaciones entre diferentes observables ENL. Ilustramos esto obteniendo límites en la máxima deformation que un material puede tolerar, lo cual puede ser expresado en función de otros observables ENL. Un caso de especial interés son los sólidos invariantes de escala (IE). Esto incluye dos sub-casos distintos, puesto que la IE puede ser realizada de manera manifiesta o como una simetría rota espontáneamente. El primer caso corresponde a un punto fijo no trivial y requiere el uso de métodos holográficos (AdS/CFT). El segundo caso puede ser descrito con métodos TCE estándar. Comparamos los resultados obtenidos en ambos casos y encontramos que los límites elásticos difieren significativamente en los dos sub-casos.
The goal of this thesis is to apply modern field theory methods to understand the nonlinear elastic (NLE) response of solids. The NLE response contains a large number of low-energy observable quantities, not always easy to derive from the microscopic composition of the material. An essential actor in the elastic response are the phonons, which can be described as the Goldstone bosons of the spontaneously broken spacetime symmetries. As such, their low energy dynamics (including non-linearities) can be captured systematically by standard low energy Effective Field Theory (EFT) methods. This offers naturally a novel approach to tackle NLE phenomenology. One main conclusion is that indeed the low energy effective methods can provide non-trivial information, as relations among various different NLE observables. We illustrate this by obtaining bounds on the maximum deformation that a material can tolerate, which can be expressed in function of other NLE observables. A case of special interest is that of scale invariant (SI) solids. This includes two distinct sub-cases, since SI can be realized either as a manifest symmetry or a spontaneously broken symmetry. The former case corresponds to a nontrivial fixed point and requires the use of holographic (AdS/CFT) techniques. The latter case instead can be described with more standard EFT methods. We compare the results obtained in the two cases, and find that the obtained elasticity bounds differ significantly in the two sub-cases.
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Wood, Joseph D. "Brittle mixed-mode cracks between linear elastic layers". Thesis, Loughborough University, 2017. https://dspace.lboro.ac.uk/2134/24177.
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Original analytical theories are developed for partitioning mixed-mode fractures on rigid interfaces in laminated orthotropic double cantilever beams (DCBs) based on 2D elasticity by using some novel methods. Note that although the DCB represents a simplified case, it provides a deep understanding and predictive capability for real applications and does not restrict the analysis to a simple class of fracture problems. The developed theories are generally applicable to so-called 1D fracture consisting of opening (mode I) and shearing (mode II) action only with no tearing (mode III) action, for example, straight edge cracks, circular blisters in plates and shells, etc. A salient point of the methods is to first derive one loading condition that causes one pure fracture mode. It is conveniently called the first pure mode. Then, all other pure fracture modes can be determined by using this pure mode and the property of orthogonality between pure mode I modes and pure mode II modes. Finally, these 2D-elasticity-based pure modes are used to partition mixed-mode fractures into contributions from the mode I and mode II fracture modes by considering a mixed-mode fracture as the superposition of pure mode I and mode II fractures. The partition is made in terms of the energy release rate (ERR) or the stress intensity factor (SIF). An analytical partition theory is developed first for a DCB composed of two identical linear elastic layers. The first pure mode is obtained by introducing correction factors into the beam-theory-based mechanical conditions. The property of orthogonality is then used to determine all other pure modes in the absence of through-thickness-shear forces. To accommodate through-thickness shear forces, first two pure through-thickness-shear-force pure modes (one pure mode I and one pure mode II) are discovered by extending a Timoshenko beam partition theory. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness-ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II ERR correction factor. Both correction factors closely follow a normal distribution around a symmetric DCB geometry. The property of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a DCB with bending moments, axial forces and through-thickness shear forces. Fracture on bimaterial interfaces is an important consideration in the design and application of composite materials and structures. It has, however, proved an extremely challenging problem for many decades to obtain an analytical solution for the complex SIFs and the crack extension size-dependent ERRs, based on 2D elasticity. Such an analytical solution for a brittle interfacial crack between two dissimilar elastic layers is obtained in two stages. In the first stage the bimaterial DCB is under tip bending moments and axial forces and has a mismatch in Young s modulus; however, the Poisson s ratios of the top and bottom layers are the same. The solution is achieved by developing two types of pure fracture modes and two powerful mathematical techniques. The two types of pure fracture modes are a SIF-type and a load-type. The two mathematical techniques are a shifting technique and an orthogonal pure mode technique. In the second stage, the theory is extended to accommodate a Poisson s ratio mismatch. Equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be transformed into cases for which the analytical solution does exist. It is now possible to use a completely analytical 2D-elasticity-based theory to calculate the complex SIFs and crack extension size-dependent ERRs. The original partition theories presented have been validated by comparison with numerical simulations. Excellent agreement has been observed. Moreover, one partition theory is further extended to consider the blister test and the adhesion energy of mono- and multi-layered graphene membranes on a silicon oxide substrate. Use of the partition theory presented in this work allows the correct critical mode I and mode II adhesion energy to be obtained and all the experimentally observed behaviour is explained.
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Placidi, Luca. "Solution of St.-Venant's and Almansi-Michell's Problems". Thesis, Virginia Tech, 2002. http://hdl.handle.net/10919/35451.
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We use the semi-inverse method to solve a St. Venant and an Almansi-Michell problem for a prismatic body made of a homogeneous and isotropic elastic material that is stress free in the reference configuration. In the St. Venant problem, only the end faces of the prismatic body are loaded by a set of self-equilibrated forces. In the Almansi-Michell problem self equilibrated surface tractions are also applied on the mantle of the body. The St. Venant problem is also analyzed for the following two cases: (i) the reference configuration is subjected to a hydrostatic pressure, and (ii) stress-strain relations contain terms that are quadratic in displacement gradients. The Signorini method is also used to analyze the St. Venant problem. Both for the St. Venant and the Almansi-Michell problems, the solution of the three dimensional problem is reduced to that of solving a sequence of two dimensional problems. For the St. Venant problem involving a second-order elastic material, the first order deformation is assumed to be an infinitesimal twist. In the solution of the Almansi-Michell problem, surface tractions on the mantle of the cylindrical body are expressed as a polynomial in the axial coordinate. When solving the problem by the semi-inverse method, displacements are also expressed as a polynomial in the axial coordinate. An explicit solution is obtained for a hollow circular cylindrical body with surface tractions on the mantle given by an affine function of the axial coordinateMaster of Science
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Maerten, Frantz. "Geomechanics to solve geological structure issues : forward, inverse and restoration modeling". Thesis, Montpellier 2, 2010. http://www.theses.fr/2010MON20031.
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Différentes applications de l'élasticité linéaire en géologie structurale sont présentées dans cette thèse à travers le développement de trois types de codes numériques. Le premier utilise la modélisation directe pour étudier les déplacements et champs de contraintes autour de zones faillées complexes. On montre que l'ajout de contraintes inégalitaires, telles que la friction de Coulomb, permet d'expliquer l'angle d'initiation des dominos dans les relais extensifs. L'ajout de matériaux hétérogènes et d'optimisations, telles la parallélisation sur processeurs multi-coeurs ainsi que la réduction de complexité des modèles, permettent l'étude de modèles beaucoup plus complexes. Le second type de code numérique utilise la modélisation inverse, aussi appelée estimation de paramètres. L'inversion linéaire de déplacements sur les failles ainsi que la détermination de paléo-contraintes utilisant une approche géomécanique sont développées. Le dernier type de code numérique concerne la restoration de structures complexes plissées et faillées. Il est notamment montré qu'une telle méthode permet de vérifier l'équilibre de coupes géologiques, ainsi que de retrouver la chronologie des failles. Finalement, nous montrons que ce même code permet de lisser des horizons 3D faillés, plissés et bruités en utilisant la géomécaniqueDifferent applications of linear elasticity in structural geology are presented in this thesis through the development of three types of numerical computer codes. The first one uses forward modeling to study displacement and perturbed stress fields around complexly faulted regions. We show that incorporating inequality constraints, such as static Coulomb friction, enables one to explain the angle of initiation of jogs in extensional relays. Adding heterogeneous material properties and optimizations, such as parallelization on multicore architectures and complexity reduction, admits more complex models. The second type deals with inverse modeling, also called parameter estimation. Linear slip inversion on faults with complex geometry, as well as paleo-stress inversion using a geomechanical approach, are developed. The last type of numerical computer code is dedicated to restoration of complexly folded and faulted structures. It is shown that this technique enables one to check balanced cross-sections, and also to retrieve fault chronology. Finally, we show that this code allows one to smooth noisy 3D interpreted faulted and folded horizons using geomechanics
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Shahzad, Summer. "Stress singularities, annihilations and invisibilities induced by polygonal inclusions in linear elasticity". Doctoral thesis, Università degli studi di Trento, 2016. https://hdl.handle.net/11572/368863.
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Notches, wedges, cracks, sti?eners, inclusions and defects in plane elastostatics are known to generate singular stresses and limit the overall strength of a composite material. In the present thesis, after showing experimentally that the singular stress ?eld predicted by the linear elastic solution for the rigid inclusion model can be generated in reality and with great accuracy within a material, attention is devoted then in achieving the out-of-plane response of an in?nite plane containing polygonal and hypocycloidal-shaped voids and rigid inclusions subject to generalized remote loading conditions. The analytical solution obtained for the case of polygonal inclusions shows some unexpected and interesting features such as an in?nite set of geometries and loading conditions exist for which not only the singularity is absent, but the stress vanishes (annihilates) at the corners. Thus the material, which even without the inclusion corners would have a ?nite stress, remains unstressed at these points in spite of the applied remote load. Moreover, similar conditions are determined in which a star-shaped crack or sti?ener leaves the ambient stress completely unperturbed, thus reaching a condition of ‘quasi-static invisibility’. The solution in closed-form is also obtained for the case of hypocycloidalshaped voids and rigid inclusions, showing that cusps may in certain conditions act as stress reducers, situations for which the stress at the cusp tip in the presence of the inclusion is smaller than in the case when the inclusion is absent. Ph.D. Thesis – Summer Shahzad vThe obtained solutions provide closed-form expressions for Stress Intensity Factors and Notch Stress Intensity Factors at varying the inclusion geometry and of loading conditions, fundamental quantities in de?ning criteria of fracture initiation/propagation or inclusion detachment. The ?ndings of stress annihilation, stress reduction and inclusion invisibility de?ne optimal loading modes for the overall strength of a composite and are useful in the design of ultra-resistant materials.
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Shahzad, Summer. "Stress singularities, annihilations and invisibilities induced by polygonal inclusions in linear elasticity". Doctoral thesis, University of Trento, 2016. http://eprints-phd.biblio.unitn.it/1769/1/Shahzad_Summer_Phd_thesis.pdf.
Texto completoResumen
Notches, wedges, cracks, stiffeners, inclusions and defects in plane elastostatics are known to generate singular stresses and limit the overall strength of a composite material. In the present thesis, after showing experimentally that the singular stress field predicted by the linear elastic solution for the rigid inclusion
model can be generated in reality and with great accuracy within a material, attention is devoted then in achieving the out-of-plane response of an infinite plane containing polygonal and hypocycloidal-shaped voids and rigid inclusions subject to generalized remote loading conditions.
The analytical solution obtained for the case of polygonal inclusions shows some unexpected and interesting features such as an infinite set of geometries and loading conditions exist for which not only the singularity is absent, but the stress vanishes (annihilates) at the corners. Thus
the material, which even without the inclusion corners would have a finite stress, remains unstressed at these points in spite of the applied remote load. Moreover, similar conditions are determined in which a star-shaped
crack or stiffener leaves the ambient stress completely unperturbed, thus reaching a condition of ‘quasi-static invisibility’. The solution in closed-form is also obtained for the case of hypocycloidalshaped voids and rigid inclusions, showing that cusps may in certain conditions act as stress reducers, situations for which the stress at the cusp tip in the presence of the inclusion is smaller than in the case when the inclusion is absent.
Ph.D. Thesis – Summer Shahzad vThe obtained solutions provide closed-form expressions for Stress Intensity Factors and Notch Stress Intensity Factors at varying the inclusion
geometry and of loading conditions, fundamental quantities in defining criteria of fracture initiation/propagation or inclusion detachment. The findings of stress annihilation, stress reduction and inclusion invisibility define optimal loading modes for the overall strength of a composite
and are useful in the design of ultra-resistant materials.
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Topol, Heiko [Verfasser]. "Acoustic and mechanical properties of viscoelastic, linear elastic, and nonlinear elastic composites / Heiko Topol". Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1028213352/34.
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De, Villiers Magdaline. "Existence theory for linear vibration models of elastic bodies". Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-10072009-201522.
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Peng, Xuan. "Isogeometric boundary element methods for linear elastic fracture mechanics". Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/92543/.
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We develop in this work a procedure for obtaining the fatigue life of complex structures directly from Computer-Aided Design (CAD) data, without any mesh generation or regeneration as the cracks evolve. The method relies on a standard isogeometric boundary element method (IGABEM) where the same basis functions are used to both describe the geometry of the component and approximate the displacement and traction fields. The contributions of this work include: (1) Dual boundary integral equations have been applied to model 2D/3D fracture problems in the framework of IGA and that such simulations require no meshing or remeshing in the conventional sense; (2) Graded knot insertion and partition of unity enrichment have been used to capture the stress singularity around the crack tip. The contour-integral based methods and the virtual crack closure integral method are adopted to extract stress intensity factors in the framework of IGABEM; (3) Modifications on the singularity subtraction technique for (hyper-)singular integration are proposed to enhance the quadrature on distorted elements which commonly arise in IGA; (4)ANURBS-based geometry modification algorithm is developed to simulate fatigue crack growth in 2D/3D. smooth crack trajectory and crack front are obtained; (5) An implementation on trimmed NURBS is realized based on a localized double mapping method to perform the quadrature on trimmed elements. A phantom element method is subsequently proposed to model the surface crack (breaking crack) problem and the displacement discontinuity can be introduced without any reparametrization on the original patch.
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Tsarouchas, Dimitris. "Fibre network materials : architecture and effective linear elastic properties". Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610878.
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Seitenfuss, Alan Bourscheidt. "On the behavior of a linear elastic peridynamic material". Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-22062017-100938/.
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The peridynamic theory is a generalization of classical continuum mechanics and takes into account the interaction between material points separated by a finite distance within a peridynamic horizon δ. The parameter δ corresponds to a length scale and is treated as a material property related to the microstructure of the body. Since the balance of linear momentum is written in terms of an integral equation that remains valid in the presence of discontinuities, the peridynamic theory is suitable for studying the material behavior in regions with singularities. The first part of this work concerns the evaluation of the properties of a linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which uses the difference displacement quotient field in the neighborhood of a material point and considers both length and relative angle changes. This material model is based upon a free energy function that contains four material constants, being, therefore, different from other peridynamic models found in the literature, which contain only two material constants. Using convergence results of the peridynamic theory to the classical linear elasticity theory in the limit of small horizons and a correspondence argument between the free energy function and the strain energy density function from the classical theory, expressions were obtained previously relating three peridynamic constants to the classical elastic constants of an isotropic linear elastic material. To calculate the fourth peridynamic material constant, which couples both bond length and relative angle changes, the correspondence argument is used once again together with the strain field of a linearly elastic beam subjected to pure bending. The expression for the fourth constant is obtained in terms of the Poisson\'s ratio and the shear elastic modulus of the classical theory. The validity of this expression is confirmed through the consideration of other experiments in mechanics, such as bending of a beam by terminal loads and anti-plane shear of a circular cylinder. In particular, numerical results indicate that the expressions for the constants are independent of the experiment chosen. The second part of this work concerns an investigation of the behavior of a one-dimensional linearly elastic bar of length L in the context of the peridynamic theory; especially, near the ends of the bar, where it is expected that the behavior of the peridynamic bar may be very different from the behavior of a classical linear elastic bar. The bar is in equilibrium without body force, is fixed at one end, and is subjected to an imposed displacement at the other end. The bar has micromodulus C, which is related to the Young\'s modulus E in the classical theory through different expressions found in the literature. Depending on the expression for C, the displacement field may be singular near the ends, which is in contrast to the linear behavior of the displacement field observed in classical linear elasticity. In spite of the above, it is also shown that the peridynamic displacement field converges to its classical counterpart as the peridynamic horizon tends to zero.A teoria peridinâmica é uma generalização da teoria clássica da mecânica do contínuo e considera a interação de pontos materiais devido a forças que agem a uma distância finita entre si, além da qual considera-se nula a força de interação. Por ter o balanço de momento linear formulado como uma equação integral que permanece válida na presença de descontinuidades, a teoria peridinâmica é adequada para o estudo do comportamento de materiais em regiões com singularidades. A primeira parte deste trabalho consiste no cálculo das propriedades de um material peridinâmico elástico linear no contexto de uma teoria peridinâmica de estado, linearmente elástica e tridimensional, que utiliza o campo quociente de deslocamento relativo na vizinhança de um ponto material e leva em conta mudanças relativas angulares e de comprimento. Esse modelo utiliza uma função energia livre que apresenta quatro constantes materiais, sendo, portanto, diferente de outros modelos peridinâmicos investigados na literatura, os quais contêm somente duas constantes materiais. Utilizando resultados de convergência da teoria peridinâmica para a teoria de elasticidade linear clássica no limite de pequenos horizontes e um argumento de correspondência entre as funções energia livre proposta e densidade de energia de deformação da teoria clássica, expressões para três constantes peridinâmicas foram obtidas em função das constantes de um material elástico e isotrópico da teoria clássica. O argumento de correspondêmcia, em conjunto com o campo de deformações de uma viga submetida à flexão pura, é utilizado para calcular a quarta constante peridinâmica do material, que relaciona mudanças angulares relativas e de comprimentos das ligações entre as partículas. Obtem-se uma expressão para a quarta constante em termos do coeficiente de Poisson e do módulo de elasticidade ao cisalhamento da teoria clássica. A validade dessa expressão é confirmada por meio da consideração de outros experimentos da mecânica, tais como flexão de um viga por cargas terminais e cisalhamento anti-plano de um eixo cilíndrico. Em particular, os resultados numéricos indicam que as expressões para as constantes são independentes do experimento escolhido. A segunda parte deste trabalho consiste em uma investigação do comportamento de uma barra unidimensional linearmente elástica de comprimento L no contexto da teoria peridinâmica; especialmente, próximo às extremidades da barra, onde espera-se que o comportamento da barra peridinâmica possa ser muito diferente do comportamento de uma barra elástica linear clássica. A barra está em equilíbrio e sem força de corpo, fixa em uma extremidade, e sujeita a deslocamento imposto na outra extremidade. A barra possui micromódulo C, o qual está relacionado ao módulo de Young E da teoria clássica por meio de diferentes expressões encontradas na literatura. Dependendo da expressão para C, o campo de deslocamento pode ser singular próximo às extremidades, o que contrasta com o comportamento linear do campo de deslocamento observado na elasticidade linear clássica. Apesar disso, é mostrado também que o campo de deslocamento peridinâmico converge para o campo de deslocamento da teoria clássica quando o horizonte peridinâmico tende a zero.
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Quinelato, Thiago de Oliveira. "Mixed hybrid finite element method in elasticity and poroelasticity". Laboratório Nacional de Computação Científica, 2017. https://tede.lncc.br/handle/tede/273.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Esta tese é focada no desenvolvimento e na análise de aproximações em dimensão finita das equações que descrevem problemas de elasticidade linear e poroelasticidade. A estratégia de aproximação é baseada em formulações de elementos finitos mistas hibridas desses problemas e a construção dos espaços de dimensão finita é guiada por várias propriedades desejadas: continuidade das trações (conservação do momento linear), simetria do tensor de tensão (conservação do momento angular), número reduzido de graus de liberdade globais e robustez sob distorção de malha. A principal dificuldade está relacionada com o atendimento simultâneo da condição inf-sup e da simetria do tensor de tensão. O ultimo requisito é relaxado, sendo satisfeito de maneira fraca pela introdução de um multiplicador de Lagrange. A maior contribuição é o desenvolvimento e a análise de espaços de dimensão finita estáveis para aproximação mista dos problemas de elasticidade linear e poroelasticidade em malhas quadrilaterais arbitrárias. Esses espaços são capazes de fornecer convergência com taxa ótima do campo de tensão na norma H(div) em malhas de quadriláteros arbitrários, o que é provado pela análise numérica e confirmado por experimentação.
This thesis is focused on the development and analysis of finite dimensional approximations of the equations describing linear elasticity and poroelasticity problems. The approximation strategy is based on mixed hybrid finite element formulations of those problems and the construction of the finite dimensional spaces is guided by several desired properties: continuity of the tractions (conservation of linear momentum), symmetry of the stress tensor (conservation of angular momentum), reduced number of global degrees of freedom, and robustness under mesh distortion. The main difficulty is related with the simultaneous fulfillment of the inf-sup condition and the symmetry of the stress tensor. The last requirement is relaxed, being enforced in the weak sense through the introduction of a Lagrange multiplier. The main contribution is the development and analysis of stable finite dimensional spaces for mixed approximation of linear elasticity and poroelasticity problems on arbitrary quadrilateral meshes. These spaces are capable of providing optimal order convergence of the stress field in the H(div)-norm on meshes of arbitrary quadrilaterals, which is proved by numerical analysis and confirmed by experimentation.
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Chung, Wai-Nang. "Fracture toughness and creep fracture studies of polyethylenes". Thesis, Imperial College London, 1991. http://hdl.handle.net/10044/1/46720.
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Goodsell, G. "Gradient superconvergance in the finite element method with applications to planar linear elasticity". Thesis, Brunel University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383122.
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Abbate, Emanuela. "Numerical methods for all-speed flows in fluid-dynamics and non-linear elasticity". Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0409/document.
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Dans cette thèse on s’intéresse à la simulation numérique d’écoulements des matériaux compressibles, voir fluides et solides élastiques. Les matériaux considérés sont décrits avec un modèle monolithique eulérian, fermé avec une loi d’état hyperélastique qui considère les différents comportements des matériaux. On propose un nouveau schéma de relaxation qui résout les écoulements compressibles dans des différents régimes, avec des nombres de Mach très petits jusqu’à l’ordre 1. Le schéma a une formulation générale qui est la même pour tous le matériaux considérés, parce que il ne dépend pas directement de la loi d’état. Il se base sur une discrétisation complétement implicite, facile à implémenter grâce à la linéarité de l’opérateur de transport du système de relaxation. La discrétisation en espace est donnée par la combinaison de flux upwind et centrés, pour retrouver la correcte viscosité numérique dans les différents régimes. L’utilisation de mailles cartésiennes pour les cas 2D s’adapte bien à une parallélisation massive, qui permet de réduire drastiquement le temps de calcul. De plus, le schéma a été adapté pour la résolution sur des mailles quadtree, pour implémenter l’adaptativité de la maille avec des critères entropiques. La dernière partie de la thèse concerne la simulation numérique d’écoulements multi-matériaux. On a proposé une nouvelle méthode d’interface “sharp”, en dérivant les conditions d’équilibre en implicite. L’objectif est la résolution d’interfaces physiques dans des régimes faiblement compressibles et avec un nombre de Mach faible, donc les conditions multi-matériaux sont couplées au schéma implicite de relaxationIn this thesis we are concerned with the numerical simulation of compressible materials flows, including gases, liquids and elastic solids. These materials are described by a monolithic Eulerian model of conservation laws, closed by an hyperelastic state law that includes the different behaviours of the considered materials. A novel implicit relaxation scheme to solve compressible flows at all speeds is proposed, with Mach numbers ranging from very small to the order of unity. The scheme is general and has the same formulation for all the considered materials, since a direct dependence on the state law is avoided via the relaxation. It is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in different Mach regimes. The scheme is validated with one and two dimensional simulations of fluid flows and of deformations of compressible solids. We exploit the domain discretization through Cartesian grids, allowing for massively parallel computations (HPC) that drastically reduce the computational times on 2D test cases. Moreover, the scheme is adapted to the resolution on adaptive grids based on quadtrees, implementing adaptive mesh refinement techinques. The last part of the thesis is devoted to the numerical simulation of heterogeneous multi-material flows. A novel sharp interface method is proposed, with the derivation of implicit equilibrium conditions. The aim of the implicit framework is the solution of weakly compressible and low Mach flows, thus the proposed multi-material conditions are coupled with the implicit relaxation scheme that is solved in the bulk of the flow
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Liang, Xiaoqing. "Dynamic Response of Linear/Nonlinear Laminated Structures Containing Piezoelectric Laminas". Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30348.
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The three-dimensional linear theory of piezo-elasticity is used to analyse steady state vibrations of a simply supported rectangular laminated composite plate with piezoelectric (PZT) actuator and sensor patches either embedded in it or bonded to the its surfaces. It is assumed that different layers are perfectly bonded to each other. The method of Fourier series is used to find an analytical solution of the problem. The analytical solution is then applied to study the shape control of a steadily vibrating composite plate by exciting different regions of a PZT actuator. Numerical results for a thin and a thick plate containing one embedded actuator layer and one embedded sensor layer are presented. For the former case, the optimum location of the centroid of the excited rectangular region that will require minimum voltage to control the out-of-plane displacements is determined. Keeping the location of the centroid and the shape of the excited region fixed, we ascertain the voltage required as a function of the length of its diagonal to nullify the deflections of the plate. The maximum shear stress at the interface between the sensor and the lamina is found to be lower than that between the actuator and the lamina. The point of maximum output voltage from the sensor coincides with that of its peak out-of-plane displacement. The variations of displacement and stress components through the thickness for the thin and thick plates are similar.
The transient finite deformations of a neo-Hookean beam or plate with PZT patches bonded to its upper and lower surfaces are simulated by the finite element method. The constitutive relation for the piezoelectric material is taken to be linear in the Green-Lagrange strain tensor but quadratic in the driving voltage. A code using 8-noded brick elements has been developed and validated by comparing computed results with either analytical solutions or experimental observations. The code is then used to study flexural waves generated by PZT actuators and propagating through a cantilever beam both with and without a defect in it. The computed results are compared with test observations and with the published results for the linear elastic beam. The effects of both geometrical and material nonlinearities are discussed. A simple feedback control algorithm is shown to annul the motion of a neo-Hookean plate subjected to an impulsive load.Ph. D.
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Knabe, Coleman Scott. "Design of Linear Series Elastic Actuators for a Humanoid Robot". Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/53511.
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Series elastic actuators (SEAs) have numerous benefits for force controlled robotic applications. This thesis presents the design and assembly of a set of compact, lightweight, low-friction linear SEAs for the legs of the Tactical Hazardous Operations Robot (THOR). The THOR SEA pairs a ball screw driven linear actuator with a configurable titanium leaf spring. A removable pivot changes the effective cantilever length, setting the compliance to either 372 or 655 kN/m. Unlike typical SEAs which measure actuator load through spring deflection, an in-line axial load cell directly measures actuator forces up to the commandable peak of 2225 N. The continuous operating range of the actuator is computed, along with an evaluation of the range of motion and torque profiles for the parallel hip and ankle joints. With a focus on a large power-to-weight ratio and small packaging size, the THOR SEAs are well-suited for accurate torque control of the parallel joints on the robot.
Linearly actuated joints, especially ones driven through a crank arm, tend to suffer from a loss of mechanical advantage toward the ends of its limited range of motion. To augment the range of motion and mechanical advantage profile on THOR, an inverted Hoeken's linkage straight line mechanism is paired with a linear SEA at the hip and knee pitch joints on the robot. The resulting linkage assembly is capable of delivering nearly constant peak torque of 115 Nm across its 150 degree range of motion. The mechanical advantage profile of the Hoeken's linkage actuator is computed for the nominal case, as well the deviation resulting from maximum deflection of the titanium beam.Master of Science
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Bordignon, Nicola. "Bifurcations and instability in non-linear elastic solids with interfaces". Doctoral thesis, Università degli studi di Trento, 2018. https://hdl.handle.net/11572/368975.
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The study of local and global instability and bifurcation phenomena is crucial for many engineering applications in the field of solid mechanics.
In particular, interfaces within solid bodies are of great importance in the bifurcation analysis, as they constitute localized zones in which discontinuities or jumps in displacement, strain or stress may occur. Different instability phenomena, heavily conditioned by the presence of interfaces, were analyzed in the present thesis.
The first phenomenon that has been considered is the propagation of a shear band, which is a localized shear deformation developing in a ductile material. This shear band, assumed to be already present inside of a ductile
matrix material (obeying von Mises plasticity with linear hardening), is modelled as a discontinuity interface following two different approaches.
In the first approach, the conditions describing the behavior of a layer of material in which localized strain develop are introduced and implemented in a finite element computer code. A shear deformation is simulated by imposing appropriate displacement conditions on the boundaries of the matrix material, in which the shear band is present and modelled through an imperfect interface, having null thickness.
The second approach is based on a perturbative technique, developed for a J2-deformation theory material, in which the shear band is modeled as the emergence of a discontinuity surface for displacements at a certain stage of a uniform deformation process, restricted to plane strain conditions.
Both the approaches concur in showing that shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration is expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials [results of this study have been reported in (Bordignon et al. 2015)].
The second type of interface analyzed in the present thesis is a perfectly frictionless sliding interface, subject to large deformations and assumed to be present within a uniformly strained nonlinear elastic solid. This type of interface may model lubricated sliding contact between soft solids, a topic of interest in biomechanics and for the design of small-scale engineering devices.
The analyzed problem is posed as follows. Two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so that this formulation has been developed in the thesis. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or ‘spring-type’ interfacial conditions are not able to predict bifurcations in tension, while experiments (one of which, ad hoc designed, is reported) show that these bifurcations are a reality and can be predicted when the correct sliding interface model is used. Therefore, the presented approach introduces a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact [results of this study have been reported in (Bigoni et al. 2018)].
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Bordignon, Nicola. "Bifurcations and instability in non-linear elastic solids with interfaces". Doctoral thesis, University of Trento, 2018. http://eprints-phd.biblio.unitn.it/2863/1/PhD_thesis_Nicola_Bordignon.pdf.
Texto completoResumen
The study of local and global instability and bifurcation phenomena is crucial for many engineering applications in the field of solid mechanics.
In particular, interfaces within solid bodies are of great importance in the bifurcation analysis, as they constitute localized zones in which discontinuities or jumps in displacement, strain or stress may occur. Different instability phenomena, heavily conditioned by the presence of interfaces, were analyzed in the present thesis.
The first phenomenon that has been considered is the propagation of a shear band, which is a localized shear deformation developing in a ductile material. This shear band, assumed to be already present inside of a ductile
matrix material (obeying von Mises plasticity with linear hardening), is modelled as a discontinuity interface following two different approaches.
In the first approach, the conditions describing the behavior of a layer of material in which localized strain develop are introduced and implemented in a finite element computer code. A shear deformation is simulated by imposing appropriate displacement conditions on the boundaries of the matrix material, in which the shear band is present and modelled through an imperfect interface, having null thickness.
The second approach is based on a perturbative technique, developed for a J2-deformation theory material, in which the shear band is modeled as the emergence of a discontinuity surface for displacements at a certain stage of a uniform deformation process, restricted to plane strain conditions.
Both the approaches concur in showing that shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration is expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials [results of this study have been reported in (Bordignon et al. 2015)].
The second type of interface analyzed in the present thesis is a perfectly frictionless sliding interface, subject to large deformations and assumed to be present within a uniformly strained nonlinear elastic solid. This type of interface may model lubricated sliding contact between soft solids, a topic of interest in biomechanics and for the design of small-scale engineering devices.
The analyzed problem is posed as follows. Two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so that this formulation has been developed in the thesis. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or ‘spring-type’ interfacial conditions are not able to predict bifurcations in tension, while experiments (one of which, ad hoc designed, is reported) show that these bifurcations are a reality and can be predicted when the correct sliding interface model is used. Therefore, the presented approach introduces a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact [results of this study have been reported in (Bigoni et al. 2018)].
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ANGELICI, Marco. "Vibrazioni non lineari in mezzi piezoelettrici finiti". Doctoral thesis, La Sapienza, 2004. http://hdl.handle.net/11573/916891.
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Issaoui, Abderrahman [Verfasser]. "hp-BEM for contact problems and extended Ms-FEM in linear elasticity / Abderrahman Issaoui". Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2014. http://d-nb.info/1058241516/34.
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Meyer, Arnd y Cornelia Pester. "The Laplace and the linear elasticity problems near polyhedral corners and associated eigenvalue problems". Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601506.
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The solutions to certain elliptic boundary value problems have singularities with a typical structure near polyhedral corners. This structure can be exploited to devise an eigenvalue problem whose solution can be used to quantify the singularities of the given boundary value problem. It is necessary to parametrize a ball centered at the corner. There are different possibilities for a suitable parametrization; from the numerical point of view, spherical coordinates are not necessarily the best choice. This is why we do not specify a parametrization in this paper but present all results in a rather general form. We derive the eigenvalue problems that are associated with the Laplace and the linear elasticity problems and show interesting spectral properties. Finally, we discuss the necessity of widely accepted symmetry properties of the elasticity tensor. We show in an example that some of these properties are not only dispensable, but even invalid, although claimed in many standard books on linear elasticity.
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Merkert, Dennis [Verfasser] y Bernd [Akademischer Betreuer] Simeon. "Numerical Homogenization for Linear Elasticity in Translation Invariant Spaces / Dennis Merkert ; Betreuer: Bernd Simeon". Kaiserslautern : Technische Universität Kaiserslautern, 2018. http://d-nb.info/1163274607/34.
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Suliman, Ridhwaan. "A quadratic non-linear elasticity formulation for the dynamic behaviour of fluid-loaded structures". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277824.
Texto completoResumen
This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.
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Leckar, Hamilton F. y Rubens Sampaio. "Problems in incompressible linear elasticity involving tangential and normal components of the displacement field". Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96316.
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We consider the linear system -∆ u + grad p = f plus the divergence-free condition div u = O, in a bounded and conected but non simply connected open set Ω of R³, with a boundary ᴦ of C∞ class. Using orthogonal decompositions of the Hilbert space of square integrable vector fields on Ω, we show well posedness for two boundary value problems involving normal or tangential components of the displacement field on ᴦ.