Singular limits for the bi-laplacian operator with exponential nonlinearity in R4\R^4

Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for some integer $d\geq1$ its $d$-th singular cohomology group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any given number $m$.Comment: 30 pages, to appear in Ann. IHP Non Linear Analysi

Non-linear numerical analysis of the Iosipescu specimen for composite materials

A nonlinear elastic finite element analysis is presented of the Iosipescu shear specimen tested in the modified Wyoming fixture for unidirectional graphite/epoxy composites. It is shown that the nonlinear effects due to specimen-to-fixture contact interactions and specimen geometry on the overall shear response are negligible. It is proposed that the tangential shear modulus should be used to characterize the shear resistance of composite materials with highly nonlinear shear response. The correction factors, which are needed to compensate for the nonuniformity of the shear stress or strain distribution in the specimen test section for shear modulus measurement, have to be defined carefully. Strain contours in the nonlinear response ranges are presented and the initiation of failure in the notch regions is investigated

Development of a simplified analytical method for representing material cyclic response

Development of a simplified method for estimating structural inelastic stress and strain response to cyclic thermal loading is presented. The method assumes that high temperature structural response is the sum of time independent plastic and time dependent elastic/creep components. The local structural stress and strain response predicted by linear elastic analysis is modified by the simplified method to predict the inelastic response. The results with simulations by a nonlinear finite element analysis and used time independent plasticity and unified time dependent material model are compared

Approche multimodale de la mobilité urbaine : développement d'un outil d'aide à la prise de décision

La voiture individuelle a permis d'agir directement sur les contraintes associées aux temps de déplacements en facilitant la mobilité individuelle et a engendré une évolution des villes qui se caractérise par des processus qui s'autoalimentent : une dispersion urbaine, une spécialisation fonctionnelle des zones et une croissance du trafic automobile. Le transport de masse conventionnel (métro, tramway, train\ud léger), comme seule alternative à la dépendance automobile, s'adapte difficilement à cette nouvelle réalité pour répondre à une mobilité qui s'exprime variablement dans le temps et dans l'espace. Dans ce contexte, les Systèmes de Transport Cybernétiques (STC) se présentent comme une alternative technologique propice à répondre à cette mobilité collective individualisée en offrant, en tout temps, un service sur demande par le partage de véhicules automatisés fonctionnant en\ud réseau. Si la voiture est synonyme de liberté individuelle, en revanche son utilisation privilégiée mène à un déséquilibre du système de mobilité qui se traduit par les phénomènes d'engorgements du réseau routier. À l'inverse, le transport de masse\ud est stable à l'extrême en assujettissant les usagers à son mode opératoire rigide (corridors et cadences des véhicules préétablis). En rupture avec ces deux modes de fonctionnement, la dynamique du système de mobilité par STC repose sur la capacité à anticiper le besoin ainsi que sur la configuration des véhicules dans le réseau pour desservir adéquatement la demande individuelle formulée aux différents lieux du périmètre urbain desservi. Les résultats de la recherche ont montré que le besoin individuel en déplacements peut être appréhendé comme un phénomène chaotique. La reconstruction de l'espace d'encastrement à sept dimensions associées à la série chronologique du\ud besoin en déplacements pour un édifice au centre-ville de Montréal permet de reconstruire le profil du besoin par pas de temps de deux minutes, à partir des événements préalablement enregistrés. Basée sur la capacité des véhicules d'un STC d'emprunter l'ensemble des voies de guidages et l'identification des stations de départ et d'arrivée de chaque demande préalablement aux déplacements,\ud l'application du principe du maximum d'entropie permet d'identifier les itinéraires individuels des véhicules. L'application du principe, développé à partir des relations de l'entropie statistique et de la théorie de l'information, permet de diffuser les\ud véhicules dans le réseau sous contrainte du respect des demandes des usagers et ainsi de minimiser le phénomène d'engorgement. Dans une approche dynamique de l'évolution du système, la configuration des véhicules dans un réseau STC se\ud modifie en fonction des demandes et doit s'organiser pour répondre aux besoins à venir. Par analogie avec les systèmes naturels, l'application des principes thermodynamiques de l'enthalpie et de l'entropie permettent d'expliciter la relation entre le besoin en déplacement et l'état du système. Par raisonnement déductif, les résultats explicitent le principe d'une configuration des véhicules dans\ud le réseau basée sur des critères caractérisant l'état du système dans sa globalité plutôt que sur des critères de proximité et de distances à parcourir.\ud Les résultats obtenus sur la base de l'application des lois comportementales des systèmes naturels (phénomènes chaotiques et principes thermodynamiques) sont intégrables dans un modèle. Ce dernier, en tant qu'outil de représentation, permet de mettre en évidence les fonctionnalités dynamiques qui d'une part animent le système et, d'autre part en assurent la cohérence pour satisfaire les besoins individuels dans le temps et dans l'espace. Cette capacité de s'adapter aux caractéristiques du milieu dans lequel un STC est implanté, permet de générer une\ud synergie avec les transports conventionnels pour une diversification de l'offre en transport collectif apte à s'adapter aux multiples dimensions de la demande individualisée en mobilité. Finalement, la démarche développée initie un changement de paradigme dans le domaine du transport collectif en privilégiant la variété des moyens (multiples modes et multiples itinéraires) pour rejoindre les\ud différents lieux plutôt que la singularité d'un transport de masse. Ce changement de paradigme trouve également un écho en urbanisme où une organisation multifonctionnelle des zones urbaines favorise une accessibilité de proximité diversifiée

I. Experimental tests on the positive column in pure rare gases and their binary mixtures. II. Kinetics of hydrocarbon reactions in the positive column of D.C. and pulsed D.C. discharges

Part I: A TM011 microwave cavity was used to measure the radially averaged electron density n¯e and the electron-neutral collision frequency νen in d.c. glow discharge positive columns of pure rare gases and their binary mixtures. Electric field E was measured by measuring the floating potential across pairs of probes in the plasma. The pure gases studied were He, Ne and Ar at pressures of 1-8 torr and discharge currents I of 5-20 mA. The calculated values of the electron drift velocity vd in He and Ne are substantially lower than the Bradbury and Nielson drift tube values, indicating substantial ionization via metastables in the range of p and I investigated. Discharges in He-Ar and He-Ne mixtures at p = 2-5 torr and I = 15 mA exhibit time and space dependent values of n¯e, νen due to the effect of cataphoresis. The results indicate that the Shair and Remer model is a reasonable description of the phenomenon of cataphoresis in these mixtures where the impurity (Ar or Ne) content is in the range of 2-20%. Part II: By employing a positive column flow reactor with low residence times (&#60; 100 msec) in d.c. discharges with low currents (&#60; 5 mA), it is possible to convert up to 5% of the feed methane into ethane, ethylene and hydrogen with negligible formation of solid and liquid products. The percent methane in the argon or helium feed Co affects the product distribution, with good selectivity for Co &#62; 5%. Average steady-state electron densities in the discharge were simultaneously measured by perturbation of the resonance of a TM010 microwave cavity. A pulsed d.c. discharge enabled the residence time to be effectively reduced even further. The pulsed discharge experiments were conducted at 3-9 torr with pulse durations ~ 1 msec and pulse intervals of 20-50 msec. Pulse current was measured as a function of time with a current probe. The TM010 cavity was used to obtain transient electron densities in the discharge, which varied between 109 and 1010 electrons/cm3. The kinetic results are consistent with a free radical mechanism with electron-impact dissociation as the initiating step. Derived values of the integrated cross-section for CH4 + e →α CH3 + H + e and CH4 + e → β CH2 + H2 + e are in the range 3.6 - 15.5 x 10-11cm3sec-1, and that for C2H4 + e →γ C2H2 + H2 + e is ~ 9 x 10-10cm3sec-1. α and β fall with Co in the range 4.0 - 12.6%, indicating a shift of the electron energy distribution function fe(ε) to lower values of ε. Calculations are presented for the case of H2 dissociation to illustrate the strong effect of the tail end of fe(ε) on the rate of chemical reaction.</p

Avaliação computacional da reserva de carga de "regiões B e D" de concreto armado considerando a distribuição das armaduras, modelos constitutivos não-lineares para os materiais e danificação do concreto

Orientador: Prof. Dr. Roberto Dalledone MachadoDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa : Curitiba, 20/02/2020Inclui referências: p.169-174Área de concentração: Mecânica dos Sólidos ComputacionalResumo: O dimensionamento de estruturas de concreto armado visa definir a quantidade e a distribuição de armaduras necessárias nas peças. Em regiões que apresentam perturbações no campo de tensões (conhecidas na literatura como "Regiões D"), o Método das Bielas é empregado para o dimensionamento das peças. Uma das dificuldades na aplicação do método é a determinação prévia do campo de tensões, pois este depende da própria geometria da peça e do detalhamento das armaduras. Por esse motivo, preliminarmente, análises elásticas geralmente são empregadas para sugerir uma provável distribuição de tensões que pode definir o modelo de escoras e tirantes. Entretanto, considerando o Estado Limite Último (ELU), a distribuição de tensões pode ser afetada por efeitos não-lineares decorrentes das relações constitutivas dos materiais (concreto e aço), do processo de danificação que a peça venha a sofrer e da distribuição de armaduras. O presente trabalho tem como objetivo apresentar análises computacionais não-lineares em diversas peças de concreto armado, considerando a distribuição de armaduras, a fim de avaliar o seu real comportamento no ELU, e comparar com os resultados estimados pelos métodos usuais de dimensionamento, notadamente o Método das Bielas. Para tanto, são desenvolvidos modelos computacionais de concreto armado através do software de elementos finitos ABAQUS, considerando a Mecânica do Dano Plástico. Os modelos aqui elaborados reproduzem detalhadamente as armaduras utilizadas, inclusive, as construtivas, procurando avaliar a influência da distribuição de armaduras no campo de tensões da peça e na sua capacidade resistente. Diversas situações são examinadas e os resultados são comparados com os processos convencionais de cálculo ou com o Método das Bielas. Os exemplos desenvolvidos confirmam que a distribuição de tensões e a capacidade resistente são afetadas pela distribuição de armaduras adotada. Dessa forma, pretendese avaliar como ocorre a evolução das tensões no interior dos elementos e como as armaduras influenciam em sua topologia e resistência final. Palavras-chave: 1. Escora e Tirantes 2. Método dos Elementos Finitos 3. Método das Bielas 4. Concreto Armado 5. Análise Não-LinearAbstract: The design phase of reinforced concrete structures aims to define the amount and distribution of steel rebars (reinforcement) required in the elements to support the project loads. In regions where the stress field is complex ("D Regions"), the Strut and Tie Method is used to design the concrete elements. One of the difficulties in the application of the method is the determination of stress field that the element will possess, since it depends on the element geometry and the amount of reinforcement used. For this reason, on an initial step, elastic analyzes can be used to suggest a probable field of stresses to be used in the definition of the Strut and Tie Model. However, in the ultimate strength, the stress distribution can be affected by non-linear effects like non regular constitutive relations of the materials (concrete and steel), by damage processes that the part will suffer and by the distribution of reinforcements. The objective of this work is to present nonlinear computational analysis of several elements of reinforced concrete, considering the distribution of reinforcement, in order to evaluate its real behavior in the ultimate state, and to compare with the results predicted by the usual methods of design, mainly the Strut and Tie method. In order to reach this objective, the models of reinforced concrete are developed through the software of finite elements ABAQUS, considering Concrete Damage Plasticity. The models constructed on this paper consider the reinforcement distribution, including the constructive ones, trying to evaluate its influence in the field of tensions and its resistant capacity. Several situations are examined, and the results are compared with the conventional design methods or with the Strut and Tie Model. The developed examples confirm that the stress field and the resistance capacity are affected by the reinforcement distribution. In this way, the present work intends to discuss how the Strut and Tie models are affected by non-linear behavior and by the designed enforcements. Keywords: 1. Strut and Tie 2. Finite Element Method 3. Truss Models 4. Reinforced Concrete 5. Non-Linear Analysi

1995 BRAC Commission

Naval Research Lab: Data Call 12. Tabular data, memos, documents. Box 178, L-110

Non-linear idealisation error analysis of a metallic stiffened panel loaded in compression

The SAFESA procedure is an idealisation error control process developed for linear static finite element (FE) analysis. This paper investigates the application of this process to non-linear FE in order to provide an equivalent methodology valid for non-linear problems. The post-bucked collapse of a stiffened panel in compression is used as the case study for this investigation. The main part of the paper presents the critical analysis of important modelling assumptions, including the material model, the panel to stiffener contact, boundary conditions and geometrical imperfections. Several potential idealisation error sources are identified using the process and then investigated using the non-linear FE code ABAQUS. The outcome of the analysis is an improved FE model and a quantification of the idealisation error, showing that the idealisation error control process can be applied to non-linear analysi