Une étude paléomagnétique et structurale au nord du Chili met en évidence que le remplissage sédimentaire du bassin d'Atacama s'est accumulé dans un contexte compressif depuis le Crétacé Supérieur. Les données paléomagnétiques montrent des rotations horaires et suggèrent qu'une zone de cisaillement transpressif dextre NE-NNE a contrôlé les rotations pendant le Paléogène. Une étude de restauration en carte de la déformation des Andes Centrales indique que la formation de l'orocline est principalement associée à la déformation de la Cordillère Orientale. La variabilité spatiale et la grande quantité des rotations dans la marge chilienne suggèrent deux épisodes de rotation, un épisode de rotation dans l'avant arc au cours du Paléogène et une rotation globale de toute la marge pendant la déformation de la Cordillère Orientale. En conclusion les résultats de cette étude démontrent que la déformation compressive et les rotations tectoniques sont des éléments clef de la déformation Andine.

In spite of all electronic navigation devices on a modern ship bridge, navigators still lose their orientation. Reasons for this might be excessive cognitive workload caused by too many instruments to read and compile, navigation information that is displayed in a cognitively demanding way, short decision times due to high speed or fatigue due to minimum manning and long work hours. This work addresses the problem of map information displayed in a less than optimal way. Three new concepts are presented: the bridge perspective, the NoGO area polygons and a dual lane seaway network. Map reading can be difficult due to the problem of mental rotations. By allowing a 3-D nautical chart to be viewed from an egocentric bridge perspective, the need for mental rotations can be removed. The cognitively demanding calculations necessary to find out if there is enough water under the keel can be made by the chart system and the result displayed as of free water and NoGo areas. On land car driving is facilitated by a road-network and a sign system. This notion can be further developed on sea and make navigation easier and safer. These concepts were then tested in a laboratory experiment, in interviews and in a prototyping project. The results were very promising. The experiment in a laboratory maze showed that map reading from an egocentric perspective was more efficient than using traditional paper and electronic maps. Interviews and expert evaluation of prototypes also showed great interest from practitioners in the field. / Trots all elektronisk utrustning på en modern skeppsbrygga händer det att navigatörerna förlorar orienteringen. Anledningen kan vara hög kognitiv belastning därför att för många olika instrument måste avläsas och integreras samtidigt, att informationen på instrumenten behöver tolkas på ett kognitivt krävande sätt, att tiden för att fatta beslut blir allt kortare på grund av högre hastigheter till sjöss eller på grund av trötthet. I detta arbete presenteras tre nya koncept för visualisering av navigationsinformation: bryggperspektivet, djupvarningspolygoner och sjövägar. Kartläsning kan ibland vara svårt på grund av de mentala rotationer en användare tvingas genomföra för att kunna jämföra kartan med verkligheten. Genom att göra det möjligt för en användare att se sjökortet ur ett egocentriskt bryggperspektiv, så onödiggörs dessa mentala rotationer. De kognitivt krävande beräkningar som navigatören behöver göra för att försäkra sig om att det finns tillräckligt med vatten under kölen, kan utföras av kartsystemet och resultatet visas istället som fria vattenytor och djupvarningsområden (NoGo areas). På land underlättas bilkörning av ett vägnät med körbanor, filer och skyltar. Detta system kan i högre utsträckning införas till sjöss för att underlätta säker navigering. Dessa koncept har sedan testats genom ett laboratorieexperiment, genom intervjuer och i ett prototyputvecklingsprojekt. Resultaten var mycket lovande. Experimentet i en laboratorielabyrint visade klart att 3D-sjökortet var effektivare än både papperskartan och traditionell elektroniska kartor och intervjuerna och expertutvärderingarna visad på stort intresse från yrkesutövare i branschen.

A study was conducted to determine (1) the N contribution of lentil (<i>Lens culinaris</i> Medikus) and its effect on subsequent wheat (<i>Triticum aestivum</i> L.) crops in the Dark Brown and Brown soil zones of Saskatchewan, (2) if synchronization of available N contributes to the rotation benefit, and (3) N fertilizer replacement value of the N effect of lentil on the subsequent wheat crop. Two approaches were used: a landscape-scale study established at Dinsmore in 1994, and a repeated small-plot study established at several locations (Dinsmore, 1993 and 1994; Clavet, Conquest, Eston and Zealandia, 1995). In the landscape-scale study, N2 fixation by lentil ranged from 28 to 46 kg ha-1, with an average of 34 kg ha -1 N and an N balance of -36 kg ha-1. In the small-plot study, N2 fixation ranged from 10 to 112 kg ha -1 with an average of 59 kg ha-1 N and an N balance of -22 kg ha-1. In the landscape-scale study, preseeding available N on the rotation that incorporated lentil was 29 and 61% higher than in the monocropped wheat in the first and second subsequent crops, respectively. The corresponding values for the small-plot study were 59 and 14%, respectively. N availability was well synchronized with the period of maximum N demand by the wheat crop in both rotations. However, both lentil-residue N and wheat-residue N were poorly synchronized with the period of maximum N demand by the wheat. The rotation effect was exhibited in higher grain yield (23% higher in the landscape-scale study, and 21% higher in the small-plot study). Approximately 10 and 70% of the rotation benefit in the landscape-scale and small plot studies, respectively, were attributed to the N effect. Nitrogen fertilizer replacement value ranged from 47 to 89 kg ha-1 N. Therefore, lentil can fix enough N and indirectly contribute to greater available N in subsequent crops than in crops following non-legumes. However, the actual amount of N derived from lentil residue is small. The greater available N is attributed to spared N and enhanced soil N mineralization. Hence, under the conditions of this study, enhancement of available N contributed more to the rotation benefit than synchronization. The high NFRV show that inclusion of lentil in the rotation can enhance available N in the cropping system and potentially reduce fertilizer N application.

The purpose of this thesis is to develop corotational beam elements for the nonlinear dynamic analyse of flexible beam structures. Whereas corotational beam elements in statics are well documented, the derivation of a corotational dynamic formulation is still an issue. In the first journal paper, an efficient dynamic corotational beam formulation is proposed for 2D analysis. The idea is to adopt the same corotational kinematic description in static and dynamic parts. The main novelty is to use cubic interpolations to derive both inertia terms and internal terms in order to capture correctly all inertia effects. This new formulation is compared with two classic formulations using constant Timoshenko and constant lumped mass matrices. In the second journal paper, several choices of parametrization and several time stepping methods are compared. To do so, four dynamic formulations are investigated. The corotational method is used to develop expressions of the internal terms, while the dynamic terms are formulated into a total Lagrangian context. Theoretical derivations as well as practical implementations are given in detail. Their numerical accuracy and computational efficiency are then compared. Moreover, four predictors and various possibilities to simplify the tangent inertia matrix are tested. In the third journal paper, a new consistent beam formulation is developed for 3D analysis. The novelty of the formulation lies in the use of the corotational framework to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. Cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. Four numerical examples are considered to assess the performance of the new formulation against two other ones based on linear interpolations. Finally, in the fourth journal paper, the previous 3D corotational beam element is extended for the nonlinear dynamics of structures with thin-walled cross-section by introducing the warping deformations and the eccentricity of the shear center. This leads to additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. The performance of the formulation is assessed through five examples and comparisons with Abaqus 3D-solid analyses. / <p>QC 20131017</p>

The object of the thesis research is to realize a complex-valued QR decomposition (QRD) algorithm on FPGAs for MIMO communication systems. The challenge is to implement a QRD processor that efficiently utilizes hardware resources to meet throughput requirements in MIMO systems. By studying the basic QRD algorithm using Givens rotations and the CORDIC algorithm, the thesis develops a master-slave structure to more efficiently implement CORDIC-based Givens rotations compared to traditional methods. Based on the master-slave structure, an processing-element array architecture is proposed to further improve result precision and to achieve near-theoretical latency with parallelized normalization and rotations. The proposed architecture also demonstrates flexible scalability through implementations for different sizes of QRDs. The QRD implementations can process 7.41, 1.90 and 0.209 million matrices per second for two by two, four by four and eight by eight QRDs respectively. This study has built the foundation to develop QRD processors that can fulfill high throughput requirements for MIMO systems.

O objetivo deste estudo foi avaliar e comparar o equilíbrio de força muscular e o tempo de retardo eletromecânico na articulação do ombro entre atletas de diferentes modalidades esportivas, os quais utilizam predominantemente rotações internas e externas de ombro durante as suas práticas esportivas. Fizeram parte do estudo 41 sujeitos do sexo masculino, sendo 15 atletas profissionais de Voleibol (24,07 ± 5,13 anos; 91,60 ± 11,67 kg; 198,47 ± 5,90 cm), 14 atletas profissionais de Judô (26,64 ± 7,30 anos; 87,36 ± 15,20 kg; 178,07 ± 6,90 cm) e 12 atletas universitários de Handebol (23,17 ± 4,70 anos; 84,75 ± 13,50 kg; 182,08 ± 6,20 cm). Para a mensuração de força máxima, de diferença contralateral (i.e. lados direito vs. esquerdo) e para o cálculo das razões entre rotação interna e externa de ombro, os participantes realizaram testes de dinamometria isocinética em condições isométricas e isocinéticas. Durante os testes isométricos foi realizada a coleta do sinal eletromiográfico dos músculos peitoral maior e infraespinal, o que possibilitou o cálculo do retardo eletromecânico. Os resultados demonstram que atletas de Judô possuem força isométrica de rotação interna de ombro significativamente (p<0,01) maior quando comparados com atletas de Voleibol e de Handebol. Atletas de Judô apresentam valores de razão agonista/antagonista isométrica de membro direito significativamente (p<0,03) inferiores aos grupos Voleibol e Handebol, bem como significativamente (p<0,01) inferiores ao grupo Voleibol em relação ao membro esquerdo O tempo de retardo eletromecânico apresentou diferenças entre os grupos somente na rotação externa, em que o grupo Voleibol apresentou valores do membro direito significativamente (p<0,01) mais curtos quando comparados com o grupo Handebol e valores de membro esquerdo significativamente (p<0,01) mais curtos quando comparados com os grupos Handebol e Judô. Picos de torque isocinéticos apresentaram diferença somente para rotação interna de membro direito, em que o grupo Judô apresentou valores significativamente (p<0,001) maiores quando comparados com o grupo Voleibol. Já para membro esquerdo, detectou-se diferença significativa (p<0,01) no ângulo de pico de torque de rotação interna de membro esquerdo entre o grupo Judô e Handebol. Os resultados do estudo permitem concluir que a prática de cada modalidade esportiva avaliada neste estudo promoveu adaptação dos músculos do ombro, de acordo com a demanda da modalidade esportiva. Assim, atletas de Judô necessitam realizar reforço dos músculos rotadores externos do ombro, tanto concêntrica quanto excentricamente, visto o desequilíbrio muscular causado pela especificidade da modalidade. Por outro lado, atletas de Voleibol apresentam satisfatório equilíbrio muscular na articulação do ombro por conta de altos níveis de força excêntrica de rotação externa exigidos na prática deste esporte; além disso, os curtos períodos de tempo de retardo eletromecânico apresentados por estes atletas reforçam a constatação de equilíbrio desta articulação. Atletas de Handebol apresentam satisfatório equilíbrio muscular na articulação do ombro, entretanto apresentam valores altos de retardo eletromecânico, sendo indicado que estes atletas realizem reforço de rotação externa de ombro, sobretudo em velocidade elevada, com o objetivo de diminuir o tempo necessário para ativar estes grupos musculares. / The purpose of this study was to evaluate and compare the muscular balance and the electromechanical delay time of the shoulder joint between athletes of different sports modalities who use predominantly internal and external rotations of the shoulder. The study consisted of a total of 41 male subjects, of whom 15 were professional Volleyball players (n = 15, 24.07 ± 5.13 years, 91.60 ± 11.67 kg, 198.47 ± 5.90 cm), 14 professional Judo athletes (26.64 ± 7.30 years, 87.36 ± 15.20 kg, 178.07 ± 6.90 cm) and 12 university Handball athletes (23.17 ± 4.70 years, 84.75 ± 13.50 kg, 182.08 ± 6.20 cm). To evaluate peak torque, upper limb side-to-side asymmetry and for the calculation of conventional and functional ratios, all subjects performed isokinetic dynamometry tests under isometric and dynamic conditions. During the isomeric tests, the electromyographic signal was collected from the pectoralis major and infraspinal muscles, which allowed the calculation of the electromechanical delay. The results demonstrate that Judo athletes have internal shoulder rotation isometric strength significantly (p<0.01) higher when compared to Volleyball and Handball athletes. Judo athletes presented isometric agonist/antagonist ratio of right limb significantly (p<0.03) lower than the Volleyball and Handball groups, as well as significantly (p<0.01) lower than the Volleyball group in relation to the left limb. The electromechanical delay time presented differences between the groups only in the external shoulder rotation, which the Volleyball group presented significantly lower values of right limb (p<0.01) when compared to the Handball group and left limb times significantly (p<0.01) shorter when compared with the Handball and Judo groups Dynamic peak torque presented difference only for internal shoulder rotation of the right limb, which the Judo group presented values significantly (p<0.001) higher when compared to the Volleyball group. For the left upper limb, a significant difference (p<0.01) was detected in the peak torque angle of internal shoulder rotation between the Judo and Handball groups. The results of the study allow to considering that the practice of each evaluated sports modalities adapts the shoulder of its athletes in different ways. Judo athletes need to perform external shoulder rotation muscular strengthening, both in concentric and eccentric modes due to muscle imbalance caused by the specificity of the modality. Volleyball athletes have reasonable muscle balance in the shoulder joint due to the high levels of eccentric strength of external rotation, in addition the short time periods of electromechanical delay presented by these athletes reinforce even more the balance of this joint. Handball athletes have reasonable muscle balance in the shoulder joint; however, they presented high values of electromechanical delay, so it is indicated that these athletes need to perform muscular strengthening of external rotation of the shoulder in order to reduce the time required to activate these muscles.

Resumo: O objetivo da pesquisa descrita nesta tese foi estudar possíveis aplicações do método das rotações modificadas de Givens na solução de sistemas de equações lineares tipicamente observados em problemas de melhoramento animal. Duas aplicações foram consideradas: a predição de valores genéticos com base em informação fenotípica e genealógica, por meio da metodologia dos modelos mistos; e a predição de valores genéticos com base em informação molecular, obtida pela genotipagem de painéis densos de SNPs. Na primeira aplicação, delineou-se o emprego de um modelo animal reduzido, combinado a uma ordenação do sistema que permitiu uma abordagem multi-frontal de decomposição. As matrizes frontais foram definidas como sendo as partes da triangular superior pertinentes a cada rebanho. Com isso, o problema pôde ser desmembrado em n subproblemas em que n é o número de rebanhos. Um conjunto de programas foi desenvolvido de modo a decompor as matrizes de dados de cada rebanho independentemente, e depois combinar as informações de todos eles na solução do sistema triangular geral, por retro-substituição. Concluiu-se que o método pode ser empregado em um sistema para atualização de predições de valor genético sob modelo animal reduzido, em que se aninham os efeitos de vacas dentro de rebanhos. Na segunda aplicação, comparou-se o emprego das rotações de Givens com o método do Gradiente Conjugado, na solução de sistemas lineares envolvidos na estimação de efeitos de SNPs em valores genéticos. O método das rotações demandou menos tempo de processamento e mais memória. Concluiu-se que, dado o crescente avanço em capacidade computacional, o método das rotações pode ser um método numérico viável e apresenta a vantagem de permitir o cálculo dos erros-padrão das estimativas. / Abstract: The aim of this study was to investigate possible applications of the modified Givens rotations on the solution of linear systems that typically arise in animal breeding problems. Two applications were considered: prediction of breeding values based on phenotypes and relationships, using mixed model methods; and prediction of breeding values based on molecular information, using genotypes from high density SNP chips. In the first application, the use of a reduced animal model, combined with a specific ordering of the system, made it possible to apply a multi-frontal decomposition approach. The frontal matrices were defined as the parts of the upper triangular corresponding to each herd. In this way, the problem could be partitioned into n subproblems, where n is the number of herds. A set of programs was developed in order to factorize the data matrix of each herd independently, and then combine the information from all of them while solving the overall triangular system, by back-substitution. The conclusion was that Givens rotations can be used as a numerical method for updating predicted breeding values under a reduced animal model, if dam effects are nested within herds. In the second application, the modified Givens rotations were compared to the Conjugate Gradient method for solving linear systems that arise in the estimation of SNP effects on breeding values. Givens rotations required less processing time but a greater amount of high speed memory. The conclusion was that, given the increasing rate of advance in computer power, Givens rotations can be regarded as a feasible numerical method which presents the advantage that it allows for the calculation of standard errors of estimates. / Orientador: Sandra Aidar de Queiroz / Coorientador: Luiz Alberto Fries / Coorientador: Flávio Schramm Schenkel / Banca: João Meidanis / Banca: Ricardo da Fonseca / Banca: Roberto Carvalheiro / Banca: Adhemar Sanches / Doutor

O objetivo deste estudo foi avaliar e comparar o equilíbrio de força muscular e o tempo de retardo eletromecânico na articulação do ombro entre atletas de diferentes modalidades esportivas, os quais utilizam predominantemente rotações internas e externas de ombro durante as suas práticas esportivas. Fizeram parte do estudo 41 sujeitos do sexo masculino, sendo 15 atletas profissionais de Voleibol (24,07 ± 5,13 anos; 91,60 ± 11,67 kg; 198,47 ± 5,90 cm), 14 atletas profissionais de Judô (26,64 ± 7,30 anos; 87,36 ± 15,20 kg; 178,07 ± 6,90 cm) e 12 atletas universitários de Handebol (23,17 ± 4,70 anos; 84,75 ± 13,50 kg; 182,08 ± 6,20 cm). Para a mensuração de força máxima, de diferença contralateral (i.e. lados direito vs. esquerdo) e para o cálculo das razões entre rotação interna e externa de ombro, os participantes realizaram testes de dinamometria isocinética em condições isométricas e isocinéticas. Durante os testes isométricos foi realizada a coleta do sinal eletromiográfico dos músculos peitoral maior e infraespinal, o que possibilitou o cálculo do retardo eletromecânico. Os resultados demonstram que atletas de Judô possuem força isométrica de rotação interna de ombro significativamente (p<0,01) maior quando comparados com atletas de Voleibol e de Handebol. Atletas de Judô apresentam valores de razão agonista/antagonista isométrica de membro direito significativamente (p<0,03) inferiores aos grupos Voleibol e Handebol, bem como significativamente (p<0,01) inferiores ao grupo Voleibol em relação ao membro esquerdo O tempo de retardo eletromecânico apresentou diferenças entre os grupos somente na rotação externa, em que o grupo Voleibol apresentou valores do membro direito significativamente (p<0,01) mais curtos quando comparados com o grupo Handebol e valores de membro esquerdo significativamente (p<0,01) mais curtos quando comparados com os grupos Handebol e Judô. Picos de torque isocinéticos apresentaram diferença somente para rotação interna de membro direito, em que o grupo Judô apresentou valores significativamente (p<0,001) maiores quando comparados com o grupo Voleibol. Já para membro esquerdo, detectou-se diferença significativa (p<0,01) no ângulo de pico de torque de rotação interna de membro esquerdo entre o grupo Judô e Handebol. Os resultados do estudo permitem concluir que a prática de cada modalidade esportiva avaliada neste estudo promoveu adaptação dos músculos do ombro, de acordo com a demanda da modalidade esportiva. Assim, atletas de Judô necessitam realizar reforço dos músculos rotadores externos do ombro, tanto concêntrica quanto excentricamente, visto o desequilíbrio muscular causado pela especificidade da modalidade. Por outro lado, atletas de Voleibol apresentam satisfatório equilíbrio muscular na articulação do ombro por conta de altos níveis de força excêntrica de rotação externa exigidos na prática deste esporte; além disso, os curtos períodos de tempo de retardo eletromecânico apresentados por estes atletas reforçam a constatação de equilíbrio desta articulação. Atletas de Handebol apresentam satisfatório equilíbrio muscular na articulação do ombro, entretanto apresentam valores altos de retardo eletromecânico, sendo indicado que estes atletas realizem reforço de rotação externa de ombro, sobretudo em velocidade elevada, com o objetivo de diminuir o tempo necessário para ativar estes grupos musculares. / The purpose of this study was to evaluate and compare the muscular balance and the electromechanical delay time of the shoulder joint between athletes of different sports modalities who use predominantly internal and external rotations of the shoulder. The study consisted of a total of 41 male subjects, of whom 15 were professional Volleyball players (n = 15, 24.07 ± 5.13 years, 91.60 ± 11.67 kg, 198.47 ± 5.90 cm), 14 professional Judo athletes (26.64 ± 7.30 years, 87.36 ± 15.20 kg, 178.07 ± 6.90 cm) and 12 university Handball athletes (23.17 ± 4.70 years, 84.75 ± 13.50 kg, 182.08 ± 6.20 cm). To evaluate peak torque, upper limb side-to-side asymmetry and for the calculation of conventional and functional ratios, all subjects performed isokinetic dynamometry tests under isometric and dynamic conditions. During the isomeric tests, the electromyographic signal was collected from the pectoralis major and infraspinal muscles, which allowed the calculation of the electromechanical delay. The results demonstrate that Judo athletes have internal shoulder rotation isometric strength significantly (p<0.01) higher when compared to Volleyball and Handball athletes. Judo athletes presented isometric agonist/antagonist ratio of right limb significantly (p<0.03) lower than the Volleyball and Handball groups, as well as significantly (p<0.01) lower than the Volleyball group in relation to the left limb. The electromechanical delay time presented differences between the groups only in the external shoulder rotation, which the Volleyball group presented significantly lower values of right limb (p<0.01) when compared to the Handball group and left limb times significantly (p<0.01) shorter when compared with the Handball and Judo groups Dynamic peak torque presented difference only for internal shoulder rotation of the right limb, which the Judo group presented values significantly (p<0.001) higher when compared to the Volleyball group. For the left upper limb, a significant difference (p<0.01) was detected in the peak torque angle of internal shoulder rotation between the Judo and Handball groups. The results of the study allow to considering that the practice of each evaluated sports modalities adapts the shoulder of its athletes in different ways. Judo athletes need to perform external shoulder rotation muscular strengthening, both in concentric and eccentric modes due to muscle imbalance caused by the specificity of the modality. Volleyball athletes have reasonable muscle balance in the shoulder joint due to the high levels of eccentric strength of external rotation, in addition the short time periods of electromechanical delay presented by these athletes reinforce even more the balance of this joint. Handball athletes have reasonable muscle balance in the shoulder joint; however, they presented high values of electromechanical delay, so it is indicated that these athletes need to perform muscular strengthening of external rotation of the shoulder in order to reduce the time required to activate these muscles.

Este trabalho apresenta uma formulação do Método dos Elementos Discretos (MED) utilizando uma abordagem vetorial para o tratamento das rotações. As rotações são calculadas com a parametrização de Rodrigues. As principais contribuições do trabalho são: o cálculo dos deslocamentos tangentes utilizando o vetor das rotações incrementais da parametrização de Rodrigues; e, a integração do movimento de rotação utilizando o método leapfrog com as expressões da parametrização das rotações de Rodrigues. A formulação é apresentada para partículas esféricas e superelipsóides. O cálculo do deslocamento tangente, que é utilizado para o cálculo das forças de atrito, é feito a partir da velocidade angular da partícula. Em geral, o deslocamento tangente é calculado a partir da velocidade linear instantânea do ponto de contato. Aqui, o deslocamento do ponto de contato é dado pelo movimento da partícula, tanto de translação quanto de rotação. Apesar da abordagem por meio de rotações, é mostrado este cálculo pode ser feito sem o uso de tensores de segunda ordem. O movimento da partícula é descrito por uma abordagem incremental. É apresentada uma formulação do método de integração leapfrog com a utilização da expressão das rotações sucessivas da parametrização de Rodrigues. A detecção do contato entre superelipsóides é feita por um método do tipo \"vetor normal comum\", resolvido como um problema de minimização. Os resultados mostram que a parametrização de Rodrigues pode ser utilizada com método dos elementos discretos tanto para a execução da rotação quanto para o cálculo de grandezas que envolvem este tipo de movimento como o deslocamento tangente. / This work presents a formulation for Discrete Element Method (DEM) adopting a vector ap-proach to solve rotations. Herein, rotations are solved using Rodrigues parameterization. The main contributions of this work are: tangential displacements using the incremental rotation vector from Rodrigues parameterization, and integration of the rotation movement using leap-frog method and Rodrigues rotation tensor. The formulations are presented to spheres and superelliptical particles. Tangential displacements, which are used to get friction forces, are calculated through angular velocity. In most of DEM implementations, tangential displacements are calculated through the instantaneous linear velocity of the contact point. Instead, here the displacement of the contact point is given through the rotation of the particle. It is showed that the vector of in-cremental rotations can be calculated through the angular velocity. Particle movement is described using an updated Lagrangian approach. Leapfrog method is formulated in such a way to use the Rodrigues expression for successive rotations. Contact detection between superellipsoids is solved using a technic called \"common normal approach\", and it is solved as a minimization problem. The results show that the Rodrigues parameterization can be applied to discrete element method to both execute rotations and to evaluate physical quantities that are related to this kind of movement as tangential displacement.

Flexible beam structures are popular in civil and mechanical engineering. Many of these structures undergo large displacements and finite rotations, but with small deformations. Their dynamic behaviors are usually investigated using finite beam elements. A well known method to derive such beam elements is the corotational approach. This method has been extensively used in nonlinear static analysis. However, its application in nonlinear dynamics is rather limited. The purpose of this thesis is to investigate the nonlinear dynamic behavior of flexible beam structures using the corotational method. For the 2D case, a new dynamic corotational beam formulation is presented. The idea is to adopt the same corotational kinetic description in static and dynamic parts. The main novelty is to use cubic interpolations to derive both inertia terms and internal terms in order to capture correctly all inertia effects. This new formulation is compared with two classic formulations using constant Timoshenko and constant lumped mass matrices. This work is presented in the first appended journal paper. For the 3D case, update procedures of finite rotations, which are central issues in development of nonlinear beam elements in dynamic analysis, are discussed. Three classic and one new formulations of beam elements based on the three different parameterizations of the finite rotations are presented. In these formulations, the corotational method is used to develop expressions of the internal forces and the tangent stiffness matrices, while the dynamic terms are formulated into a total Lagrangian context. Many aspects of the four formulations are investigated. First, theoretical derivations as well as practical implementations are given in details. The similarities and differences between the formulations are pointed out. Second, numerical accuracy and computational efficiency of these four formulations are compared. Regarding efficiency, the choice of the predictor at each time step and the possibility to simplify the tangent inertia matrix are carefully investigated. This work is presented in the second appended journal paper. To make this thesis self-contained, two chapters concerning the parametrization of the finite rotations and the derivation of the 3D corotational beam element in statics are added. / QC 20120521