Surface mesh generation is a critical component of the mesh generation process. The objective of the described effort was to determine if a combination of constrained Delaunay triangulation (for triangles), advancing front method (for quadrilaterals), curvature-based refinement, smoothing, and reconnection is a viable approach for discretizing a NURBS patch holding the boundary nodes fixed. The approach is significant when coupled with recently developed geometry specification that explicitly identifies common edges. This thesis describes the various techniques used to achieve the above objectives. Application of this approach to several representative geometries demonstrates that it is an effective alternative to traditional approaches.

Glass fiber based polymer composites based injection molded parts provide a light-weight high-strength alternative for use in automobile applications. These composites have enhanced mechanical properties compared to those of pure polymers, if the fibers are oriented in the right direction. One of the major challenges in processing of these composites is to control the fiber orientation in the final product. The evolution of short glass fiber orientation in a center-gated disk was experimentally determined along the radial direction at three different heights representative of the shell, transition and core layers, respectively. Orientation data along the shell and transition layers in the lubrication region show shear flow effects, which tends to align the fibers along the flow direction. In the core layer, where the extension in the "-direction dominates, fibers tend to get aligned along the "-direction. In the frontal flow region orientation in the flow direction drops in all three layers due to fountain flow effects. Fiber orientation predictions in coupled and decoupled transient simulations using the Folgar-Tucker model, and the two slow versions of the Folgar-Tucker model, namely the slip Folgar-Tucker model and the reduced strain closure (RSC) model were compared with the experimental data. Measured inlet orientation was used in all simulations and model parameters were determined by fitting model predictions to rheological data under startup of shear. Pseudo-concentration method was implemented for the modeling of the advancing front and fountain flow effects in the region near the front. Discontinuous Galerkin finite element method and a third order Runge-Kutta total variance diminishing time integration scheme were implemented for the solution of the orientation and transport equations. In the lubrication region of the shell layer, all three orientation models provided a good match with the experimental data. In the frontal region, fountain flow simulations showed characteristic features seen in r- and z-profiles of orientation, although the experimental data showed these features at a relatively larger distance behind the front while the simulations predicted these effects only up to a small distance behind the front. On the other hand, orientation predictions with the Hele-Shaw flow approximation showed significant over-predictions in the frontal region. With model parameters determined from fitting to rheological data, coupling did not show any significant improvements. However, with the use of a smaller value of the fiber interaction parameter, coupling showed significant improvement in orientation predictions in all three layers in the frontal region. The simulation scheme was extended to long fiber systems by comparing available long fiber orientation data in a center-gated disk with model predictions using the Bead-Rod model which considers fiber bending, a property exhibited by long semi-flexible fibers. The Bead-Rod model showed improvements over rigid fiber models in the lubrication region of the shell layer. However, close to the front, both models showed similar predictions. In fountain flow simulations, the flow features seen in the r- and z-profiles were much better predicted with both the models while Hele-Shaw flow approximation showed over-prediction of orientation in the flow direction, especially in the shell layer. / Ph. D.

[pt] O objetivo deste trabalho é apresentar uma nova estratégia para o problema de empacotamento de discos sem sobreposição para gerar arranjos aleatórios densos. O algoritmo geométrico adota uma abordagem frente de avanço que, com o apoio de uma malha poligonal, utiliza novas heurísticas para determinar as próximas posições para as próximas partículas. Além disso, propomos esquemas de realocação para melhorar o empacotamento no interior do arranjo e perto das bordas dos objetos arbitrários que contêm as partículas. Os resultados provam que nosso algoritmo pode superar trabalhos anteriores, não apenas com a função de distribuição de raios de partículas desejada, mas também aumentando a densidade de empacotamento e o número médio de contatos. / [en] This work aims to present a new strategy for the non-overlapping disk packing problem to generate dense random assemblies. The geometric algorithm adopts an advancing front approach that uses new heuristics to determine the next positions for the incoming particles with the support of a polygonal mesh. Furthermore, we propose relocation schemes to improve the packing at the pack s interior and near the container borders. Experiments prove that our algorithm outperforms previous results, w.r.t the desired particle radii distribution function and increases the packing density and mean number of particle contacts.