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Ultrafast spectroscopy of 2D hybrid perovskites / Spectroscopie ultrarapide des 2D pérovskites hybridesAbdel Baki, Katia 05 December 2014 (has links)
Les pérovskites hybrides organiques-inorganiques ont attiré l'attention en raison de leurs applications potentielles dans des dispositifs optiques et plus récemment dans les dispositifs photovoltaïques. L'arrangement cristallin des pérovskites forme une structure en multi-puits quantiques dans laquelle les états excitoniques présentent une grande force d'oscillateur et une énergie de liaison importante, ce qui rend la réalisation de microcavités dans le régime de couplage fort possible à la température ambiante. Etant un matériau relativement nouveau, les pérovskites ont encore beaucoup de comportements qui ne sont pas bien compris et beaucoup de travail de recherche est nécessaire. Ce manuscrit est divisé en deux parties. Dans la première partie, la dynamique des excitons sur une pérovskite particulière (C6H5-C2H4-NH3)2PbI4 (PEPI) est étudiée à température ambiante par mesure de type pompe-sonde sous faible et fort régime d'excitation. Sous forte densité d'excitation, un processus de recombinaison Auger des excitons est présent. Une relaxation intrabande ultra-rapide a été observée. La deuxième partie du manuscrit est consacrée à l'étude de la microphotoluminescence à temperature ambiante de microcavités à base de PEPI à haut facteur de qualité. Des nouvelles pérovskites avec des propriétés optimisées (propriétés optiques d'émission, rugosité de surface et photostabilité) ont également été synthétisées. / The reason for choosing this thesis comes from the fact that in the near future,I would like to gain more knowledge and experience in scientific research and especially in the study of non linear effects in optical microcavities where new opportunities are opened and high efficient light sources could be exploited.In last ten years, an increasing number of studies are dedicated on hybrid organic-inorganic materials, due to the possibility of combining the properties both of inorganic(high mobility, electrical pumping, band engineering ) and of organic materials (low cost technology, high luminescence quantum yield at room temperature).In this context , organic-inorganic perovskites having a chemical formula (R-NH3)2MX4 where M is a metal, X halogen and R an organic chains presents a natural hybrid system . When deposited by spin coating, the molecules self-organize to form a multiple quantum wells structure. Because of the strong binding energy, optical features can be seen at room temperature. Moreover, such pervoskite presents great flexibility in their optical properties such that the spectral position of the excitonic transitions can be tailored by substituting different halides X, and the photoluminescence efficiency can be tailored by changing the organic part R. This kind of perovskites has been studied both for fundamental studies and for applications in optoelectronics. In order to increase the coupling between light and matter (exciton), perovskite has been inserted in planar microcavity and strong coupling regime has been achieved at room temperature. The strong coupling of light with exciton give rise to polariton quasi-particles, which have new properties not seen in either photons or excitons. In order to go further and have better study in stimulated scattering of polaritons in these microcavities ,a better understanding of the electronic structure as well as the excitonic interactions in these quantum wells are necessary due to the lack of information on the dynamic and on the carrier interaction of these structures. In order to study the hybrid polaritons, it will be first necessary to improve the knowledge about the relaxation in the perovskite layers. So, ultrafast pump-probe experiments will be performed on hybrid microcavities, and also on perovskite layers.
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Ribonomic and Mechanistic Analysis of the Human Pum1 RNA Binding ProteinMorris, Adam Remy January 2010 (has links)
<p>Much of the regulation of gene expression occurs at the posttranscriptional level, and much of this regulation is controlled and coordinated by RNA binding proteins (RBPs). Many RBPs have multiple mRNA targets, and the proteins encoded by these targets often share functional relationships, forming posttranscriptional RNA operons. These operons often reflect the function of the RBP, thus determination of the genome-wide targets of RBPs allows insight into their functions.</p>
<p>The PUF family of RBPs is characterized by the presence of an extremely well conserved RNA binding domain, typically consisting of 8 repeats of an RNA binding motif, with each repeat binding to one RNA base. PUF proteins are proposed to have an ancestral role in self-renewal of stem cells and have been shown to affect a number of developmental processes. Human and other vertebrate genomes contain two canonical PUF genes, Pum1 and Pum2, and at the outset of this study there was very little known about functions or targets of either protein, especially Pum1.</p>
<p>In order to identify the genome-wide targets of human Pum1 we used RNA immunoprecipitation followed by microarray, or RIP-Chip, analysis. RIP-Chip allowed us to identify Pum1 target mRNAs in human HeLa cells. We found that there were numerous functional relationships among the proteins encoded by these mRNAs, forming putative RNA operons. Some of these potential operons are progression of cell cycle, cell differentiation and proliferation, and regulation of transcription. We were also able to find a consensus Pum1 binding motif, UGUAHAUA, in the 3' UTRs of Pum1 target mRNAs. </p>
<p>The genome-wide targets of PUF proteins from other species have been previously identified, and by comparing the targets of human Pum1 to targets of Drosophila Pumilio and yeast Puf3, both of which bind to the same RNA sequence as Pum1, we determined that there has been evolutionary rewiring of regulation by Puf proteins. While the PUF RNA binding domain and consensus binding sequence have remained almost identical through evolution, the surrounding protein sequence and the mRNAs bound have changed dramatically, indicating that evolutionary rewiring is occurring in a modular fashion. </p>
<p>After identifying Pum1 associated mRNAs, we went on the study the function of Pum1. Through Pum1 knockdown assays we found that Pum1 enhances decay of target mRNAs, and that this effect is likely due to Pum1 enhancing deadenylation of these mRNAs. We also showed by immunofluorescence that Pum1 protein has a cytoplasmic granular subcellular localization and upon oxidative stress relocates to stress granules but not processing bodies. We were, however, unable to detect any difference in Pum1 mRNA targeting after stress. We were also unable to detect any changes in progression through cell cycle after Pum1 knockdown. </p>
<p>In this study we identified the genome-wide mRNAs associated with Pum1, determined functional relationships among these targets related to the proposed ancestral role of PUF proteins in self-renewal of stem cells, and identified a sequence motif to which Pum1 binds in these mRNAs. We also demonstrated that Pum1 enhances decay of associated mRNAs, and that this effect is likely due to Pum1 enhancing deadenylation of associated mRNAs. These results provide a description of mRNA targets and mechanisms of action of Pum1 proteins, which will provide a strong foundation for future experiments to further explore the functions of the Pum1, especially as they relate to human stem cells.</p> / Dissertation
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Study of shoulder flow zone formation in thick section FSW of 6061 Al alloy using scroll shoulder toolYan, David January 2008 (has links)
Friction stir welding (FSW) is a relatively new solid-state welding technology invented at The Welding Institute of UK in 1991. It is versatile and has been widely adopted to join various materials. There has been strong research activity on revealing the details of the material flow pattern in the nugget zone induced by the conventional shoulder tool. However, there is insufficient understanding on the aspects of the scroll shoulder tool design and the shoulder flow zone formation utilizing this type of tool. The major objective of this study was to conduct experiments, analyse results and then reveal the shoulder flow zone forming mechanism for the scroll shoulder tool. The method used was to identify the flow pattern in the shoulder flow zone using a ‘marker insert’ technique, and then to suggest the forming mechanism of the shoulder flow zone based on the obtained flow pattern; although the ‘marker insert’ technique has never been used to study the shoulder flow zone flow pattern induced by the scroll shoulder tool. Experiments were conducted to examine the thick sections 6061 aluminium ‘marker insert’ welds, which were welded using a scroll shoulder tool at a range of welding parameters. These were followed by quantifying the mass of the accumulated work piece material within the scroll groove (pick up material-PUM), evaluating the effect of welding parameters on the shoulder flow zone formation, and documenting the shoulder flow zone flow pattern. The major finding was that there is a simple banded structure which forms in a layer to layer manner in the bottom portion of the shoulder flow zone, but it disappears in the top portion of the shoulder flow zone. Accordingly, the forming mechanism of the shoulder flow zone for the scroll shoulder tool was suggested as follows. Firstly, the tool pin is plunged into the work piece; the work piece material is extruded by the pin and pushed up into the scroll groove forming the PUM. Secondly, after the tool shoulder is plunged into the work piece to a certain depth, the scroll groove is fully filled up with the PUM. Finally, during the forward movement of the tool, the central portion of PUM is driven downward by the root portion of the pin and then detaches from the pin (tip portion) in a layer to layer manner. It has also found that the thickness of the shoulder flow zone varies with a thicker on the advancing side than on the retreating side, and there is a positive linear relationship between the mass of PUM and the weld quality. This study has revealed for the first time the forming mechanism of the shoulder flow zone, and has improved the understanding of the shoulder flow zone formation using a scroll shoulder tool. It is recommended that a ‘shoulder-breaking’ technique is developed to break the rotating shoulder suddenly and hence embed it into the work piece during FSW, in which a real-time shoulder-work piece couple could be produced for a better three-dimensional examination of the shoulder flow zone.
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Study of shoulder flow zone formation in thick section FSW of 6061 Al alloy using scroll shoulder toolYan, David January 2008 (has links)
Friction stir welding (FSW) is a relatively new solid-state welding technology invented at The Welding Institute of UK in 1991. It is versatile and has been widely adopted to join various materials. There has been strong research activity on revealing the details of the material flow pattern in the nugget zone induced by the conventional shoulder tool. However, there is insufficient understanding on the aspects of the scroll shoulder tool design and the shoulder flow zone formation utilizing this type of tool. The major objective of this study was to conduct experiments, analyse results and then reveal the shoulder flow zone forming mechanism for the scroll shoulder tool. The method used was to identify the flow pattern in the shoulder flow zone using a ‘marker insert’ technique, and then to suggest the forming mechanism of the shoulder flow zone based on the obtained flow pattern; although the ‘marker insert’ technique has never been used to study the shoulder flow zone flow pattern induced by the scroll shoulder tool. Experiments were conducted to examine the thick sections 6061 aluminium ‘marker insert’ welds, which were welded using a scroll shoulder tool at a range of welding parameters. These were followed by quantifying the mass of the accumulated work piece material within the scroll groove (pick up material-PUM), evaluating the effect of welding parameters on the shoulder flow zone formation, and documenting the shoulder flow zone flow pattern. The major finding was that there is a simple banded structure which forms in a layer to layer manner in the bottom portion of the shoulder flow zone, but it disappears in the top portion of the shoulder flow zone. Accordingly, the forming mechanism of the shoulder flow zone for the scroll shoulder tool was suggested as follows. Firstly, the tool pin is plunged into the work piece; the work piece material is extruded by the pin and pushed up into the scroll groove forming the PUM. Secondly, after the tool shoulder is plunged into the work piece to a certain depth, the scroll groove is fully filled up with the PUM. Finally, during the forward movement of the tool, the central portion of PUM is driven downward by the root portion of the pin and then detaches from the pin (tip portion) in a layer to layer manner. It has also found that the thickness of the shoulder flow zone varies with a thicker on the advancing side than on the retreating side, and there is a positive linear relationship between the mass of PUM and the weld quality. This study has revealed for the first time the forming mechanism of the shoulder flow zone, and has improved the understanding of the shoulder flow zone formation using a scroll shoulder tool. It is recommended that a ‘shoulder-breaking’ technique is developed to break the rotating shoulder suddenly and hence embed it into the work piece during FSW, in which a real-time shoulder-work piece couple could be produced for a better three-dimensional examination of the shoulder flow zone.
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Estudo experimental de uma bomba de solução rica em refrigerador por absorção operando pela diferença de pressão do refrigerador / Experimental study of one pump of rich solution in refrigerator for absorption operation for the difference of pressure of the refrigeratorQuinteros Panesi, Andre Ricardo 28 February 2005 (has links)
Orientador: Jose Ricardo Figueiredo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-04T09:31:53Z (GMT). No. of bitstreams: 1
QuinterosPanesi_AndreRicardo_M.pdf: 5200860 bytes, checksum: 50a776e6a73c01814b4bfb64919bb6d7 (MD5)
Previous issue date: 2005 / Resumo: Foi projetada e construída uma bomba de diafragma para um sistema de refrigeração por absorção de água-amônia que opera empregando vapor expandido entre os mesmos níveis de pressão de bombeamento. Através de uma bancada experimental, verificaram-se as condições de funcionamento da bomba que simula um sistema de absorção nas fases de sucção e recalque da solução água-amônia do absorvedor para o gerador através de um nível de baixa pressão para um nível de alta pressão. No teste utilizou-se um recipiente contendo água sujeito a baixa pressão no reservatório representando o absorvedor, um cilindro hermético a alta pressão com entradas e saídas necessárias para a tomada de ar e água representando o gerador, um compressor de ar para pressurização do sistema e dispositivos de controle e comando para a automação do sistema. Foi demonstrada a viabilidade de operação do equipamento como também as limitações encontradas do protótipo / Abstract: Was projected and constructed one diaphragm pump for one system of refrigeration for water-ammonia absorption that operates using expanded vapor it enters the same levels of pump action pressure. Through an experimental group of benches, the conditions of functioning of the pump had been verified that simulates a system of absorption in the suction phases and stresses of the solution water-ammonia of the absorber for the generator through an leveI of low pressure for an high-pressure leveI. In the test one container was used contains water subject to lowers pressure in the reservoir representing the absorber, an air-tight cylinder the high pressure with entrances and necessary exits for the water and air scoop representing the generator, an air compressor for pressurization of the system and devices of control and command for the a automation of the system. The viability of operation of the equipment was demonstrated as also the joined limitations of the archetype / Mestrado / Termica e Fluidos / Mestre em Engenharia Mecânica
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VERA - Virtual Emergency RoomAdministrator : En prototyp av framtidens digitala akutjournal / VERA - Virtual Emergency Room Administrator : A future digital emergency journal prototypeAtoui, Josef, Bäckman, Viktor, Lindgren, Felix, Runestam, Johan, Homssi, Rachel, Johansson, Tommy, Jonsson, Jesper, Wijk Stranius, Simon January 2020 (has links)
Denna rapport är en beskrivning av ett kandidatarbete utfört som del av kursen TDDD96 - Kandidatprojekt i programvaruutveckling vid Linköpings universitet. Teamet som utförde arbetet bestod av åtta ingenjörsstudenter som studerar på data- respektive mjukvaruteknikprogrammet. Syftet med projektet var att ta fram en prototyp till en digitaliserad akutjournal åt Region Östergötland för deras arbete på akutmottagningarna i Linköping, Norrköping och Motala. Denna digitala akutjournal ämnar i ett senare skede ersätta den nuvarande pappersbaserade lösningen. I utvecklingsprocessen användes en modifierad version av det agila ramverket Scrum. Resultatet blev en webbapplikation för fullstorleksskärmar med vyer såsom en enhetsöversikt och en patientvy, och med möjlighet att definiera patienter i systemet och ta emot notifikationer. Förutom att redovisa och diskutera det gemensamma arbetet finns också individuella delrapporter som behandlar relaterade ämnen.
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Transcriptome-wide Identification of mRNA Targets of NanosMarhabaie, Mohammad January 2020 (has links)
No description available.
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Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmicaMazzochi, Rudimar January 2014 (has links)
Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmicaMazzochi, Rudimar January 2014 (has links)
Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmicaMazzochi, Rudimar January 2014 (has links)
Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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