Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

Comportamento mecânico de espumas de ligas de alumínio modeladas com recurso a micro-tomografia computorizada de raios-X

In recent years, there has been an increase in interest in cellular materials for structural applications, especially cellular metals (e.g., metal foams made of aluminium and its alloys). These closed-cell and open-cell foams usually have complex cellular structures resulting from the foaming process and their mechanical properties are governed by their cellular structures and by the properties of the base material. However, their mechanical characterization is difficult and most of the times can result in the destruction of the foam specimen. In this study, X-ray microcomputed tomography (µCT) was used together with finite element modelling to develop numerical models to estimate the elastic moduli and evaluate the effects of processing of the information obtained with the µCT scans in the final results. Such a technique complements experimental testing and brings great versatility. In order to accomplish this task, different thresholding techniques (segmentation) were applied to the 2D slices, which are the result of µCT scans, with special focus on a manual global technique with the mass as a quality indicator. Then, some reconstruction algorithms (e.g. Marching Cubes 33) were used to create 3D tessellated models in the STL format, which were oversampled (excessive number of faces) and with errors. Therefore, a simplification/clean-up procedure was applied to solve those issues, being analysed in terms of mass maintenance, shape maintenance with the Hausdorff algorithm and face quality, i.e., face aspect ratio. Two different procedures were evaluated, with and without small structural imperfections, so that the impact of the procedures could be analysed as well as the effect of the presence of small defects. The results obtained were evaluated and compared to several analytical and theoretical models, models based on representative unit-cells and experimental results in terms of the relation between the relative density and the relative Young’s modulus. Results demonstrated that the developed procedures were very good at minimizing changes in mass and shape of the geometries while providing good face quality, i.e., face aspect ratio. The models were also shown to be able to predict the properties of metallic foams in accordance with the findings of other researchers. In addition, the process of obtaining the models and the presence of small structural imperfections were shown to have a great impact on the final results.Nos últimos anos, tem-se verificado um aumento do interesse na área dos materiais celulares, mais especificamente metais celulares, para aplicações estruturais (por exemplo, espumas metálicas de alumínios e as suas ligas). Estas espumas de célula aberta e fechada têm, normalmente, uma estrutura celular complexa resultante do processo de espumação e as suas propriedades mecânicas dependem das suas estruturas celulares e das propriedades do material base. No entanto, a caracterização mecânicas destes materiais é difícil e resulta, regularmente, na destruição dos specimens de espuma. Neste estudo, Micro-Tomografia Computorizada de Raios-X (µCT) foi aplicada juntamente com modelação por elementos finitos para desenvolver modelos numéricos que conseguem estimar os módulos de elasticidade e avaliar os efeitos do processamento da informação obtida pelos scans de µCT nos resultados finais. Esta técnica complementa os procedimentos experimentais e traz uma grande versatilidade. Para se completar a tarefa proposta, diferentes métodos de segmentação foram aplicados às fatias 2D, que são resultantes dos scans de µCT, com especial atenção num método de segmentação manual global que utiliza a massa como indicador de qualidade. Depois disso, alguns algoritmos de reconstrução, por exemplo, Marching Cubes 33, foram aplicados para criar modelos 3D de faces triangulares no formato STL que demonstram sobreamostragem (excessiva quantidade de faces) e alguns erros. Por essa razão, um procedimento de simplificação/limpeza foi aplicado para resolver estes problemas, sendo analisados em termos de preservação de massa, preservação de forma com o algoritmo de Hausdorff e qualidade das faces, ou seja, razão de proporção. Dois procedimentos diferentes foram avaliados, um com e outro sem pequenos defeitos estruturais para que se consiga analisar não só o impacto do processamento dos modelos assim como o efeito da presença de pequenos defeitos. Os resultados obtidos foram comparados com vários modelos analíticos e teóricos, modelos baseados em células unitárias representativas e resultados experimentais com base na relação entre a densidade relativa e o modulo de Young relativo. Os resultados demonstraram que os procedimentos desenvolvidos são bons a preservar a massa e forma das geometrias deixando as faces com boa qualidade. Verificou-se também que os modelos foram capazes de prever as propriedades das espumas metálicas em concordância com o trabalho de outros investigadores. Adicionalmente, mostrou-se que o processo de obtenção dos modelos e a presença de pequenas imperfeiçoes estruturais tem um impacto relevante nos resultados finais.Mestrado em Engenharia Mecânic

Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure

Modelling the induced magnetic signature of naval vessels

In the construction of naval vessels stealth is an important design feature. With recent advances in electromagnetic sensor technology the war time threat to shipping posed by electromagnetically triggered mines is becoming more significant and consequently the need to understand, predict and reduce the electromagnetic signature of ships is growing. There are a number of components to the electromagnetic field surrounding a ship, with each component originating from different physical processes. The work presented in this study is concerned with the magnetic signature resulting from the magnetisation of the ferromagnetic material of the ship, under the influence of the earth's magnetic field. The detection threat arising from this induced magnetic signature has been known for many years, and consequently, warships are generally fitted with degaussing coils which aim to generate a masking field to counteract this signature. In this work computational models are developed to enable the induced magnetic signature and the effects of degaussing coils to be studied. The models are intended to provide a tool set, to aid the electromagnetic signature analyst in ensuring that pre-production designs of a vessel lie within specified induced magnetic signature targets. Techniques presented where also allow the rapid calculation of currents in degaussing coils. This is necessary because the induced magnetisation of a vessel changes with orientation. Three models are presented within this work. The first model represents a ship as a simple geometric shape, a prolate spheroidal shell, of a given relative permeability. Analytical expressions are derived which characterise the magnetic perturbation to a previously uniform magnetic field, the earth's magnetic field, when the spheroid is placed within its influence. These results provide a quantitative insight into the shielding of large internal magnetic sources by the hull. This model is intended for use in preliminary design studies. A second model is described which is based on the finite element method. This is a numerical model which has the capability of accurately reproducing the relatively complex geometry of a ship and of including the effects of degaussing coils. For these reasons this model is intended for detailed quantitative studies of the induced magnetic signature. A method is described to calculate the optimal set of degaussing coil currents required to minimise the induced magnetic signature. The induced signature without and with degaussing is presented. For the successful application of the finite element method the generation of a mesh is of extreme importance. In this work a mesh generation procedure is described which permits meshes to be generated around a collection of planar surfaces. The relatively complex geometry of a ship can be easily specified as a number of planar surfaces and from this, the finite element mesh can be automatically generated. The automatic mesh generation detailed in this work eliminates an otherwise labour intensive step in the analysis procedure. These techniques are sufficiently powerful to allow meaningful calculations for real ships to be performed on desk-top computers of modest power. An example is presented which highlights the application of this model to a hypothetical ship structure. The third model detailed is specifically designed to study the induced magnetic signature of mine countermeasures vessels. Here the induced magnetic signature is no longer dominated by the gross structure of the ship, which is constructed from non-magnetic materials, but arises from the combined effect of the individual items of machinery onboard the craft

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part I: Theory, Concept and Implementation

Due to steadily increasing problem sizes and accuracy requirements as well as storage restrictions on single-processor systems, the efficient numerical simulation of realistic fire scenarios can only be obtained on modern high-performance computers based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical concepts which must guarantee the same result as a potentially corresponding serial execution and preserve the convergence order of the original serial method. Because of its low degree of inherent parallelizm, especially the efficient parallelization of the elliptic pressure equation is still a big challenge in many simulation programs for fire-induced flows such as the Fire Dynamics Simulator (FDS). In order to avoid losses of accuracy or numerical instabilities, the parallelization process must definitely take into account the strong global character of the physical pressure. The current parallel FDS solver is based on a relatively coarse-grained parallellization concept which can’t guarantee these requirements in all cases. Therefore, an alternative parallel pressure solver, ScaRC, is proposed which ensures a high degree of global coupling and a good computational performance at the same time. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness