Tesis para optar al grado de Magíster en Ciencias de la Ingeniería, Mención Mecánica / Both the CAD software and FEM software have a significant impact on engineering nowadays. Even though both are powerful tools for design and analysis, the main drawback is that CAD geometries and Finite Element models do not entirely match, which results in the necessity to re-parameterize the geometry many times during the solution cycle in FEM. Isogeometric Analysis (IGA) was proposed to fulfill this gap and create the direct link between the CAD design and FEM analysis. The main idea of IGA is to substitute the shape functions used in FEM by the shape functions used in the CAD software. In particular, one of the main drawbacks of NURBS basis functions, and therefore of IGA, is the lack of local refinement, which makes them computationally highly expensive in applications that demands a non-uniform refinement of the geometry. Polynomial splines over Hierarchical T-meshes (PHT-splines) were introduced by Deng et al. as a type of spline that allows local refinement and adaptability by means of a polynomial basis capable of parameterizing the geometry. In this work, we demonstrate the application of PHT-splines for two type of problems: time-harmonic acoustic problems, modeled by the Helmholtz equation, and fracture mechanics of thin plate problems, modeled by the Kirchhoff-Love theory. Solutions of the Helmholtz equation have two features: global oscillations associated with the wave number and local gradients caused by geometrical irregularities. The results show that after a sufficient number of degrees of freedom is used to approximate global oscillations, adaptive refinement can capture local features of the solution. The residual-based and recovery-based error estimators are compared and the performance of $p$-refinement is investigated. Moreover, an eXtended Geometry Independent Field approximaTion (XGIFT) formulation based on Polynomials Splines Over Hierarchical T-meshes (PHT-splines) for modeling both static and dynamic fracture mechanic problems for plates described by the Kirchhoff-Love theory is presented. Adaptive refinement is employed using a recovery-based error estimator. Results show that adaptive refinement can capture local features of the solution around the crack tip, improving results in both static and dynamic examples. In both cases, the simulations are done in the context of recently introduced Geometry Independent Field approximaTion (GIFT), where PHT-splines are only used to approximate the solution, while the computational domain is parameterized with NURBS. This approach builds on the natural adaptation ability of PHT-splines and avoids the re-parameterization of the NURBS geometry during the solution refinement process.

Submitted by Cleide Dantas (cleidedantas@ufpa.br) on 2014-10-31T16:49:13Z No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MigracaoProfundidadeSolucao.pdf: 2614276 bytes, checksum: 4c6495ea7cb216062cd9c3623481dc55 (MD5) / Approved for entry into archive by Ana Rosa Silva (arosa@ufpa.br) on 2014-11-03T13:08:31Z (GMT) No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MigracaoProfundidadeSolucao.pdf: 2614276 bytes, checksum: 4c6495ea7cb216062cd9c3623481dc55 (MD5) / Made available in DSpace on 2014-11-03T13:08:31Z (GMT). No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MigracaoProfundidadeSolucao.pdf: 2614276 bytes, checksum: 4c6495ea7cb216062cd9c3623481dc55 (MD5) Previous issue date: 2001 / ANP - Agência Nacional do Petróleo / Nos últimos anos tem-se verificado um interesse crescente no desenvolvimento de algoritmos de imageamento sísmico com a finalidade de obter uma imagem da subsuperfície da terra. A migração pelo método de Kirchhoff, por exemplo, é um método de imageamento muito eficiente empregado na busca da localização de refletores na subsuperficie, quando dispomos do cálculo dos tempos de trânsito necessários para a etapa de empilhamento, sendo estes obtidos neste trabalho através da solução da equação eiconal. Primeiramente, é apresentada a teoria da migração de Kirchhoff em profundidade baseada na teoria do raio, sendo em seguida introduzida a equação eiconal, através da qual são obtidos os tempos de trânsitos empregados no empilhamento das curvas de difrações. Em seguida é desenvolvido um algoritmo de migração em profundidade fazendo uso dos tempos de trânsito obtidos através da equação eiconal. Finalmente, aplicamos este algoritmo a dados sintéticos contendo ruído aditivo e múltiplas e obtemos como resultado uma seção sísmica na profundidade. Através dos experimentos feitos neste trabalho observou-se que o algoritmo de migração desenvolvido mostrou-se bastante eficiente e eficaz na reconstrução da imagem dos refletores. / In the last years we have seen an increasing interest in seismic imaging algorithms in order to obtain better informations about the earth interior. The Kirchhoff migration method is very useful for determining the position of seismic reflectors, if is known the seismic wave velocity model and the traveltimes are well determined through the earth model. The traveltime calculation is a necessary step for stacking the seismic data by means of the Kirchhoff migration operator. In this work the traveltimes are obtained by solving the eiconal equation of the ray theory. At first, the theory of Kirchhoff migration is reviewed, by considering depth migration in heterogeneous media with arbitrary curved reflectors. Secondly, the numerical solution of the eiconal equation is presented for transmited, diffracted and head waves. There offer, the depth migration algorithm is presented, must makes use of traveltimes obtained by the eiconal equation. Finally, the developed migration algorithm is applied to synthetic models, providing a very good image resolution in comparison with the conventional ray tracing migration methods, even in the presence of random or coherent (multiple reflections) noise.

Improvements to isogeometric blended shells are introduced which blend traditional Reissner-Mindlin shells, and Kirchhoff-Love shells, with an exact interpolation of the shell director increment. A gradient extraction operator is introduced which allows derivatives of basis functions to be exactly expressed as a linear combination of the basis functions themselves. Several benchmarks are investigated and the new blended shell is compared with different shell elements in ABAQUS and NASTRAN. In addition, the effect of different quadrature schemes is included in the comparisons. The new isogeometric blended shell performs comparably in some benchmarks, and even outperforms commercial shell finite elements in some benchmarks. Future improvements to the formulation are discussed.

Tese de mestrado integrado. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 2012

Ce travail a pour cadre la diffusion des ondes électromagnétiques par une ou deux interfaces rugueuses séparant des milieux homogènes. Il s'intéresse plus particulièrement aux modèles asymptotiques, qui permettent de résoudre le problème posé de manière rapide, au détriment d'un domaine de validité restreint.<br />Pour le cas simple interface, après un panorama des méthodes existantes, une étude approfondie de l'approximation dite de Kirchhoff est menée pour le cas de la diffraction en réflexion et en transmission par une simple interface. Cette méthode est réduite à l'approximation dite de l'optique géométrique, valide pour des interfaces fortement rugueuses comparativement à la longueur d'onde, pour calculer plus simplement et plus rapidement la puissance diffusée. Le phénomène d'ombrage de la surface, bien connu pour le cas de la réflexion, l'est beaucoup moins pour le cas de la transmission ; c'est pourquoi il est étudié en détail dans cette thèse. <br />Pour le cas double interface, une étude bibliographique des méthodes existantes nous permet de constater l'absence de méthode basée sur l'extension de l'approximation de Kirchhoff au cas de deux interfaces fortement rugueuses. Ainsi, la méthode développée dans cette thèse permet de pallier ce manque. Cette méthode est exposée en supposant que les deux surfaces sont décorrélées, afin de pouvoir obtenir une expression de la puissance diffusée simple à mettre en œuvre. Par comparaison avec une méthode numérique de référence, la méthode développée a été validée dans le cas bidimensionnel. Une application à la détection de nappes de pétrole sur la surface de la mer est présentée, et la méthode est étendue au cas tridimensionnel.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

High-resolution seismic images of lithospheric structures allow us to infer the tectonics that modified the lithosphere. We apply such methods to understand Cenozoic modification of the lithosphere by tectonic and magmatic processes in the tectonically active western United States. Using USArray Transportable and Flexible Array data, we present high-resolution images for three regions in this thesis. (1) In the Mendocino triple junction, we use a joint inversion of Rayleigh-wave dispersion data and receiver functions to obtain a new crust and upper Vs model to ~150km depth. The model shows four distinct, young lithosphere-asthenosphere boundary systems. A low-Vs anomaly beneath the Great Valley-Sierra Nevada reconciles existing slab window models with the mantle-wedge geochemical signatures in Coast Range volcanics, and explains the ~3 Myr delay of the onset of volcanism after slab removal. Uppermost mantle low velocities provide evidence for forearc mantle serpentinization extending along the Cascadia margin. (2) In the Colorado Plateau, a Rayleigh wave tomography model sheds light on the volcanism along the margins and plateau uplift. Strong upper mantle heterogeneity across the plateau edge results from the combined effect of a ~200-400 K temperature difference and ~1% partial melt. A ring of low velocities under the plateau periphery suggests that the rehydrated Proterozoic lithosphere is progressively removed by convective processes. Particularly, a high-Vs anomaly imaged beneath the western plateau adds evidence for a downwelling/delamination hypothesis [Levander et al., 2011]. Thermo-chemical edge-driven convection causing localized lithospheric downwelling provides uplift along the margins and magmatic encroachment into the plateau center. (3) In the final study, we developed a 3-D teleseismic scattering wave imaging technique based on the Kirchhoff approximation and 3-D inverse Generalized Radon Transform. Synthetic tests demonstrate higher resolution imaging for continuous, irregular interfaces or localized scatterers, in comparison to conventional methods. Applied to the High Lava Plains dataset, the transmission coefficient structure shows a deepening Moho near 117.6°W and three negative events that correlate well with the Rayleigh wave low-Vs zones. Images made with the Mendocino data clearly show rapidly decreasing lithosphere-asthenosphere boundary depths from the subduction to transform regime.

We describe a preconditioner for the Kirchhoff plate equation for use of Bogner-Fox-Schmidt finite elements based on a hierarchical technique.

Submitted by Automação e Estatística (sst@bczm.ufrn.br) on 2018-06-05T21:59:56Z No. of bitstreams: 1 FranciscoJosaCoutinhoDaSilva_DISSERT.pdf: 5686013 bytes, checksum: e432c521a5b176e7deae602bdbf20378 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2018-06-11T21:07:44Z (GMT) No. of bitstreams: 1 FranciscoJosaCoutinhoDaSilva_DISSERT.pdf: 5686013 bytes, checksum: e432c521a5b176e7deae602bdbf20378 (MD5) / Made available in DSpace on 2018-06-11T21:07:44Z (GMT). No. of bitstreams: 1 FranciscoJosaCoutinhoDaSilva_DISSERT.pdf: 5686013 bytes, checksum: e432c521a5b176e7deae602bdbf20378 (MD5) Previous issue date: 2018-02-08 / Agência Nacional do Petróleo, Gás Natural e Biocombustíveis - ANP / A aquisição de dados sísmicos terrestres pode ocorrer ocasionalmente sobre forte influência de um relevo muito variante ou de uma camada intemperizada consideravelmente heterogênea e espessa, ou de ambas as formas. Nesse contexto, os métodos de correções estáticas geralmente fornecem ajustes temporais incorretos, resultando em seções empilhadas de baixa qualidade. A razão é que as correções temporais se baseiam em trajetórias de raios verticais entre a superfície e o datum, comumente escolhido abaixo da zona intemperizada. Para essa situação, propomos um método de redatumação como meio de mover os dados para um novo datum usando algoritmos de migração e demigração Kirchhoff adaptados, em vez da aplicação de correções estáticas. / The land seismic data acquisition may occasionally occur either on the strong influence of a very variant relief or a very heterogeneous and thick weathering layer, or both. In this context, static correction methods often provide incorrect temporal adjustments, resulting in poor quality stacked sections. The reason is that temporal corrections are based on trajectories of vertical rays between the surface and the datum, commonly chosen below the weathered zone. For this situation, we propose a redatuming method as way to move the data to a new datum using adapted Kirchhoff migration and demigration algorithms, instead of applying static corrections.

Este trabalho tem como objetivo a análise vibratória livre de placas retangulares bem como resultados analíticos precisos e abrangentes, baseando-se na equação biharmônica, obtida a partir das hipóteses de Kirchhoff-Love. São fixadas as condições de duas bordas opostas como simplesmente apoiadas e outras seis combinações possíveis, para as demais bordas, de acordo com as condições engastada (fixa), simplesmente apoiada (apoiada) e livre. São apresentadas as seis equações características exatas. Os modos são determinados simbolicamente através de uma formulação matricial genérica a qual permite o uso de uma base espectral clássica ou de uma base dinâmica. Este procedimento amplia a metodologia introduzida por Navier e por Levy, obtendo-se uma equação matricial singular. Parâmetros de frequência precisos, assim como os modos, são apresentados para uma faixa de razões de aspecto (a/b = 2/5, 2/3, 1, 3/2 e 3/5) para cada caso avaliado. Observa-se que para materiais isotrópicos as frequências naturais são influenciadas significativamente pela razão de Poisson (v). Devido à simetria geométrica existente em relação ao eixo y, os modos podem ser separados em uma parte simétrica e outra anti-simétrica, permitindo diminuir a complexidade computacional. / This work has, as its main objective, the free vibration analysis of rectangular plates as well as comprehensive and accurate analytical results, based on the biharmonic equation, obtained from Kirchho -Love assumptions. We set the boundary conditions of two opposite edges as simply-supported and other six possible combinations, for the other two edges, of clamped, simply-supported, and free conditions. The six characteristic equations are given. The mode shapes are simbolically determined through general matrix formulation which allows the use of the classic espectral base or the dynamic base. These procedure enlarge the Navier and L evy methodology, producing a singular matrix equation. Accurate frequency parameters, as well as the mode shapes, are presented for a range of aspect ratios (a=b = 2=5, 2=3, 1, 3=2 e 3=5) for each case. It has been noticed that for isotropic materials, the natural frequencys were signi cantly in uenced by the Poisson's ratio ( ). Because of the geometric symmetry which exists about the y axis, vibration modes can be separated into a y-symmetric part and a y- antisymmetric part, allowing to decrease the computational e orts.