A bilinear formulation is used for developing the time finite element method (TFM) to obtain transient responses of both linear, nonlinear, damped and undamped systems. Also the formulation, used in the h-, p- and hp-versions, is extended and found to be readily amenable to multi-degree-of-freedom systems. The resulting linear and nonlinear algebraic equations for the transient response are differentiated to obtain the sensitivity of the response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, Hermite, Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of TFM, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various design parameters can be obtained. Since a considerable effort is spent in determining the sensitivity of the response with respect to system parameters in many algorithms for parametric identification, an identification procedure based on the TFM is developed and tested for a number of nonlinear single-and two-degree-of-freedom system problems. An advantage of the TFM is the easy calculation of the sensitivity of the transient response with respect to various design parameters, a key requirement for gradient-based parameter identification schemes. The method is simple, since one obtains the sensitivity of the response to system parameters by differentiating the algebraic equations, not original differential equations. These sensitivities are used in Levenberg-Marquardt iterative direct method to identify parameters for nonlinear single- and two-degree-of-freedom systems. The measured response was simulated by integrating the example nonlinear systems using the given values of the system parameters. To study the influence of the measurement noise on parameter identification, random noise is added to the simulated response. The accuracy and the efficiency of the present method is compared to a previously available approach that employs a multistep method to integrate nonlinear differential equations. It is seen, for the same accuracy, the present approach requires fewer data points. Finally, the TFM for optimal control problems based on Hamiltonian weak formulation is proposed by adopting the p- and hp-versions as a finite element discretization process. The p-version can be used to improve the accuracy of the solution by adding more unknowns to each element without refining the mesh. The usage of hierarchical type of shape functions can lead to a significant saving in computational effort for a given accuracy. A set of Legendre polynomials are chosen as higher order shape functions and applied to two simple minimization problems for optimal control. The proposed formulation provides very accurate results for these problems. / Ph. D.

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This work concerns the simulation of viscoelastic behavior of polymer at different states. Viscoelastic modeling of polymer was performed from the solid state to the liquid state via a multiphase approach which is largely used to deal with the fluid structure interaction. To ensure the appreciation of the FSI, viscoelasticity is considered in two parts: an elastic one and viscous other where the main idea is to use a mixed formulation in three fields (u, v, p) (displacement, velocity, pressure), with u and v, represented the primary variables of a strain and a strain rate formulation. We are led to the Navier-Stokes compressible problem with extra-stress, which is solved by using the Mixed Finite Element. The present work contributes some stabilization elements to the numerical simulation of multiphase problem by the monolithic approach.Comparison between the literature and experiments was performed through the validation of an elastic case and the viscoelastic Kelvin-Voigt model in the context of Lagrangian framework as well as Eulerian framework. The extension of the methodology to a visco-hyper-elastic is given through the modeling and validation on material point on the finite elements library CimLib®. Finally, a stabilization scheme of the EVSS type is adopted for viscoelastic Kelvin-Voigt model, hyper-elastic Neo-Hookean model, and also visco-hyper-elastic model which proposed an open door in computational modeling, not only with viscoelasticity but also complex dynamic application.

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

京都大学 / 新制・課程博士 / 博士(農学) / 甲第23239号 / 農博第2446号 / 新制||農||1083(附属図書館) / 学位論文||R3||N5329(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 / DGAM

Ce travail a été effectué dans le cadre du projet Rem3D® dans lequel participent plusieurs entreprises avec l'objectif de développer un logiciel d'injection en 3D par éléments finis. L'objectif est de développer une méthode numérique pour modéliser le comportement viscoélastique des polymères de l'état solide à l'état liquide à travers une approche multiphasique qui est largement utilisé pour traiter le problème de l'interaction fluide-structure (IFS). La philosophie est d'utiliser une formulation mixte de trois champs (u, v, p) (déplacement, vitesse, pression), où u et v représentent les principales variables de déformation et de vitesse de déformation. Nous sommes amenés au problème de Navier-Stokes compressibles avec l'extra-contrainte, qui est résolu en utilisant la méthode des éléments finis mixte. Le présent travail contribue aussi certains éléments de stabilisation pour la simulation numérique des problèmes multiphasiques par l'approche monolithique.Comparaison entre la littérature et l'expérience est accompli par la validation du cas élastique et cas modèle viscoélastique de Kelvin-Voigt dans le lagrangien approche ainsi qu'eulérien approche. L'extension de la méthodologie au modèle visco-hyper-élastique est débuté par la modélisation et la validation au point matériel, puis l'implémentation dans la bibliothèque des éléments finis CimLib®. Enfin, un schéma stabilisation de résolution du type EVSS est adopté pour le modèle viscoélastique de Kelvin-Voigt, le modèle visco-hyper-élastique de Néo-Hookean, et aussi le modèle visco-hyper-élastique qui propose une prometteuse porte ouverte dans la simulation et modélisation, non seulement pour la viscoélasticité, mais aussi pour les applications dynamique complexes. / This work concerns the simulation of viscoelastic behavior of polymer at different states. Viscoelastic modeling of polymer was performed from the solid state to the liquid state via a multiphase approach which is largely used to deal with the fluid structure interaction. To ensure the appreciation of the FSI, viscoelasticity is considered in two parts: an elastic one and viscous other where the main idea is to use a mixed formulation in three fields (u, v, p) (displacement, velocity, pressure), with u and v, represented the primary variables of a strain and a strain rate formulation. We are led to the Navier-Stokes compressible problem with extra-stress, which is solved by using the Mixed Finite Element. The present work contributes some stabilization elements to the numerical simulation of multiphase problem by the monolithic approach.Comparison between the literature and experiments was performed through the validation of an elastic case and the viscoelastic Kelvin-Voigt model in the context of Lagrangian framework as well as Eulerian framework. The extension of the methodology to a visco-hyper-elastic is given through the modeling and validation on material point on the finite elements library CimLib®. Finally, a stabilization scheme of the EVSS type is adopted for viscoelastic Kelvin-Voigt model, hyper-elastic Neo-Hookean model, and also visco-hyper-elastic model which proposed an open door in computational modeling, not only with viscoelasticity but also complex dynamic application.

The aim of this diploma thesis is the part of evolution of the new bicycle frame for mountain biking, category enduro. The first part of this thesis is focused on creating dimensional modified model of the bike frame in CAD system SolidWorks. Subsequently this frame will be detailed by FEM analysis in software ANSYS Workbench and determine boundary conditions for this analysis. The final part is about visualization of the new bike frame.