京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第21374号 / 農博第2298号 / 新制||農||1066(附属図書館) / 学位論文||H30||N5147(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 藤原 正幸, 教授 渦岡 良介 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

This paper describes simulations of the generalized modified Benjamin-Bona-Mahony (BBM) equation, using finite difference methods (FDM). Well-posed boundary conditions (BCs) as well as stable semi-discrete approximations are derived using summations-by-parts (SBP) operators combined with the projection method. For time integration, explicit Runge-Kutta 4 (RK4) is used, as well as SBP-SAT, which discretizes the temporal domain using SBP operators and imposes initial conditions using simultaneous approximation term (SAT). These time-marching methods are evaluated and compared in terms of accuracy and computing times, and soliton-boundary interaction is studied. It is shown that SBP-SAT time-marching perform well and is more suitable than RK4 for this type of non-linear, dispersive problem. Generalized summation-by-parts (GSBP) time-marching perform particularly well, due to high accuracy with few solution points.

This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.

On s'intéresse à la résolution numérique de problèmes de contact et de fissuration en dynamique. Le problème de contact envisagé est le problème de Signorini avec ou sans frottement de Coulomb. Quant au problème de fissuration, il s'agit d'un modèle de zone cohésive avec trajet de fissuration pré-défini. Ces problèmes se caractérisent par la présence d'une condition aux limites non-régulière et se formulent comme des inéquations variationnelles d'évolution ou des inclusions différentielles. Pour les résoudre numériquement, nous combinons, comme il est courant en dynamique des solides, une discrétisation en espace par éléments finis et des schémas d'intégration en temps (de types différences finies). Pour le problème de contact, nous commençons par comparer les principales méthodes proposées dans la littérature. Nous étudions ensuite plus particulièrement la méthode dite de masse modifiée récemment introduite par H. Khenous, P. Laborde et Y. Renard. Nous en proposons une variante semi-explicite. Par ailleurs, nous prouvons un résultat de convergence des solutions semi-discrètes en espace vers une solution continue dans le cas d'un problème de Signorini sans frottement et d'un matériau viscoélastique. Nous analysons également les methodes semi-discrètes en espace et totalement discrètes dans le cas d'un problème de Signorini avec frottement de Coulomb. Pour le problème de fissuration dynamique, la non-régularité de la condition aux limites rend impossible ou peu robuste l'utilisation de schémas totalement explicites. Nous proposons donc des schémas où cette condition aux limites est traitée de façon implicite. Enfin, nous présentons et analysons des méthodes de lagrangien augmenté pour la résolution numérique du problème de fissuration en statique / The present work deals with the numerical solution of dynamic contact and fracture problems. The contact problem is a Signorini problem with or without Coulomb friction. The fracture problem uses a cohesive zone model with a prescribed crack path. These problems are characterized by a non-regular boundary condition and can be formulated with evolutionary variational inequations or differential inclusions. For the numerical solution, we combine, as usual in solid dynamics, a finite element discretization in space and time-integration schemes. For the contact problem, we begin by comparing the main methods proposed in the literature. We then focus on the so-called modified mass method recently introduced by H. Khenous, P. Laborde et Y. Renard, for which we propose a semi-explicit variant. In addition, we prove a convergence result of the space semi-discrete solutions to a continuous solution in the frictionless viscoelastic case. We also analyze the space semi-discrete and fully discrete problems in the friction Coulomb case. For the dynamic fracture problem, using a fully explicit scheme is impossible or not robust enough. Therefore, we propose time-integration schemes where the boundary condition is treated in an implicit way. Finally, we present and analyze augmented Lagrangian methods for static fracture problems

Cette étude est consacrée à la modélisation du comportement thermo-mécanique des argiles raides saturées et au développement d'un algorithme d'intégration efficace de contrainte correspondant. Le comportement mécanique de l'argile de Boom naturelle dans des conditions isothermes a été caractérisé. Le modèle Cam Clay modifié (MCC) a été ensuite appliquée pour simuler le comportement de l'argile de Boom naturel. Il a été constaté que le MCC donne des prédictions de mauvaise qualité pour le comportement de l'argile de Boom naturel. Ainsi, un modèle Cam Clay (ACC-2) adapté a été développé en introduisant une nouvelle surface de charge et un nouveau potentiel plastique ainsi que d'un mécanisme plastique de Deux surfaces. Ce modèle permet la description satisfaisante des caractéristiques principales du comportement mécanique de l'argile de Boom naturelle. De plus, les équations de ce modèle peuvent être formulées mathématiquement comme dans un modèle élasto-plastique classique. L'algorithme d'intégration de contrainte classique peut donc être appliqué. Les effets thermiques ont été examinés par l'évaluation de la pertinence de trois lois thermomécaniques avancées (Cui et al, 2000; Abuel-Naga et al, 2007; Laloui et François, 2008; 2009). Il apparaît que tous les trois modèles peuvent décrire les caractéristiques principales du comportement thermo-mécanique des argiles saturées. Cependant, chaque modèle a ses limites ou des points peu clairs du point de vue théorique. L'algorithme d'intégration de contrainte du modèle thermo-mécanique de Cui et al. (2000) au point de contrainte a également été développé spécifiquement en utilisant une méthode adaptive du pas de temps. Le temps de calcul nécessaire pour obtenir une précision donnée est ainsi largement réduit pour des chemins de chargements thermiques et mécaniques. Un modèle thermo-mécanique à Deux surfaces (modèle TEAM) a été développé en se basant sur le mécanisme plastique de Deux surfaces. Le modèle proposé a étendu le modèle de Cui et al. (2000) à une formulation de Deux surfaces considérant le couplage entre les déformations plastiques des chemins de chargements thermiques et mécaniques. La simulation des essais drainés montre que ce modèle peut décrire les caractéristiques principales thermo-mécaniques de l'argile de Boom naturelle le long de différents chemins de chargements. Le modèle TEAM a finalement été étendu à des conditions non drainées. Après la clarification du concept des contraintes effectives et la définition d'une condition de déformation volumique, le processus d'échauffement non drainé est analysé. La validité des équations thermo-hydro-mécaniques de ce modèle a été examinée en se basant sur des résultats d'essais typiques / This study is devoted to the thermo-mechanical constitutive modeling for saturated stiff clays and the development of a corresponding efficient stress integration algorithm. The mechanical behavior of natural Boom Clay in isothermal conditions was first characterized. The Modified Cam Clay model (MCC) was then applied to simulate the natural Boom Clay behavior. It has been found that the MCC gives poor-quality predictions of the natural Boom Clay behavior. Thereby, an adapted Cam Clay model (ACC-2) was developed by introducing a new yield surface and a new plastic potential as well as a Two-surface plastic mechanism. This model allows satisfactory prediction of the main features of the mechanical behavior of natural Boom Clay. Moreover, the constitutive equations of this model can be formulated mathematically as in a classic elasto-plastic model. Thus, the classic stress integration algorithm can be applied. The thermal effects were considered by assessing the performance of some advanced thermo-mechanical models (Cui et al., 2000; Abuel-Naga et al., 2007; Laloui and François, 2008; 2009). It appears that all the three models can capture the main features of the thermo-mechanical behavior of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. The stress integration algorithm of the thermo-mechanical model proposed by Cui et al. (2000) at the stress point level was also developed using a specifically designed adaptive time-stepping scheme. The computation time required to achieve a given accuracy is largely reduced with the adaptive sub-stepping considered for both mechanical and thermal loadings. A Two-surface thermo-mechanical model (TEAM model) was developed based on the Two-surface plastic mechanism. The proposed model extends the model of Cui et al. (2000) to a Two-surface formulation, considering the plastic strain coupling between the thermal and the mechanical loading paths. The simulation of drained tests shows that this model can capture the main thermo-mechanical features of natural Boom Clay along different loading paths. The TEAM model was finally extended to undrained conditions. After setting up an appropriate effective stress principle and defining a volumetric strain condition, the undrained heating process was analyzed. The validity of the thermo-hydro-mechanical constitutive equations was examined based on the data from typical tests

Dans ce travail, on s'intéresse au développement d'une méthode hybride qui couple spatialement les schémas d'intégration temporelle explicite et implicite. Afin de répondre aux contraintes du solveur industriel FLUSEPA, les schémas explicite Heun et implicite Crank-Nicolson ont été hybridés via un paramètre de transition : l'approche mise en place est appelée schéma AION. Cette dernière est étudiée en détails avec une attention particulière sur son comportement spectral et sa capacité à maintenir l'ordre de précision. On montre que le traitement hybride a d'intéressants comportements dissipatif et dispersif tout en empêchant la réflexion d'ondes parasites et en maintenant la précision attendue. De plus, l'approche hybride est validée sur plusieurs cas académiques à la fois pour les flux convectifs et pour les flux diffusifs. Et comme espéré, la méthode est plus intéressante en terme de temps de calcul que les méthodes standards d'intégration temporelle. Pour l'extension de cette approche à la méthode temporelle adaptative présente dans FLUSEPA, il a été nécessaire d'améliorer le traitement qui permet à la méthode d’être conservative tout en obtenant des propriétés spectrales acceptables. Finalement l'approche hybride a été aussi étendue pour la modélisation RANS/LES de la turbulence avec des temps de calcul intéressants tout en capturant la physique de l'écoulement / This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics.

A mechatronic system is an assembly of technological components, such as a mechanism, sensors, actuators, and a control unit. Recently, a number of researchers and industrial manufacturers have highlighted the potential advantages of lightweight parallel mechanisms with respect to the accuracy, dynamic performances, construction cost, and transportability issues. The design of a mechatronic system with such a mechanism requires a multidisciplinary approach, where the mechanical deformations have to be considered. This thesis proposes two original contributions in this framework. (i) First, a modular and systematic method is developed for the integrated simulation of mechatronic systems, which accounts for the strongly coupled dynamics of the mechanical and non-mechanical components. The equations of motion are formulated using the nonlinear Finite Element approach for the mechanism, and the block diagram language for the control system. The time integration algorithm relies on the generalized-alpha method, known in structural dynamics. Hence, well-defined concepts from mechanics and from system dynamics are combined in a unified formulation, with guaranteed convergence and stability properties. Several applications are treated in the fields of robotics and vehicle dynamics. (ii) Usual methods in flexible multibody dynamics lead to complex nonlinear models, not really suitable for control design. Therefore, a systematic nonlinear model reduction technique is presented, which transforms an initial high-order Finite Element model into a low-order and explicit model. The order reduction is obtained using the original concept of Global Modal Parameterization: the motion of the assembled mechanism is described in terms of rigid and flexible modes, which have a global physical interpretation in the configuration space. The reduction procedure involves the component-mode technique and an approximation strategy in the configuration space. Two examples are presented: a four-bar mechanism, and a parallel kinematic machine-tool. Finally, both simulation and modeling tools are exploited for the dynamic analysis and the control design of an experimental lightweight manipulator with hydraulic actuators. A Finite Element model is first constructed and validated with experimental data. A reduced model is derived, and an active vibration controller is designed on this basis. The simulation of the closed-loop mechatronic system predicts remarkable performances. The model-based controller is also implemented on the test-bed, and the experimental results agree with the simulation results. The performances and the other advantages of the control strategy demonstrate the relevance of our developments in mechatronics.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-04T11:17:29Z No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:32:59Z (GMT) No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) / Made available in DSpace on 2017-01-31T10:32:59Z (GMT). No. of bitstreams: 1 daniellerosanydemedeirosleal.pdf: 19032116 bytes, checksum: 03bebf3d76cd23f21fc6a647e7c00d77 (MD5) Previous issue date: 2016-08-29 / Este trabalho apresenta um novo esquema explícito de marcha no tempo para a análise problemas de propagação de ondas compatível com qualquer método de discretização espacial que seja baseado em elementos (e.g., Método dos Elementos Finitos, etc.). Por ser explícito, isto é, sem necessidade da solução de um sistema de equações, o método é de fácil implementação. Baseado em integradores de tempo adaptativos, a técnica aqui proposta contempla dissipação numérica local e otimizada, permitindo a minimização de oscilações espúrias e aumento da precisão. Também, com o emprego de discretização temporal local (subciclagem), acrescenta-se robustez ao algoritmo do método, flexibilizando a estabilidade e aumentando a eficiência da análise em foco. / This work presents a new explicit time marching procedure for wave propagation problems, which is compatible with any spatial discretization method based on elements (e.g. Finite Element Method - FEM, etc.). Because it does not require any system of equations to be solved, its implementation is very simple. Based on adaptive time integrators, it provides local and optimized numerical damping, allowing the influence of spurious oscillations to be minimized, improving accuracy. In addition, by employing local time discretization, considering a subclycing technique, the performance to the method is improved, enhancing the flexibility of the method regarding stability and increasing the efficiency of the proposed approach.

Least Square Kinetic Upwind Method (LSKUM) belongs to the class of mesh-less method that solves compressible Euler equations of gas dynamics. LSKUM is kinetic theory based upwind scheme that operates on any cloud of points. Euler equations are derived from Boltzmann equation (of kinetic theory of gases) after taking suitable moments. The basic update scheme is formulated at Boltzmann level and mapped to Euler level by suitable moments. Mesh-less solvers need only cloud of points to solve the governing equations. For a complex configuration, with such a solver, one can generate a separate cloud of points around each component, which adequately resolves the geometric features, and then combine all the individual clouds to get one set of points on which the solver directly operates. An obvious advantage of this approach is that any incremental changes in geometry will require only regeneration of the small cloud of points where changes have occurred. Additionally blanking and de-blanking strategy along with overlay point cloud can be adapted in some applications like store separation to avoid regeneration of points. Naturally, the mesh-less solvers have advantage in tackling complex geometries and moving components over solvers that need grids. Conventionally, higher order accuracy for space derivative term is achieved by two step defect correction formula which is computationally expensive. The present solver uses low dissipation single step modified CIR (MCIR) scheme which is similar to first order LSKUM formulation and provides spatial accuracy closer to second order. The maximum time step taken to march solution in time is limited by stability criteria in case of explicit time integration procedure. Because of this, explicit scheme takes a large number of iterations to achieve convergence. The popular explicit time integration schemes like four stages Runge-Kutta (RK4) are slow in convergence due to this reason. The above problem can be overcome by using the implicit time integration procedure. The implicit schemes are unconditionally stable i.e. very large time steps can be used to accelerate the convergence. Also it offers superior robustness. The implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is very attractive due to its low numerical complexity, moderate memory requirement and unconditional stability for linear wave equation. Also this scheme is more efficient than explicit counterparts and can be implemented easily on parallel computers. It is based on the factorization of the implicit operator into three parts namely lower triangular matrix, upper triangular matrix and diagonal terms. The use of LU-SGS results in a matrix free implicit framework which is very economical as against other expensive procedures which necessarily involve matrix inversion. With implementation of the implicit LU-SGS scheme larger time steps can be used which in turn will reduce the computational time substantially. LU-SGS has been used widely for many Finite Volume Method based solvers. The split flux Jacobian formulation as proposed by Jameson is most widely used to make implicit procedure diagonally dominant. But this procedure when applied to mesh-less solvers leads to block diagonal matrix which again requires expensive inversion. In the present work LU-SGS procedure is adopted for mesh-less approach to retain diagonal dominancy and implemented in 2-D and 3-D solvers in matrix free framework. In order to assess the efficacy of the implicit procedure, both explicit and implicit 2-D solvers are tested on NACA 0012 airfoil for various flow conditions in subsonic and transonic regime. To study the performance of the solvers on different point distributions two types of the cloud of points, one unstructured distribution (4074 points) and another structured distribution (9600 points) have been used. The computed 2-D results are validated against NASA experimental data and AGARD test case. The density residual and lift coefficient convergence history is presented in detail. The maximum speed up obtained by use of implicit procedure as compared to explicit one is close to 6 and 14 for unstructured and structured point distributions respectively. The transonic flow over ONERA M6 wing is a classic test case for CFD validation because of simple geometry and complex flow. It has sweep angle of 30° and 15.6° at leading edge and trailing edge respectively. The taper ratio and aspect ratio of the wing are 0.562 and 3.8 respectively. At M∞=0.84 and α=3.06° lambda shock appear on the upper surface of the wing. 3¬D explicit and implicit solvers are tested on ONERA M6 wing. The computed pressure coefficients are compared with experiments at section of 20%, 44%, 65%, 80%, 90% and 95% of span length. The computed results are found to match very well with experiments. The speed up obtained from implicit procedure is over 7 for ONERA M6 wing. The determination of the aerodynamic characteristics of a wing with the control surface deflection is one of the most important and challenging task in aircraft design and development. Many military aircraft use some form of the delta wing. To demonstrate the effectiveness of 3-D solver in handling control surfaces and small gaps, implicit 3-D code is used to compute flow past clipped delta wing with aileron deflection of 6° at M∞ = 0.9 and α = 1° and 3°. The leading edge backward sweep is 50.4°. The aileron is hinged from 56.5% semi-span to 82.9% of semi-span and at 80% of the local chord from leading edge. The computed results are validated with NASA experiments

Les structures soumises à des vibrations sont rencontrées dans diverses applications. Dans denombreux cas, elles sont de nature linéaires, mais quand les amplitudes des oscillations deviennentimportantes, cela provoque un comportement non-linéaire. Par ailleurs, les oscillations desstructures dans un milieu fluide entrainent une interaction fluide-structure. Cette thèse porte surla modélisation du problème fluide-structure non-linéaire. Les cas de non-linéarités étudiés sont lanon-linéarité grands-déplacements caractéristique des structures minces, la non-linéarité localiséegéométrique décrivant une liaison non-linéaire entre deux structures et la non-linéarité acoustiqueparticularité des très hauts niveaux de pression.Pour la modélisation de ces problèmes, il se peut que le calcul en réponse demeure infaisable enraison du temps de calcul. D’une part, on est amené à résoudre des systèmes matriciels (symétriquesou non) de grandes tailles générés par la méthode des éléments finis et d’autre part, cetterésolution demande une évaluation de la force non-linéaire à chaque itération. Afin de diminuer lecoût de calcul, la réduction de modèle par des bases de réductions couplées avec un algorithmeparallélisant l’évaluation de la force non-linéaire, est une alternative à la résolution du systèmecomplet. La construction des bases de réduction doit s’adapter au mieux à chaque problème traité.La base modale du problème linéaire est une première approximation puis elle est enrichie par desinformations qui proviennent à la fois de la nature du couplage et du comportement non-linéaire / Structures subjected to vibrations are found in various applications. In many cases, they behave ina linear way, but when the amplitudes of the oscillations become important, it causes a nonlinearbehavior. Moreover, the oscillations of structures in a fluid field lead to a fluid-structureinteraction. This thesis focuses on the modeling of nonlinear fluid-structure problem. Differentkind of nonlinearities are studied in this work including the large-displacement nonlinearitycharacteristic of thin structures, the localized geometrical nonlinearity describing a nonlinear linkbetween two structures, and the acoustic nonlinearity characteristic of very high levels ofpressure.Modeling such problems are time and memory consuming, that may lead to a limitations of themodel. Therefore, it is necessary to solve a large matrix system (either symmetric or not)generated by the finite element method and the resolution needs an evaluation of the nonlinearforce at each iteration. In order to reduce the computational cost, model reduction with reducedbases combined with parallelization of the nonlinear force evolution is proposed as an alternative tothe resolution of complete systems. Building reduction bases must be adapted to each concernedproblem. The eigenmode of the linear problem is a first approximation and it is enriched withinformation coming from both coupling and nonlinear behaviors.