This study deals with the use of high-order spectral/hp approximation functions in the finite element models of various nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order p greater than or equal to 4) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., p < 3) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements for beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. The higher-order spectral/hp basis functions avoid the interpolation error in the numerical schemes, thereby making them accurate and stable. Furthermore, for fluid flows, when combined with least-squares variational principles, such technology allows us to develop efficient finite element models, that always yield a symmetric positive-definite (SPD) coefficient matrix, and thereby robust direct or iterative solvers can be used. The least-squares formulation avoids ad-hoc stabilization methods employed with traditional low-order weak-form Galerkin formulations. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities (e.g., dilatation, volume, and mass) and stable evolution of variables with time in the case of unsteady flows. The present study uses spectral/hp approximations in the (1) weak-form Galerkin finite element models of viscoelastic beams, (2) weak-form Galerkin displacement finite element models of shear-deformable elastic shell structures under thermal and mechanical loads, and (3) least-squares formulations for the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical simulations using the developed technology of several non-trivial benchmark problems are presented to illustrate the robustness of the higher-order spectral/hp based finite element technology.

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-12-11Bitstream added on 2014-06-13T20:50:43Z : No. of bitstreams: 1 morais_vs_me_ilha.pdf: 9848157 bytes, checksum: 187eadcaad3e9775d2aa107935283406 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Este trabalho dá continuidade e aperfeiçoa um modelo automatizado para estimativa de altura de ondas geradas em lagos de barragens, a partir dos dados característicos de vento. Infere sobre a climatologia dos ventos, a fim de determinar as maiores alturas de ondas e identificar pontos críticos, tanto para a segurança à navegação, quanto para as margens do reservatório. Lagos de barragens, foco desta dissertação são, em sua maioria, dotados de vegetação aquática. Dentro dessa temática, uma busca por modelos capazes de qualificar e quantificar o quão as ondas geradas pelo vento reagem ao atravessar esses obstáculos naturais em termos de oscilação das plantas, presentes nas margens, foi também discutida. Para os propósitos aqui expostos, um aplicativo computacional foi utilizado para a previsão de ondas e estruturado de maneira que pudesse fornecer resultados gráficos de forma automatizada com maior precisão e no menor tempo possível. O software, fruto do desenvolvimento dos estudos da equipe de pesquisa e mais recentemente aprimorado no presente trabalho, batizado de OndisaCAD, integra-se dentro de ambientes CADs, precisamente no AutoCAD da Autodesk, possibilitando, assim, a geração de ótimas interfaces e resultados gráficos. No que tange à dissipação de energia através da vegetação existente nos lagos e suas margens, o aspecto dinâmico associado à própria movimentação da vegetação foi comparado ao comportamento do movimento de vigas engastadas em sua parte inferior, o que permitiu prescrever a movimentação dos organismos vivos (plantas) frente a uma excitação provocada pela passagem de onda / This work continues and perfects an automated model for estimating the height of waves generated in lakes dams, entering the characteristic data of the wind. It follows on the climatology of the winds to determine the largest wave heights and identify critical points, for the safety of navigation and margin of the reservoir. Lakes dams, focus of this dissertation are mostly equipped with aquatic vegetation. Inside this subject, a search for models able to qualify and quantify how the waves generated by winds respond to cross these natural barriers in terms of oscillation of plants, present on the margin, was also discussed. For the purposes set out here, a software was used for predicting waves and structured so that could provide automated graphics results with more accurately and with a shortest possible time. The software, due to the development of studies of the research team and more recently extended in the present work, called OndisaCAD, works within CADs environments, specifically in AutoCAD of Autodesk's, allowing the generation of great interfaces and graphical results. With respect to the dissipating energy through the vegetation in the lakes and their margins, the dynamic aspect associated with their movement of the vegetation was compared to the behavior of the movement of beams embedded in its bottom, which allowed to prescribe the movement of living organisms (plants) front of an excitement caused by the passage of a wave

Orientador: Geraldo de Freitas Maciel / Banca: Carlos Roberto Minussi / Banca: Luiz Edival Souza / Resumo: Este trabalho dá continuidade e aperfeiçoa um modelo automatizado para estimativa de altura de ondas geradas em lagos de barragens, a partir dos dados característicos de vento. Infere sobre a climatologia dos ventos, a fim de determinar as maiores alturas de ondas e identificar pontos críticos, tanto para a segurança à navegação, quanto para as margens do reservatório. Lagos de barragens, foco desta dissertação são, em sua maioria, dotados de vegetação aquática. Dentro dessa temática, uma busca por modelos capazes de qualificar e quantificar o quão as ondas geradas pelo vento reagem ao atravessar esses obstáculos naturais em termos de oscilação das plantas, presentes nas margens, foi também discutida. Para os propósitos aqui expostos, um aplicativo computacional foi utilizado para a previsão de ondas e estruturado de maneira que pudesse fornecer resultados gráficos de forma automatizada com maior precisão e no menor tempo possível. O software, fruto do desenvolvimento dos estudos da equipe de pesquisa e mais recentemente aprimorado no presente trabalho, batizado de OndisaCAD, integra-se dentro de ambientes CADs, precisamente no AutoCAD da Autodesk, possibilitando, assim, a geração de ótimas interfaces e resultados gráficos. No que tange à dissipação de energia através da vegetação existente nos lagos e suas margens, o aspecto dinâmico associado à própria movimentação da vegetação foi comparado ao comportamento do movimento de vigas engastadas em sua parte inferior, o que permitiu prescrever a movimentação dos organismos vivos (plantas) frente a uma excitação provocada pela passagem de onda / Abstract: This work continues and perfects an automated model for estimating the height of waves generated in lakes dams, entering the characteristic data of the wind. It follows on the climatology of the winds to determine the largest wave heights and identify critical points, for the safety of navigation and margin of the reservoir. Lakes dams, focus of this dissertation are mostly equipped with aquatic vegetation. Inside this subject, a search for models able to qualify and quantify how the waves generated by winds respond to cross these natural barriers in terms of oscillation of plants, present on the margin, was also discussed. For the purposes set out here, a software was used for predicting waves and structured so that could provide automated graphics results with more accurately and with a shortest possible time. The software, due to the development of studies of the research team and more recently extended in the present work, called OndisaCAD, works within CADs environments, specifically in AutoCAD of Autodesk's, allowing the generation of great interfaces and graphical results. With respect to the dissipating energy through the vegetation in the lakes and their margins, the dynamic aspect associated with their movement of the vegetation was compared to the behavior of the movement of beams embedded in its bottom, which allowed to prescribe the movement of living organisms (plants) front of an excitement caused by the passage of a wave / Mestre