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MIRANDA, FABIO MARKUS NUNES. "VOLUME RENDERING OF UNSTRUCTURED HEXAHEDRAL MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=28921@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Importantes aplicações de engenharia usam malhas não estruturadas de hexaedros para simulações numéricas. Células hexaédricas, comparadas com tetraedros, tendem a ser mais numericamente estáveis e requerem um menor refinamento da malha. Entretando, visualização volumétrica de malhas não estruturadas é um desafio devido a variação trilinear do campo escalar dentro da célula. A solução convencional consiste em subdividir cada hexaedro em cinco ou seis tetraedros, aproximando uma variação trilinear por uma inadequada série de funções lineares. Isso resulta em imagens inadequadas e aumenta o consumo de memória. Nesta tese, apresentamos um algoritmo preciso de visualização volumétrica utilizando ray-casting para malhas não estruturadas de hexaedros. Para capturar a variação trilinear ao longo do raio, nós propomos usar uma integração de quadratura. Nós também propomos uma alternativa rápida que melhor aproxima a variação trilinear, considerando os pontos de mínimo e máximo da função escalar ao longo do raio. Uma série de experimentos computacionais demonstram que nossa proposta produz resultados exatos, com um menor gasto de memória. Todo algoritmo é implementado em placas gráficas, garantindo uma performance competitiva.
Important engineering applications use unstructured hexahedral meshes for numerical simulations. Hexahedral cells, when compared to tetrahedral ones, tend to be more numerically stable and to require less mesh refinement. However, volume visualization of unstructured hexahedral meshes is challenging due to the trilinear variation of scalar fields inside the cells. The conventional solution consists in subdividing each hexahedral cell into five or six tetrahedra, approximating a trilinear variation by an inadequate piecewise linear function. This results in inaccurate images and increases the memory consumption. In this thesis, we present an accurate ray-casting volume rendering algorithm for unstructured hexahedral meshes. In order to capture the trilinear variation along the ray, we propose the use of quadrature integration. We also propose a fast approach that better approximates the trilinear variation to a series of linear ones, considering the points of minimum and maximum of the scalar function along the ray. A set of computational experiments demonstrates that our proposal produces accurate results, with reduced memory footprint. The entire algorithm is implemented on graphics cards, ensuring competitive performance.
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Price, Mark A. "Hexahedral mesh generation by medial surface subdivision." Thesis, Queen's University Belfast, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286777.
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Woodbury, Adam C. "Localized Coarsening of Conforming All-Hexahedral Meshes." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2578.pdf.
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Roca, Navarro Xevi. "Paving the path towards automatic hexahedral mesh generation." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5858.
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Esta tesis versa sobre el desarrollo de las tecnologías para la generación de mallas de hexaedros. El proceso de generar una malla de hexaedros no es automático y su generación requiere varias horas te trabajo de un ingeniero especializado. Por lo tanto, es importante desarrollar herramientas que faciliten dicho proceso de generación. Con este fin, se presenta y desarrolla un método de proyección de mallas, una técnica de sweeping o barrido, un algoritmo para la obtención de mallas por bloques, y un entorno de generación de mallas. Las implementaciones más competitivas del método de sweeping utilizan técnicas de proyección de mallas basadas en métodos afines. Los métodos afines más habituales presentan varios problemas relacionados con la obtención de sistemas de ecuaciones normales de rango deficiente. Para solucionar dichos problemas se presenta y analiza un nuevo método afín que depende de dos parámetros vectoriales. Además, se detalla un procedimiento automático para la selección de dichos vectores. El método de proyección resultante preserva la forma de las mallas proyectadas. Esta proyección es incorporada también en una nueva herramienta de sweeping. Dicha herramienta genera capas de nodos internos que respetan la curvatura de las superficies inicial y final. La herramienta de sweeping es capaz de mallar geometrías de extrusión definidas por trayectorias curvas, secciones no constantes a lo largo del eje de sweeping, y superficies inicial y final con diferente forma y curvatura.
En las últimas décadas se han propuesto varios ataques para la generación automática de mallas de hexahedros. Sin embargo, todavía no existe un algoritmo rápido y robusto que genere automáticamente mallas de hexaedros de alta calidad. Se propone un nuevo ataque para la generación de mallas por bloques mediante la representación de la geometría y la topología del dual de una malla de hexaedros. En dicho ataque, primero se genera una malla grosera de tetraedros. Después, varió polígonos planos se añaden al interior de los elementos de la malla grosera inicial. Dichos polígonos se denotan como contribuciones duales locales y representan una versión discreta del dual de una malla de hexaedros. En el último paso, la malla por bloques se obtiene como el dual de la representación del dual generada. El algoritmo de generación de mallas por bloques es aplicado a geometrías que presentan diferentes características geométricas como son superficies planas, superficies curvas, configuraciones delgadas, agujeros, y vértices con valencia mayor que tres.
Las mallas se generan habitualmente con la ayuda de entornos interactivos que integran una interfaz CAD y varios algoritmos de generación de mallas. Se presenta un nuevo entorno de generación de mallas especializado en la generación de cuadriláteros y hexaedros. Este entorno proporciona la tecnología necesaria para implementar les técnicas de generación de mallas de hexaedros presentadas en esta tesis.
This thesis deals with the development of hexahedral mesh generation technology. The process of generating hexahedral meshes is not fully automatic and it is a time consuming task. Therefore, it is important to develop tools that facilitate the generation of hexahedral meshes. To this end, a mesh projection method, a sweeping technique, a block-meshing algorithm, and an interactive mesh generation environment are presented and developed.
Competitive implementations of the sweeping method use mesh projection techniques based on affine methods. Standard affine methods have several drawbacks related to the statement of rank deficient sets of normal equations. To overcome these drawbacks a new affine method that depends on two vector parameters is presented and analyzed. Moreover, an automatic procedure that selects these two vector parameters is detailed. The resulting projection procedure preserves the shape of projected meshes. Then, this procedure is incorporated in a new sweeping tool. This tool generates inner layers of nodes that preserve the curvature of the cap surfaces. The sweeping tool is able to mesh extrusion geometries defined by non-linear sweeping trajectories, non-constant cross sections along the sweep axis, non-parallel cap surfaces, and cap surfaces with different shape and curvature.
In the last decades, several general-purpose approaches to generate automatically hexahedral meshes have been proposed. However, a fast and robust algorithm that automatically generates high-quality hexahedral meshes is not available. A novel approach for block meshing by representing the geometry and the topology of a hexahedral mesh is presented. The block-meshing algorithm first generates an initial coarse mesh of tetrahedral elements. Second, several planar polygons are added inside the elements of the initial coarse mesh. These polygons are referred as local dual contributions and represent a discrete version of the dual of a hexahedral mesh. Finally, the dual representation is dualized to obtain the final block mesh. The block-meshing algorithm is applied to mesh geometries that present different geometrical characteristics such as planar surfaces, curved surfaces, thin configurations, holes, and vertices with valence greater than three.
Meshes are usually generated with the help of interactive environments that integrate a CAD interface and several meshing algorithms. An overview of a new mesh generation environment focused in quadrilateral and hexahedral mesh generation is presented. This environment provides the technology required to implement the hexahedral meshing techniques presented in this thesis.
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Paudel, Gaurab. "Hexahedral Mesh Refinement Using an Error Sizing Function." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/3447.
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The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.
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Malone, J. Bruce. "Two-Refinement by Pillowing for Structured Hexahedral Meshes." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3495.
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A number of methods for adaptation of existing all-hexahedral grids by localized refinement have been developed; however, none ideally fit all refinement needs. This thesis presents the structure to a method of two-refinement developed for conformal, structured, all-hexahedral grids that offers flexibility beyond what has been offered to date. The method is fundamentally based on pillowing pairs of sheets of hexes. This thesis also suggests an implementation of the method, shows the results of examples refined using it and compares these results to results from implementing three-refinement on the same examples.
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Harris, Nathan. "Conformal Refinement of All-Hexahedral Finite Element Meshes." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/3461.
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Mesh adaptation techniques are used to modify complex finite element meshes to reduce analysis time and improve accuracy. Modification of all-hexahedral meshes has proven difficult to the unique connectivity constraints they exhibit. This thesis presents an automated tool for local, conformal refinement of all-hexahedral meshes based on the insertion of multi-directional twist planes into the spatial twist continuum. The contributions of this thesis are (1) the ability to conformally refine all entities of an all-hexahedral element mesh, (2) the simplification of template insertion to multi-directional refinement. The refinement algorithm is divided into single hex sheet operations, where individual refinement steps are performed completely within a single hex sheet, and parallel sheet operation, where each refinement step occurs within two parallel hex sheets. Combining these two procedures facilitates the refinement of any mesh feature. Refinement is accomplished by replacing original mesh elements with one or more of six base templates selected by the number of nodes, flagged for refinement on the element. The refinement procedures are covered in detail with representative graphics and examples that illustrate the application of the techniques and the results of the refinement.
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Özdemir, Hüseyin. "High-order discontinuous Galerkin method on hexahedral elements for aeroacoustics." Enschede : University of Twente [Host], 2006. http://doc.utwente.nl/57867.
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Parrish, Michael H. "A selective approach to conformal refinement of unstructured hexahedral meshes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1985.pdf.
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Parrish, Michael Hubbard. "A Selective Approach to Hexahedral Refinement of Unstructured Conformal Meshes." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/979.
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Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle multiply-connected transition elements and self-intersecting hexahedral sheets. The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle the above stated problems. These two refinement methods are: 1) element by element refinement and 2) directional refinement. In element by element refinement, the three inherent directions of a hexahedron are refined in one step using one of seven templates. Because of its computational superiority over directional refinement, but its inability to handle multiply-connected transition elements, element by element refinement is used in all areas of the specified region except regions local to multiply-connected transition elements. The directional refinement scheme refines the three inherent directions of a hexahedron separately on a hexahedron by hexahedron basis. This differs from sheet refinement which refines hexahedra using hexahedral sheets. Directional refinement is able to correctly handle multiply-connected transition elements. A ranking system and propagation scheme allow directional refinement to work within the confines of the Selective Approach Algorithm.
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Walton, Kirk S. "Sculpting: An Improved Inside-out Scheme for All Hexahedral Meshing." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/3451.
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Generating all hexahedral meshes on arbitrary geometries has been an area of important research in recent history. Hexahedral meshes have advantages over tetrahedral meshes in structural mechanics because they provide more accurate results with fewer degrees of freedom. Many different approaches have been used to create all-hexahedral meshes. Grid-based, inside-out, or superposition meshing all refer to a similar meshing approach that is a very common mesh generation technique. Grid-based algorithms provide the ability to generate all hexahedral meshes by introducing a structured mesh that bounds the complete body modeled, marking hexahedra to define an interior and exterior mesh, manipulating the boundary region between interior and exterior regions of the structured mesh to fit the specific boundary of the body, and finally, discarding the exterior hexahedra from the given body. Such algorithms generally provide high quality meshes on the interior of the body yet distort element at the boundary in order to fill voids and match surfaces along these regions. The sculpting algorithm as presented here, addresses the difficulty in forming quality elements near boundary regions in two ways. The algorithm first finds more intelligent methods to define a structured mesh that conforms to the body to lessen large distortions to the boundary elements. Second, the algorithm uses collapsing templates to adjust the position of boundary elements to mimic the topology of the body prior to capturing the geometric boundary.
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Xiao, Fei. "Hexahedral Mesh Generation from Volumetric Data by Dual Interval Volume." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1532003347814656.
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Yilmaz, Asim Egemen. "Finite Element Modeling Of Electromagnetic Scattering Problems Via Hexahedral Edge Elements." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608587/index.pdf.
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In this thesis, quadratic hexahedral edge elements have been applied to the three dimensional for open region electromagnetic scattering problems. For this purpose, a semi-automatic all-hexahedral mesh generation algorithm is developed and implemented. Material properties inside the elements and along the edges are also determined and prescribed during the mesh generation phase in order to be used in the solution phase. Based on the condition number quality metric, the generated mesh is optimized by means of the Particle Swarm Optimization (PSO) technique. A framework implementing hierarchical hexahedral edge elements is implemented to investigate the performance of linear and quadratic hexahedral edge elements. Perfectly Matched Layers (PMLs), which are implemented by using a complex coordinate transformation, have been used for mesh truncation in the software. Sparse storage and relevant efficient matrix ordering are used for the representation of the system of equations. Both direct and indirect sparse matrix solution methods are implemented and used.
Performance of quadratic hexahedral edge elements is deeply investigated over the radar cross-sections of several curved or flat objects with or without patches. Instead of the de-facto standard of 0.1 wavelength linear element size, 0.3-0.4 wavelength quadratic element size was observed to be a new potential criterion for electromagnetic scattering and radiation problems.
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Shepherd, Jason F. "Interval Matching and Control for Hexahedral Mesh Generation of Swept Volumes." BYU ScholarsArchive, 1999. https://scholarsarchive.byu.edu/etd/3452.
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Surface meshing algorithms require certain relationships among the number of intervals on the curves that bound the surface. Assigning the number of intervals to all of the curves in the model such that all relationships are satisfied is called interval assignment. Volume meshing algorithms also require certain relationships among the numbers of intervals on each of the curves on the volume. These relationships are not always captured by surface meshing requirements. This thesis presents a news technique for automatically identifying volume constraints. In this technique, volume constraints are grouped with surface constraints and are solved simultaneously. A sweepable volume has source, target and linking surfaces. The technique described in this thesis uses graph algorithms to identify independent, parallel sets of linking surfaces, and determine if they correspond to through-holes or blind-holes. For blind-holes, the algorithm generates constraints that prevent the hole from being too deep in interval parameter space and, thus, penetrating opposite target surfaces. For each linking set, the adjoining source and target surfaces are partially ordered by the structure of the linking set. A small set of representative paths for each linking set is found, and the representative paths for all linking sets are gathered and distilled by Gaussian elimination into a small set of constraints.
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Kowalski, Nicolas. "Domain partitioning using frame fields : applications to quadrilateral and hexahedral meshing." Paris 6, 2013. http://www.theses.fr/2013PA066689.
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In this work, we describe a method to partition domains adapted to the generation of quadrilateral and hexahedral meshes. Given a domain D, the proposed approach proceeds in two steps: first, a frame field is defined on a background simplicial mesh of D. Then, singular elements of this field are extracted to create a skeleton that partitions D. The key element of this approach is the use of frames: at a point P of D, a frame allows to orient the quadrilateral or the hexahedral. Thus, we propose a complete study of frames and frame fields. We describe the proposed method both in dimension two and three. The main difference between the two is in the way frame fields are generated. In dimension 2, we solve a non-linear PDE, while in 2D, a heuristic is applied that uses initiallu an advancing front algorithm that takes the stability of the field into account, before using a smoothing algorithm. In both cases, a skeleton is extracted from the frame field. In dimension two, this skeleton always leads to a partition of D into quadrilateral-shaped blocks, and singularities are all of degree three and five. In dimension three, the obtained frame field leads to a partition allowing for hexahedral meshing in numerous cases. Many examples are showcased and compared to results obtained by existing methodsDans ce travail, nous décrivons une méthode de partitionnement de domaines 2D et 3D adaptée à la génération de maillages quadrangulaires et héxahédriques. Etant donné un domaine D, l'approche proposée se décompose en deux étapes: tout d'abord, un champ d'orientations est défini sur un maillage simplicial approximant D. Puis, les éléments singuliers de ce champs sont extraits pour former un squelette qui partitionne D. L'élément clé de cette approche est l'utilisation d'orientations : en un point P de D, une orientation permet d'orienter le quadrilatère ou l'héxahèdre. De ce fait, nous proposons une étude complète des orientations et des champs d'orientations. Nous décrivons ensuite la méthode proposée aussi bien en dimension deux que trois. La différence majeure entre ces deux versions réside dans la génération du champ d'orientations. En dimension 2, nous nous basons sur la résolution d'une EDP non linéaire. En dimension 3, une heuristique est appliquée en utilisant un algorithme par avancée de front tenant compte de la stabilité du champ généré suivi d'un algorithme de lissage. Dans les deux cas, un squelette est extrait du champ d'orientations. En dimension deux, ce squelette fournit toujours un partitionnement de D en blocs quadrangulaires et les singularités obtenues sont de valence trois et cinq uniquement. En dimension trois, le champ d'orientations obtenu permet un partitionnement adéquat pour de nombreuses configurations. De nombreux exemples sont présentés et comparés aux résultats obtenus par des méthodes existantes
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Natarajan, Amla. "Hexahedral meshing of subject-specific anatomic structures using registered building blocks." Thesis, University of Iowa, 2010. https://ir.uiowa.edu/etd/717.
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To extend the use of computational techniques like finite element analysis to clinical settings, it would be beneficial to have the ability to generate a unique model for every subject quickly and efficiently. To this end, we previously developed two mapped meshing tools that utilized force and displacement control to map a template mesh to a subject-specific surface. This work is an extension of those methods; the objective of this study was to map a template block structure, common to multi-block meshing techniques, to a subject-specific surface. The rationale was that the blocks are considerably less refined and may be readily edited, thereby yielding a mesh of high quality in less time than mapping the mesh itself. In this paper, the versatility and robustness of the method was verified by processing four datasets. The method was found to be robust enough to cope with the variability of bony surface size, spatial position and geometry, producing building block structures that generated meshes comparable to those produced using building block structures that were created manually.
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Bremberg, Daniel. "Automatic Mixed-Mode Crack Propagation Computations using a combined Hexahedral/Tetrahedral-Approach." Licentiate thesis, KTH, Solid Mechanics (Div.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11823.
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Edgel, Jared D. "An Adaptive Grid-Based All Hexahedral Meshing Algorithm Based on 2-Refinement." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2241.
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Adaptive all-hexahedral meshing algorithms have many desirable features. These algorithms provide a mesh that is efficient for analysis by providing a high element density in specific locations, such as areas of high stress gradient or high curvature and reduced mesh density in other areas of less importance. In addition, inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, have shown great promise in accommodating automatic all-hexahedral algorithms. In these algorithms mesh refinement is generally used to capture geometric features. Unfortunately, most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is coarse in most areas and highly refined in other areas. Because a single refined hex is subdivided into 27 new hexes, regardless of the desired refinement, there is little control on mesh density. This paper will present an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement insertion method. 2-refinement is based on dividing a hex to be refined into eight new hexes. This allows greater control on mesh density which in turn increases computational efficiency.
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Le, goff Nicolas. "Construction of a conformal hexahedral mesh from volume fractions : theory and applications." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASG033.
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Ces travaux abordent le problème de la génération automatique de maillages hexaédriques pour des codes de simulation, à partir d'un maillage portant des fractions volumiques, c'est-à-dire dont les mailles peuvent contenir plusieurs matériaux. La solution proposée doit contruire un maillage hexaédrique dans lequel chaque maille correspond à un seul matériau, et dont les interfaces entre matériaux doivent former des surfaces lisses. D'un point de vue théorique, nous cherchons à adapter et étendre des solutions existantes, et à les appliquer sur une large variété d'exemples : certains issus de modèles de CAO (plaqués sur un maillage pour obtenir des fractions volumiques), d'autres générés procéduralement et enfin d'autres utilisés dans un rôle d'intercode, récupérés en sortie de codes de simulation. Nous définissons une métrique permettant d'évaluer notre (et d'autres) méthodes, ainsi qu'un post-processus pour améliorer ces résultats; nous introduisons également une méthode de reconstruction d'interfaces discrètes inspirés de méthodes issues du domaine de la visualisation scientifique, et nous proposons un algorithme appelé {sc ELG} avec garantie sur la qualité du maillage, faisant intervenir des modifications géométriques et topologiques sur ce maillageThis thesis addresses the problem of the automatic generation of purely hexahedral meshes for simulation codes when having a mesh carrying volume fraction data as an input, meaning that there can be several materials inside one cell. The proposed approach should create an hexahedral mesh where each cell corresponds to a single material, and where interfaces between materials form smooth surfaces. From a theoretical standpoint, we aim at adapting and extending state-of-the-art techniques and we apply them on examples, some classically issued from CAD models (and imprinted onto a mesh to obtain volume fractions), some procedurally generated cases and others in an intercode capacity where we take the results of a first simulation code to be our inputs. We first define a metric that allows the evaluation of our (or others') results and a method to improve those; we then introduce a discrete material interface reconstruction method inspired from the scientific visualization field and finally we present an algorithmic pipeline, called {sc ELG}, that offers a guarantee on the mesh quality by performing geometrical and topological mesh adaptation
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Sun, Liang. "Automatic decomposition of complex thin-walled CAD models for hexahedral dominant meshing." Thesis, Queen's University Belfast, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728671.
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There is a strong demand in industry for the automatic hex meshing of complex CAD models. Fully automatic methods for hex meshing have been under investigation for many years. Although significant research has been carried out, the complexity of the models that can be meshed with well-structured meshes is very restricted. Manual decomposition is still the main industrial route to achieving this, but this process involves intensive effort from the user. In this thesis, new approaches are developed which automatically decompose complex thin-walled components into regions to which hex elements can be easily applied. The approaches are an extension and improvement of the previous ideas investigated at QUB, i.e. to decompose the thin-walled components into thin sheet, long-slender and residual regions based on local geometric characteristics. This new implementation aims at a more robust, efficient and effective method to achieve the decomposition. For the thin sheet and long-slender region, novel approaches are used to decide upon the generation of the cutting faces used to decompose the model. The resulting decomposition delivers a substantial step towards automatic hex meshing for complex thin-walled geometries. By using anisotropic hex elements in these regions, a significant saving in the number of DOF can be achieved. For the residual regions, a novel equation has been proposed to determine the net number of quad mesh singularities that are required on each face. This provides a starting point for determining the necessary patterns of volume mesh singularities to create a hex mesh. It is shown that sweepable volumes can be automatically identified. Other applications such as locating the mesh singularities and concave removal in 2D are introduced, which have the potential to be extended into 3D in the future. Finally, the idea of combining the decomposition with virtual topology is presented and some benefits are discussed.
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Wang, Jue. "A New hexahedral solid element for 3D FEM simulation of sheet metal forming /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486463321626896.
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Apel, Thomas, and Nico Düvelmeyer. "Transformation of hexahedral finite element meshes into tetrahedral meshes according to quality criteria." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601295.
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The paper is concerned with algorithms for transforming hexahedral finite element meshes into tetrahedral meshes without introducing new nodes. Known algorithms use only the topological structure of the hexahedral mesh but no geometry information. The paper provides another algorithm which can be extented such that quality criteria for the splitting of faces are respected.
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Dia, Mouhamadou. "Hexahedral and prismatic solid-shell for nonlinear analysis of thin and medium-thick structures." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEI040.
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Les structures à faibles ou moyennes épaisseurs sont naturellement présentes dans la plupart des installations de production d'énergie : bâtiment réacteur, tuyauteries sous pression, réservoirs métalliques ou bâches, cuve de réacteur, liners métalliques des enceintes de confinement pour ne citer que ceux‐là. Un besoin actuellement exprimé par les unités d'ingénierie d’EDF est la modélisation des phénomènes de cloquage de liners métalliques des bâtiments réacteur. Un liner est une structures de type tôle métallique assurant la fonction d’étanchéité des centrales nucléaires. Sa modélisation nécessite la prise en compte d’un phénomène de contact-frottement engendrant du pincement sur la coque, de la plasticité sous l’effet de cloquage et de la non linéarité géométrique (instabilité de type flambement). Pour modéliser le comportement thermomécanique d’une structure pareille, les éléments finis de plaques et coques actuellement disponible ne semblent pas être à la hauteur. Le premier verrou attribuable à ces éléments est l’hypothèse des contraintes planes qui empêche la prise en compte de certaines lois de comportement nativement tridimensionnelles. En deuxième lieu, du fait de leur formulation avec des degrés de liberté de rotations ces éléments n’offrent pas une facilité d’utilisation lorsqu’il s’agit de résoudre des problèmes prenant en compte les effets non-linéaires telles que les grande transformations géométriques, le contact-frottement bi-facial, le flambement et les pressions suiveuses. Une alternative serait d’utiliser des éléments volumiques standards. Cependant le coût de calcul prohibitif des ces derniers est difficilement accessible pour de nombreuses applications industrielles. Le but de ces travaux est de proposer une solution à cette problématique. Nous avons proposé une formulation élément fini de type solide-coque enrichie en pincement et capable de reproduire les comportements des structures minces avec une précision satisfaisante. Ce nouvel éléments fini fonctionnent avec tout type de loi de comportement tridimensionnelle sans restriction sur les champs de contraintes. On peut également l’utiliser pour tous les types de problèmes mécaniques : linéaire et non linéaire, contact frottement, grande transformation, flambement, pression suiveuse etc. Les simulations numériques réalisées montrent des performances satisfaisantesThin or medium-thick structures are naturally present in most power generation facilities: reactor building, pressurized pipelines, metal tanks or tarpaulins, reactor vessel, metal liners of containment chambers, to name but a few. A need currently expressed by EDF's engineering units is the modeling of the blistering phenomena of metal liners in reactor facilities. A liner is a metal sheet type structure that provides the impermeability function of nuclear power plants. Its modeling requires taking into account a contact-friction phenomenon causing pinching on the shell, plasticity under the effect of blistering and geometric nonlinearity (buckling type instability). To model the thermo-mechanical behavior of such a structure, the finite elements of plates and shells currently available do not seem to be up to the task. The first limitation attributable to these elements is the assumption of plane stresses which prevents the consideration of some natively three-dimensional constitutive laws. Secondly, due to their formulation with rotational degrees of freedom these elements do not offer facility of use when solving problems that take into account non-linear effects such as large geometric transformations, bi-facial friction-contact, buckling and following pressures. An alternative would be to use standard volume elements. However, the prohibitive computing cost of the latter is difficult to access for many industrial applications. The aim of this work is to propose a solution to this problem. We have proposed a solid-shell finite element formulation enriched in their pinching stress and strain and capable of reproducing accurately the behaviour of thin structures. This new finite element works with any type of three-dimensional behaviour law without restriction on stress fields. It can also be used for all types of mechanical problems: linear and nonlinear, frictional contact, large transformation, buckling, displacement-dependent pressure, etc. The numerical simulations carried out show satisfactory performances
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Miller, Timothy Ira. "Automatic All-Hex Topology Operations Using Edge Valence Prediction with Application to Localized Coarsening." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2607.
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In this work, we propose using edge valence as a quality predictor when used as a driver for adapting all hexahedral meshes. Edge valence, for hexahedra, is defined as the number of faces attached to an edge. It has shown to be a more reliable quality predictor than node valence for hexahedral meshes. An edge valence of 3, 4, or 5 within the volume of a hexahedral mesh has provided at least a positive scaled Jacobian for all observed meshes, without the presence of over constraining geometry. It is often desirable to adapt an existing mesh through sheet operations such as column collapse, sheet insertion, or sheet extraction. Examples of hexahedral mesh adaptation include refining and coarsening. This work presents a general algorithm for a priori prediction of edge valence when used with column collapse and sheet extraction operations. Using the predicted edge valence we present a method for guiding the mesh adaptation procedure which will result in an overall higher quality mesh than when driven by mesh quality alone. Other quality metrics such as the Jacobian are unfit for predictive algorithms because of their heavy dependence on node positioning instead of hex topology. Results have been derived from application of the algorithm towards the localized coarsening process.
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Earp, Matthew N. "All Hexahedral Meshing of Multiple Source, Multiple Target, Multiple Axis Geometries Via Automatic Grafting and Sweeping." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd762.pdf.
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Borden, Michael J. "Modification of All-Hexadedral Finite Element Meshes by Dual Sheet Insertion and Extraction." BYU ScholarsArchive, 2002. https://scholarsarchive.byu.edu/etd/3449.
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The development of algorithms that effectively modify all-hexahedral finite element mesh is currently an active area of research. Mesh modification can be used to improve mesh quality reduce the time required to mesh a model, and improve the finite element analysis results. However, general modification of all-hexahedral meshes has proven difficult because of the global effects of local modifications. This thesis explains the global constraints on modifying all-hexahedral meshes and then presents three mesh modification techniques that make it possible to do local modifications while accounting for the global effects. These techniques are sheet insertion, sheet extraction, and mesh cutting. Sheet insertion is used to refine a mesh by inserting sheets of hexahedral elements into existing meshes. Sheet extraction coarsens existing meshes by deleting sheets of elements from the mesh. Mesh cutting is used to modify a simple mesh to fit it to complex geometric feature. The mesh modification techniques are covered in detail with representative graphics. Examples are given that demonstrate the application of each technique to the mesh generation process.
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Clark, Brett W. "The Development and Evaluation of the knife Finite Element." BYU ScholarsArchive, 1996. https://scholarsarchive.byu.edu/etd/3456.
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This thesis presents the development and evaluation of the knife finite element which is a degenerate case of a hexahedral element. The knife connectivity is an artifact of automatic all-hexahedral mesh generators. Currently, knives are propagated to the surface of the mesh for removal. However since this disturbs the surface mesh, other alternatives are needed. This thesis investigates the option of leaving the knife connectivity in the mesh and treating it as a valid finite element. The shape functions and stiffness matrix for the knife element are derived and evaluated using theoretical and practical evaluations. It is concluded that the knife finite element is a viable element and should be used in finite element analysis when the knife connectivity occurs. Using the knife element reduces the work involved with fixing the knife connectivity by propagation or other means and will produce acceptable results in most cases.
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Yildiz, Ozgur. "Implementation Of Mesh Generation Algorithms." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1339621/index.pdf.
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In this thesis, three mesh generation software packages have been developed and
implemented. The first two were based on structured mesh generation algorithms
and used to solve structured surface and volume mesh generation problems of
three-dimensional domains. Structured mesh generation algorithms were based
on the concept of isoparametric coordinates. In structured surface mesh
generation software, quadrilateral mesh elements were generated for complex
three-dimensional surfaces and these elements were then triangulated in order to
obtain high-quality triangular mesh elements. Structured volume mesh
generation software was used to generate hexahedral mesh elements for volumes.
Tetrahedral mesh elements were constructed from hexahedral elements using
hexahedral node insertion method. The results, which were produced by the mesh
generation algorithms, were converted to a required format in order to be saved in output files. The third software package is an unstructured quality tetrahedral
mesh generator and was used to generate exact Delaunay tetrahedralizations,
constrained (conforming) Delaunay tetrahedralizations and quality conforming
Delaunay tetrahedralizations. Apart from the mesh generation algorithms used
and implemented in this thesis, unstructured mesh generation techniques that can
be used to generate quadrilateral, triangular, hexahedral and tetrahedral mesh
elements were also discussed.
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Grover, Benjamin Todd. "Surfacing Splicing: A Method of Quadrilateral Mesh Generation and Modification for Surfaces by Dual Creation and Manipulation." BYU ScholarsArchive, 2002. https://scholarsarchive.byu.edu/etd/3457.
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The effective generation high quality quadrilateral surface meshes is an area of important research and development for the finite element community. Quadrilateral elements generally lead to more efficient and accurate finite results. In addition, some all hexahedral volume meshing algorithms are based on an initial quadrilateral mesh surface mesh that has specific connectivity requirements. This thesis presents a new and unique procedure named "Surfaced Splicing". Surface Splicing allows for the generation of all quadrilateral surface meshes as well as the ability to edit these meshes via the dual. The dual contains the same data as the mesh but, unlike the mesh, the dual directly allows the visualization of how surface and volume elements interrelate and connect with one another. The dual also provides mesh connectivity information that is crucial in forming an all-quadrilateral surface mesh that can form the basis of an all-hexahedral volume mesh.
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Ramme, Austin Jedidiah. "High throughput patient-specific orthopaedic analysis: development of interactive tools and application to graft placement in anterior cruciate ligament reconstruction." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/2966.
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Medical imaging technologies have allowed for in vivo evaluation of the human musculoskeletal system. With advances in both medical imaging and computing, patient-specific model development of anatomic structures is becoming a reality. Three-dimensional surface models are useful for patient-specific measurements and finite element studies. Orthopaedics is closely tied to engineering in the analysis of injury mechanisms, design of implantable medical devices, and potentially in the prediction of injury. However, a disconnection exists between medical imaging and orthopaedic analysis; whereby, the ability to generate three-dimensional models from an imaging dataset is difficult, which has restricted its application to large patient populations. We have compiled image processing, image segmentation, and surface generation tools in a single software package catered specifically to image-based orthopaedic analysis. We have also optimized an automated segmentation technique to allow for high-throughput bone segmentation and developed algorithms that help to automate the cumbersome process of mesh generation in finite element analysis. We apply these tools to evaluate graft placement in anterior cruciate ligament reconstruction in a multicenter study that aims to improve the patient outcomes of those that undergo this procedure.
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Beegle, David J. "Three-dimensional modeling of rigid pavement." Ohio : Ohio University, 1998. http://www.ohiolink.edu/etd/view.cgi?ohiou1176842076.
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Courbet, Clément. "Compression de maillages de grande taille." Phd thesis, Ecole Centrale Paris, 2011. http://tel.archives-ouvertes.fr/tel-00594233.
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Il y a une décennie, le contenu numérique virtuel était limité à quelques applications - majoritairementles jeux vidéos, les films en 3D et la simulation numérique. Aujourd'hui, grâce à l'apparition de cartes graphiques performantes et bon marché, les objets 3D sont utilisés dans de nombreuses applications. A peu près tous les terminaux possédant des capacités d'affichage - des clusters de visualisation haute performance jusqu'aux smart phones - intègrent maintenant une puce graphique qui leur permet de faire du rendu 3D. Ainsi, les applications 3D sont bien plus variées qu'il y a quelques années. On citera par exemple la réalité virtuelle et augmentée en temps réel ou les mondes virtuels 3D. Dans ce contexte, le besoin de méthodes efficaces pour la transmission et la visualisation des données 3D est toujours plus pressant. De plus, la taille des maillages 3D ne cesse de s'accroître avec la précision de la représentation. Par exemple, les scanners 3D actuels sont capables de numériser des objets du monde réel avec une précision de seulement quelques micromètres, et génèrent des maillages contenant plusieurs centaines de millions d''el'ements. D'un autre côté, une précision accrue en simulation numérique requiert des maillages plus fins, et les méthodes massivement parallèles actuelles sont capables de travailler avec des milliards de mailles. Dans ce contexte, la compression de ces données - en particulier la compression de maillages - est un enjeu important. Durant la décennie passée, de nombreuses méthodes ont été développées pour coder les maillages polygonaux. Néanmoins, ces techniques ne sont plus adaptées au contexte actuel, car elles supposentque la compression et la d'ecompression sont des processus sym'etriques qui ont lieu sur un mat'erielsimilaire. Dans le cadre actuel, au contraire, le contenu 3D se trouve cr'e'e, compressé et distribué par des machines de hautes performances, tandis que l'exploitation des données - par exemple, la visualisation - est effectuée à distance sur des périphériques de capacité plus modeste - éventuellement mobiles - qui ne peuvent traiter les maillages de grande taille dans leur int'egralité. Ceci fait de lacompression de maillage un processus intrinsèquement asymétrique.Dans cette thèse, notre objectif est d'étudier et de proposer des méthodes pour la compression de maillages de grande taille. Nous nous intéressons plus particulièrement aux méthodes d'accès aléatoire, qui voient la compression comme un problème intrinsèquement asymétrique. Dans ce modèle, le codeur a accès à des ressources informatiques importantes, tandis que la décompression estun processus temps réel (souple) qui se fait avec du matériel de plus faible puissance. Nous décrivons un algorithme de ce type et l'appliquons au cas de la visualisation interactive. Nous proposons aussi un algorithme streaming pour compresser des maillages hexaèdriques de très grande taille utilisés dans le contexte de la simulation numérique. Nous sommes ainsi capables decompresser des maillages comportant de l'ordre de 50 millions de mailles en moins de deux minutes, et en n'utilisant que quelques mégaoctets de mémoire vive. Enfin, nous proposons, indépendamment de ces deux algorithmes, un cadre théorique général pour améliorer la compression de géométrie. Cet algorithme peut être utilisé pour développer des méthodes de prédiction pour n'importe quel algorithme basé sur un paradigme prédictif - ce qui est la cas dela majorité des méthodes existantes. Nous dérivons ainsi des schémas de prédictions compatibles avec plusieurs méthodes de la littérature. Ces schémas augmentent les taux de compression de 9% enmoyenne. Sous des hypothèses usuelles, nous utilisons aussi ces résultats pour prouver l'optimalité de certains algorithmes existants.
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Stoynov, Kiril. "High Order Edge Finite Elements." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755.
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Hsu, Ssuta S. "Automatic Meshing of Free-Form Deformation Solids." BYU ScholarsArchive, 1989. https://scholarsarchive.byu.edu/etd/3453.
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Development of computer models and subsequent finite element analysis, are important aspects of modern engineering design. In this process, the geometry creation and finite element analysis software are well developed; however, the process of discretizing a geometry into a proper finite element model is time consuming and tedious. The work presented here uses the free-form deformation method to create smooth solid models, and invokes a solid subdivision and transition method to generate the hexahedron finite elements. The combination of these two techniques provides an automatic mesh generator that is easy to use, creates acceptable hexahedron elements for finite element analysis, and can model basically any complex shape.
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Reberol, Maxence. "Maillages hex-dominants : génération, simulation et évaluation." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0021/document.
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Cette thèse s'intéresse à la génération, à l'utilisation et à l'évaluation des maillages hex-dominants, composés d'hexaèdres et de tétraèdres, dans la cadre de la simulation numérique par la méthode des éléments finis. Les éléments finis hexaédriques sont souvent préférés aux éléments tétraédriques car ils offrent un meilleur ratio entre précision et temps de calcul dans un certain nombre de situations. Cependant, si la génération automatique de maillages tétraédriques est aujourd'hui un domaine bien maîtrisé, ce n'est pas le cas de la génération de maillages hexaédriques alignés avec le bord, qui reste un problème largement ouvert. En l'absence de progrès significatifs, les approches actuelles se contentent de maillages hex-dominants afin de tirer parti des performances supérieures des hexaèdres et de la flexibilité géométrique des tétraèdres, qui rend possible le maillage automatique. Dans une première partie, nous développons des algorithmes robustes pour la génération de maillages hex-dominants à partir de champs de directions, notamment pour l'isolement et le remplissage des régions difficiles à mailler (singularités et autres dégénérescences). Dans la seconde partie, nous essayons de déterminer dans quelles situations et dans quelle mesure les maillages hexaédriques, et hex-dominants générés précédemment, sont plus intéressants que les maillages tétraédriques. Ceci implique spécifiquement d'étudier plusieurs manières d'effectuer des simulations par éléments finis avec les maillages hybrides, dont une approche où nous utilisons des contraintes de continuité pour maillages non-conformes. Pour mesurer l'influence du maillage sur l'approximation des solutions, nous proposons une nouvelle méthode d'échantillonnage pour calculer très efficacement des distances globales entre solutions éléments finis définies sur des domaines compliquésThis thesis focuses on generation, usage and evaluation of hex-dominant meshes, which are made of hexaehedra and tetrahedra, in the context of the finite element method. Hexahedron finite elements are often preferred to tetrahedron elements because they offer a better compromise between accuracy and computation time in certain situations. However, if tetrahedral meshing is a well mastered subject, it is not the case of hexahedral meshing. Generating hexahedral meshes with elements aligned to the borders is still an open and difficult problem. Meanwhile, current automated approaches can use hex-dominant meshes in order to take advantage of both hexahedron accuracy and geometrical flexibility of tetrahedra. In the first part, we develop robust algorithms for the generation of hex-dominant meshes with elements aligned with the borders. Specifically, we propose a method to extract and fill the areas where hexahedral meshing is difficult (singularities and degeneracies). In the second part, we try to identify and to quantify the advantages of hexahedral and hex-dominant meshes over tetrehedral ones. This requires to study various ways to apply the finite element method on hybrid meshes, including one in which we propose to use continuity constraints on hexahedral-tetrahedral non-conforming meshes. To measure the impact of meshes on the finite element accuracy, we develop a new sampling method which allows to compute efficiently global distances between finite element solutions defined on complicated 3D domains
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Chang, Yi-Hao, and 張益豪. "Hexahedral Mesh Generation Based on Medial Objects." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/01118447040433463639.
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碩士國立成功大學
機械工程學系碩博士班
92
For finite element analysis, hexahedral element mesh can make the computation more efficient and thus in general is a better solution. Therefore, there are more and more researches about automatic hexahedral mesh generation in these years. But the algorithms about automatic hexahedral mesh generation are not robust. This thesis reviews algorithms about hexahedral mesh generation and classifies these algorithms into three categories: direct, indirect, and spatial decomposition. Because the quadrilaterals are the basis for hexahedra mesh generation, it will also be introduced in this study. In addition, this thesis will use the medial object to divide the model into simple geometry and then utilizes the Quad-morph algorithm to construct the quadrilaterals and generates the hexahedra with mapping method.
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"Paving the path towards automatic hexahedral mesh generation." Universitat Politècnica de Catalunya, 2009. http://www.tesisenxarxa.net/TDX-1229109-132237/.
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Hernandez, Roque Julio. "Hybrid particle-element method for a general hexahedral mesh." 2009. http://hdl.handle.net/2152/6676.
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The development of improved numerical methods for computer simulation of high velocity impact dynamics is of importance in a variety of science and engineering fields. The growth of computing capabilities has created a demand for improved parallel algorithms for high velocity impact modeling. In addition, there are selected impact applications where experimentation is very costly, or even impossible (e.g. when certain bioimpact or space debris problems are of interest). This dissertation extends significantly the class of problems where particle-element based impact simulation techniques may be effectively applied in engineering design. This dissertation develops a hybrid particle-finite element method for a general hexahedral mesh. This work included the formulation of a numerical algorithm for the generation of an ellipsoidal particle set for an unstructured hex mesh, and a new interpolation kernel for the density. The discrete model is constructed using thermomechanical Lagrange equations. The formulation is validated via simulation of published impact experiments.text
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Ho, Hsin-Wei, and 何信葳. "The Study of The New Three-Dimensional Hexahedral Elements." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/34414773105240051082.
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碩士國立成功大學
機械工程學系碩博士班
91
A family of new three-dimensional hexahedral elements is proposed in this thesis. When compared with the linear 8 nodes element, quadratic Serendipity 20 nodes element, and quadratic Lagrange 27 nodes element, these new elements spent less computational time and got less approximation errors. The idea for these new elements is using extra nodes in the interior of the hexahedral elements to get high order interpolation functions in the elements. When the element equations are formed, the equations corresponding to these interior degrees of freedom can be eliminated by static condensation. When global system equations are solved, we found that iterative method is much faster than the Gauss elimination method. When new elements are used, less iterative number is needed compared Serendipity elements and Lagrange elements. Compared with the Serendipity elements, the error of the linear new element drops 38% and its computational time drops 1%. The error of the quadratic new element drops 38% and its computational time drops 20%. The error of the cubic new element drops 69% and its computational time drops 35%.
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Sbai, Mohammed Adil. "Modelling three dimensional groundwater flow and transport by hexahedral finite elements." Phd thesis, 1999. http://tel.archives-ouvertes.fr/tel-00006266.
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This research work deals with three-dimensional modeling of groundwater flow and solute transport problems in groundwater aquifer systems, with several complexities, heterogeneities and variable conditions as encountered in the field. Finite element methods are used throughout to solve a range of different problems, using in particular the Galerkin weighted residual approach based on trilinear hexahedral elements. Special emphasis is made on transient and non-linear groundwater flow problems with moving interfaces, such as the water table and the freshwater-saltwater sharp interface. A generalized Fast Updating Procedure technique is developed for these situations, which presents a number of advantageous features in comparison to classic computational techniques used to deal with such problems. One of the important contributions is the automatic construction of the generic soils characteristic curves, which are dynamically dependent upon the overall system water status. Several test examples are successfully worked out for validating this technique in different aquifer configurations, and under different initial and boundary conditions. These test cases show that the proposed method is cheap, numerically stable and accurate. Numerical stability is guaranteed through a developed solver, which is obtained by using state of the art methods for robust preconditioning and efficient numerical implementation. The accuracy is demonstrated by comparison against analytical, other numerical approaches, and laboratory experimental solutions. The usefulness of the method is clearly shown by the application of the 3-D sharp interface finite element model 'GEO-SWIM' to the coastal aquifer system of Martil in the north of Morocco. Several efficient runs are made, leading to a calibrated management model for the study area, giving a clear picture of the salinization risk in the aquifer due to saltwater encroachment. Three-dimensional modeling of solute transport problems in groundwater aquifer systems is equally investigated. It is concluded that the standard Galerkin finite element method is computationally intensive, since the obtained system of numerical equations is very large, sparse, none symmetric and usually difficult to solve with standard iterative techniques. Hence, preconditioning is necessary to improve the convergence behavior of ill-conditioned systems. In this work, we propose an M-matrix type of transformation on the general transport matrix which guarantees the existence of the preconditioning schemes, and hence improves the overall solvers performance and robustness. The usefulness of the method is demonstrated by solving several test examples with different complexities, including hypothetical and field applications in Belgium. Different solvers are tested as the minimal residual method and the stabilized biconjugate gradient method, in combination with different preconditioning schemes, as diagonal scaling and incomplete factorization. It is concluded that M-matrix preconditioning is very simple to implement, and proves to be very efficient and robust. An effort is put on packaging the computer programs, by giving modern visual support to many modules. Therefore, several GUI programs are provided as complementary tools to support the developed models, enabling their friendly use, and the possibility for future extensions.
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Yeh, Yan_Liang, and 葉彥良. "The study of enriched quadrilateral and hexahedral elements for finite element analysis." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/18573038034494179139.
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博士國立成功大學
機械工程學系碩博士班
94
Abstract The concept that adds the high order terms to the shape function of finite element method is presented to enrich the quadrilateral and hexahedral elements and the performance of the enriched elements is discussed in this thesis. The enriched elements combine the shape functions of interior nodes of the Langrage elements and the shape functions of the serendipity elements which are corrected by Kronecker delta function. Since the interior nodes of enriched elements don’t connect with any other element, their degree of freedom can be separated from the linear system. In order to simplify the use of enriched elements, both the static condensation and subparametric formulation are employed in finite element analysis. By the use of the static condensation technique at the element level, the extra computation time in using these elements can be ignored. The procedure can be seen that the coefficient matrix is applied a partial factorization. Therefore, static condensation can be regarded as a precondition. Since this precondition is applied directly to the entities of the coefficient matrix, the iterative method can use another precondition to solve the linear system. By the use of the subparametric formulation, the coordinates of the interior nodes are not necessary in the finite element analysis and the existing programs can generate the mesh for enriched elements. The plane stress problems and three dimensional elastic problems are used to evaluate the performance of enriched quadrilateral and hexahedral elements, respectively. It shows that the results obtained by using the enriched elements are more accurate than those of the traditional serendipity elements. The convergence rate of the proposed elements is the same as that of the traditional serendipity elements. In the numerical examples, the error norm of the first order enriched elements can be reduced when compared with the use of the traditional serendipity element, but the computation time is increased slightly. The use of the second and third order proposed elements not only give an improvement in element accuracy but also save computation time, when the precondition conjugate gradient method is used to solve the linear system. The saving of computation time is due to the decrease of iteration number.
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Liu, Shang-Sheng. "The definition and extraction of shape abstractions for automatic finite element hexahedral mesh generation." 1997. http://catalog.hathitrust.org/api/volumes/oclc/40063668.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1997.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 160-172).
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Bassayya, K. "Development Of A Versatile, 14-node Hexahedral Finite Element, PN5X1, Using Papcovitch-Neuber Potentials." Thesis, 1997. http://etd.iisc.ernet.in/handle/2005/2147.
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Lan, Ting-Heng, and 藍挺恆. "A Human Cervical Spine Quadratic Hexahedral Mesh Generator & Application in Whiplash Injury Simulation." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/36836876971500152817.
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碩士國立臺灣大學
醫學工程學研究所
92
Background. Commercial FE-model generation software for medical use are mostly based on tetrahedral meshes, which have superiority in mapping complex geometric structure of biological objects in the expense of efficiency for FEA (finite element analysis) due to large number of elements. Objectives. To develop a Quadratic hexahedral mesh generation system that is able to generate 3D Quadratic hexahedral meshes FE models of medical objects originally created in STL (Stereolithography) file format. Methods. The 3D STL models of cervical spine (C1-C7) created by MIMICS were imported to the mesh generation system and converted into 3D FE models mapped with 20-nodes hexahedral elements in ABAQUS file format. The models were then applied to static and dynamic mechanical simulation tests in ABAQUS program and compared with the experimental results from previous study. To access the efficiency of mesh generation system, the calculate time (Total CPU Time) to complete simulation tests were compared with tetrahedral-mesh models created by commercial software (AMIRA). Results. With respect to efficiency, the hexahedral-mesh models cost less time to complete simulation tests than tetrahedral-mesh models due to production of smaller numbers of elements. The results of dynamic mechanical simulation test were comparable with that of previous experiment and supported the mechanism of whiplash injury.
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Wang, Bin 1984. "Parallel simulation of coupled flow and geomechanics in porous media." Thesis, 2014. http://hdl.handle.net/2152/28061.
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In this research we consider developing a reservoir simulator capable of simulating complex coupled poromechanical processes on massively parallel computers. A variety of problems arising from petroleum and environmental engineering inherently necessitate the understanding of interactions between fluid flow and solid mechanics. Examples in petroleum engineering include reservoir compaction, wellbore collapse, sand production, and hydraulic fracturing. In environmental engineering, surface subsidence, carbon sequestration, and waste disposal are also coupled poromechanical processes. These economically and environmentally important problems motivate the active pursuit of robust, efficient, and accurate simulation tools for coupled poromechanical problems. Three coupling approaches are currently employed in the reservoir simulation community to solve the poromechanics system, namely, the fully implicit coupling (FIM), the explicit coupling, and the iterative coupling. The choice of the coupling scheme significantly affects the efficiency of the simulator and the accuracy of the solution. We adopt the fixed-stress iterative coupling scheme to solve the coupled system due to its advantages over the other two. Unlike the explicit coupling, the fixed-stress split has been theoretically proven to converge to the FIM for linear poroelasticity model. In addition, it is more efficient and easier to implement than the FIM. Our computational results indicate that this approach is also valid for multiphase flow. We discretize the quasi-static linear elasticity model for geomechanics in space using the continuous Galerkin (CG) finite element method (FEM) on general hexahedral grids. Fluid flow models are discretized by locally mass conservative schemes, specifically, the mixed finite element method (MFE) for the equation of state compositional flow on Cartesian grids and the multipoint flux mixed finite element method (MFMFE) for the single phase and two-phase flows on general hexahedral grids. While both the MFE and the MFMFE generate cell-centered stencils for pressure, the MFMFE has advantages in handling full tensor permeabilities and general geometry and boundary conditions. The MFMFE also obtains accurate fluxes at cell interfaces. These characteristics enable the simulation of more practical problems. For many reservoir simulation applications, for instance, the carbon sequestration simulation, we need to account for thermal effects on the compositional flow phase behavior and the solid structure stress evolution. We explicitly couple the poromechanics equations to a simplified energy conservation equation. A time-split scheme is used to solve heat convection and conduction successively. For the convection equation, a higher order Godunov method is employed to capture the sharp temperature front; for the conduction equation, the MFE is utilized. Simulations of coupled poromechanical or thermoporomechanical processes in field scales with high resolution usually require parallel computing capabilities. The flow models, the geomechanics model, and the thermodynamics model are modularized in the Integrated Parallel Accurate Reservoir Simulator (IPARS) which has been developed at the Center for Subsurface Modeling at the University of Texas at Austin. The IPARS framework handles structured (logically rectangular) grids and was originally designed for element-based data communication, such as the pressure data in the flow models. To parallelize the node-based geomechanics model, we enhance the capabilities of the IPARS framework for node-based data communication. Because the geomechanics linear system is more costly to solve than those of flow and thermodynamics models, the performance of linear solvers for the geomechanics model largely dictates the speed and scalability of the coupled simulator. We use the generalized minimal residual (GMRES) solver with the BoomerAMG preconditioner from the hypre library and the geometric multigrid (GMG) solver from the UG4 software toolbox to solve the geomechanics linear system. Additionally, the multilevel k-way mesh partitioning algorithm from METIS is used to generate high quality mesh partitioning to improve solver performance. Numerical examples of coupled poromechanics and thermoporomechanics simulations are presented to show the capabilities of the coupled simulator in solving practical problems accurately and efficiently. These examples include a real carbon sequestration field case with stress-dependent permeability, a synthetic thermoporoelastic reservoir simulation, poroelasticity simulations on highly distorted hexahedral grids, and parallel scalability tests on a massively parallel computer.text
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Gama, Isa Daniela do Carmo Oliveira. "Previsão da localização da deformação com recurso ao método dos elementos finitos." Master's thesis, 2019. http://hdl.handle.net/10316/93592.
Full textAbstract:
Dissertação de Mestrado Integrado em Engenharia Mecânica apresentada à Faculdade de Ciências e TecnologiaAtualmente, a indústria procura utilizar materiais de elevada resistência, de modo a melhorar a relação entre a resistência e o peso. No entanto, em geral, o aumento da resistência só é alcançado à custa da redução de ductilidade. Assim, surgem dificuldades no processo de conformação plástica do material. Deste modo é essencial o desenvolvimento de métodos de previsão da localização da deformação do material, que possibilitem o desenvolvimento de processos de fabrico que minimizem a ocorrência de defeitos. Neste contexto, a simulação numérica, com recurso ao Método dos Elementos Finitos, surge como uma ferramenta essencial para prever a localização da deformação e o instante em que ocorre durante o processo de conformação. O objetivo desta dissertação é estudar a capacidade do Método dos Elementos Finitos de prever o início da localização da deformação e da fratura dúctil. Neste contexto, revela-se de particular importância avaliar a influência da discretização espacial, mas também do tipo de elemento finito e regra de integração, na evolução dos parâmetros que caracterizam o estado de tensão, uma vez que estes são normalmente utilizados como variáveis internas dos modelos de dano. A influência da discretização espacial adotada foi analisada para o ensaio de tração uniaxial, visto que para este ensaio são conhecidos os parâmetros que caracterizam o estado de tensão, bem como as condições que ditam o início da estrição. O estudo foi realizado considerando diferentes discretizações espaciais e elementos finitos hexaédricos, lineares e quadráticos, com o auxílio do programa DD3IMP. O estudo foi complementado com a análise da influência da regra de integração adotada, para elementos finitos hexaédricos lineares, com o auxílio do programa ABAQUS. Os resultados mostram que, se a análise for restringida ao início da localização da deformação, o refinamento da discretização espacial resulta na convergência dos resultados numéricos, incluindo das variáveis que caracterizam o estado de tensão. No entanto, após a localização da deformação, o refinamento da discretização espacial conduz a um aumento da deformação plástica prevista para o mesmo valor de deslocamento, com a consequente alteração das variáveis que caracterizam o estado de tensão. Para além disso, estas variáveis apresentam distribuições espaciais com oscilações, cuja amplitude é função da discretização espacial, do tipo de elemento e da regra de integração adotada. Estas oscilações resultam da previsão da tensão média em cada ponto de integração. A análise da capacidade de previsão da localização da deformação foi realizada com o ensaio de estampagem de uma taça cilíndrica, com recurso ao programa DD3IMP. O modelo utilizado procurou reproduzir as condições dos ensaios experimentais realizados para determinar a Relação Limite de Estampagem de dois aços Dual Phase (DP500 e DP780). Os resultados mostram que o local onde ocorre a rotura é muito sensível às condições de fronteira adotadas. Globalmente, o local onde ocorre a rotura e, em particular, o instante, são influenciados pela descrição do comportamento plástico do material. Este exemplo permite também evidenciar que, as distribuições espaciais dos parâmetros que caracterizam o estado de tensão apresentam oscilações, incluindo entre pontos de integração do mesmo elemento. Esta variação, associada à sensibilidade à discretização espacial adotada, deve ser considerada na implementação de modelos de dano.
Nowadays, the industry looks for high strength materials to improve the strength to weight ratio. However, the increase of strength normally implies a reduction in ductility, which leads to difficulties in the forming process. Therefore, the development of methods that enable the prediction of the onset of strain localization is essential, since it allows the development of manufacturing processes that minimize the occurrence of defect. In this context, the numerical simulation using the Finite Element Method, is a crucial tool to predict the location where strain localization occurs, as well the instant, during the forming process.The aim of this dissertation is to study the ability of the Finite Element Method to predict the onset of strain localisation and ductile fracture. In this context, it is important to evaluate the influence of the spatial discretisation, as well as the finite element type and the integration rule, on the evolution of the parameters that characterise the stress state, since these are normally used as internal variables of damage models. The influence of the spatial discretisation adopted was analysed for the uniaxial tensile test, since the parameters that characterise the stress state and the conditions that dictate the beginning of necking are known for this test. The study was performed considering different spatial discretisation of hexahedral, linear and quadratic, finite elements, using DD3IMP solver. The study was complemented with the analysis of the influence of the integration rule adopted, for linear hexahedral finite elements, with ABAQUS solver. The results show that, if the analysis is performed before the onset of strain location, the refinement of the spatial discretisation results in the convergence of the numerical results, including that of the variables that characterise the stress state. However, after the onset of strain localisation, the refinement of the spatial discretisation leads to an increase of the predicted equivalent plastic strain for the same displacement value, with the subsequent change of the variables that characterise the stress state. Moreover, these variables present oscillating in their spatial distributions, whose amplitude is a function of the spatial discretization, the element type and of the integration rule adopted. These oscillations result from the mean stress predicted, for each integration point.The analysis of the capability to predict the strain location was performed considering a cylindrical cup forming test, using DD3IMP solver. The model constructed tried to reproduce the conditions of the experimental tests performed to determine the Limiting Draw Ratio of two Dual Phase steels (DP500 and DP780). The results show that the location where the rupture occurs is very sensitive to the boundary conditions adopted. Generally, the location and the instant when fracture occurs are influenced by the description of the plastic behaviour of the material. This example also shows that the spatial distributions of the parameters that characterise the stress state have oscillations, including between integration points of the same element. These oscillations, associated to the sensitivity of the spatial discretization adopted, should be considered in the implementation of damage models.
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Sukaneeyouth, Anan. "Thirty-two nodes hexahedronal element subroutine for multi-purpose program MEF." Thesis, 1986. http://hdl.handle.net/10945/22150.
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Ζάχος, Αναστάσιος. "Το πρόβλημα Fermat-Torricelli και ένα αντίστροφο πρόβλημα στο Κ-επίπεδο και σε κλειστά πολύεδρα του R^3." Thesis, 2014. http://hdl.handle.net/10889/8001.
Full textAbstract:
Το πρόβλημα Fermat-Torricelli για n μη συγγραμμικά σημεία με βαρύτητες στον R^3 (b.FT) διατυπώνεται ως εξής:
Δοθέντος n μη συγγραμμικών σημείων στον R^3 να βρεθεί ένα σημείο το οποίο ελαχιστοποιεί το άθροισμα των αποστάσεων με θετικές βαρύτητες του σημείου αυτού από τα n δοσμένα σημεία.
Το αντίστροφο πρόβλημα Fermat-Torricelli για n μη συγγραμμικά και μη συνεπίπεδα σημεία με βαρύτητες στον R^3 (αντ.FT) διατυπώνεται ως εξής:
Δοθέντος ενός σημείου που ανήκει στο εσωτερικό ενός κλειστού πολυέδρου που σχηματίζεται από n δοσμένα μη συγγραμμικά και μη συνεπίπεδα σημεία στον R^3, υπάρχει μοναδικά προσδιορίσιμο σύνολο τιμών για τις βαρύτητες που αντιστοιχούν σε κάθε ένα από τα n δοσμένα σημεία, ώστε το σημείο αυτό να επιλύει για τις τιμές αυτές των βαρυτήτων το πρόβλημα b.FT στον R^3;
Στην παρούσα διατριβή, αποδεικνύουμε μία γενίκευση της ισογώνιας ιδιότητας του σημείου b.FT για ένα γεωδαισιακό τρίγωνο σε ένα Κ-επίπεδο (Σφαίρα, Υπερβολικό επίπεδο, Ευκλείδειο επίπεδο). Στη συνέχεια, δίνουμε μία αναγκαία συνθήκη για να είναι το σημείο b.FT εσωτερικό σημείο ενός τετραέδρου και ενός πενταέδρου (πυραμίδες) στον R^3.
Η δεύτερη ομάδα αποτελεσμάτων της διατριβής περιλαμβάνει τη θετική απάντηση στο αντ.FT πρόβλημα για τρία μη γεωδαισιακά σημεία στο Κ-επίπεδο και στο αντ.FT πρόβλημα για τέσσερα μη συγγραμμικά και μη συνεπίπεδα σημεία στον R^3.
Η αρνητική απάντηση στο αντ.FT για τέσσερα μη συγγραμμικά σημεία στον R^2 θα μας οδηγήσει σε σχέσεις εξάρτησης των βαρυτήτων που ονομάζουμε εξισώσεις της δυναμικής πλαστικότητας των τετραπλεύρων. Ομοίως, δίνοντας αρνητική απάντηση στο αντ.FT πρόβλημα για πέντε μη συνεπίπεδα σημεία στον R^3, παίρνουμε τις εξισώσεις δυναμικής πλαστικότητας , διατυπώνουμε και αποδεικνύουμε την αρχή της πλαστικότητας των κλειστών εξαέδρων στον R^3, που αναφέρει ότι:
Έστω ότι πέντε προδιαγεγραμμένα ευθύγραμμα τμήματα συναντώνται στο σημείο b.FT, των οποίων τα άκρα σχηματίζουν ένα κλειστό εξάεδρο. Επιλέγουμε ένα σημείο σε κάθε ημιευθεία που ορίζει το προδιαγεγραμμένο ευθύγραμμο τμήμα, τέτοιο ώστε το τέταρτο σημείο να βρίσκεται πάνω από το επίπεδο που σχηματίζεται από την πρώτη και δεύτερη προδιαγεγραμμένη ημιευθεία και το τρίτο και πέμπτο σημείο να βρίσκονται κάτω από το επίπεδο που σχηματίζεται από την πρώτη και δεύτερη προδιαγεγραμμένη ημιευθεία. Τότε η μείωση της τιμής της βαρύτητας που αντιστοιχεί στην πρώτη, τρίτη και τέταρτη προδιαγεγραμμένη ημιευθεία προκαλεί αύξηση στις βαρύτητες που αντιστοιχούν στη δεύτερη και πέμπτη προδιαγεγραμμένη ημιευθεία.Τέλος, ένα σημαντικό αποτέλεσμα της διατριβής αφορά την επίλυση του γενικευμένου προβλήματος του Gauss για κυρτά τετράπλευρα στο Κ-επίπεδο, θέτοντας δύο σημεία στο εσωτερικό του κυρτού τετραπλεύρου με ίσες βαρύτητες, τα οποία στη συνέχεια αποδεικνύουμε ότι είναι δύο σημεία b.FT με συγκεκριμμένες βαρύτητες, αποτέλεσμα το οποίο γενικεύει το πρόβλημα b.FT για τετράπλευρα στο Κ-επίπεδo.The weighted Fermat-Torricelli for n non-collinear points in R^3 states the following: Given n non-collinear points in R^3 find a point (b.FT point) which minimizes the sum of the distances multiplied by a positive number which corresponds to a given point (weight). The inverse Fermat-Torricelli problem for n non-collinear points with weights in R^3 (inv.FT) states the following: Given a point that belongs to the interior of a closed polyhedron which is formed between n given non-collinear points in R^3, does there exist a unique set of weights which corresponds to each one of the n points such that this point solves the weighted Fermat-Torricelli problem for this particular set of weights? In the present thesis, we prove a generalization of the isogonal property of the b.FT point for a geodesic triangle on the K-plane (Sphere, Hyperbolic plane, Euclidean plane). We proceed by giving a sufficient condition to locate the b.FT point at the interior of tetrahedra and pentahedra (pyramids) in R^3. The second group of results contains a positive answer on the inv.FT problem for three points that do not belong to a geodesic arc on the K-plane and on the inv.FT problem for four non collinear points and non coplanar in R^3. The negative answer with respect to the inv.FT problem for four non-collinear points in R^2 lead us to the relations of the dependence between the weights that we call the equations of dynamic plasticity for quadrilaterals. Similarly, by giving a negative answer with respect to the inv.FT problem for five points which do not belong in the same plane in R^3, we derive the equations of dynamic plasticity of closed hexahedra and we prove a plasticity principle of closed hexahedra in R^3, which states that: Considering five prescribed rays which meet at the weighted Fermat-Torricelli point, such that their endpoints form a closed hexahedron, a decrease on the weights that correspond to the first, third and fourth ray, causes an increase to the weights that correspond to the second and fifth ray, where the fourth endpoint is upper from the plane which is formed from the first ray and second ray and the third and fifth endpoint is under the plane which is formed from the first ray and second ray. Finally, a significant result of this thesis deals with the solution of the generalized Gauss problem for convex quadrilaterals on the K-plane in which by setting two points at the interior of the convex quadrilateral with equal weights we prove that these points are weighted Fermat-Torricelli points with specific weights, that generalizes the b.FT problem for quadrilaterals on the K-plane.