Este trabalho apresenta a aplicação do Método de Otimização Topológica (MOT) considerando restrição de tensão mecânica em dois problemas de Engenharia: o projeto de estruturas mecânicas sujeitas a restrição de tensão e o projeto da distribuição de material em estruturas constituídas por Materiais com Gradação Funcional (MsGF). O MOT é um método numérico capaz de fornecer de forma automática o leiaute básico de uma estrutura mecânica para que esta atenda a um dado requisito de projeto, como o limite sobre a máxima tensão mecânica no componente. Os MsGF são materiais cujas propriedades variam gradualmente com a posição. Este gradiente de propriedades é obtido através da variação contínua da microestrutura formada por dois materiais diferentes. Neste trabalho o MOT foi implementado utilizando o modelo de material Solid Isotropic Microstructure with Penalization (SIMP) e o campo de densidades foi parametrizado utilizando a abordagem Aproximação Contínua da Distribuição de Material (ACDM). O modelo de material e utilizado em conjunto com um localizador de tensões, de modo a representar as tensões nas regiões com densidade intermediária. O projeto de estruturas tradicionais através do MOT possui dois problemas centrais aqui tratados: o fenômeno das topologias singulares, que consiste na incapacidade do algoritmo de otimização de retirar material de certas regiões da estrutura, onde a tensão mecânica supera o limite de tensão quando os valores da densidade tendem a zero, e o problema do grande número de restrições envolvidas, pois que a tensão mecânica é uma grandeza local e deve ser restrita em todos os pontos da estrutura. Para tratar o primeiro problema é utilizado o conceito de relaxação. Para o segundo são utilizadas duas abordagens: uma é a substituição das restrições locais por uma restrição global e a outra é a aplicação do Método do Lagrangeano Aumentado. Ambas foram implementadas e aplicadas para o projeto de estruturas planas e axissimétricas. No projeto da distribuição de material em estruturas constituídas por MsGF é utilizado um modelo de material baseado na interpolação dos limites de Hashin-Shtrikman. A partir deste modelo as tensões em cada fase são obtidas a partir das matrizes localizadoras de tensão. Para tratar o fenômeno das topologias singulares é proposto um índice estimativo de falha, baseado nas tensões de von Mises em cada fase da microestrutura, que evita tal problema. O grande número de restrições é tratado através da restrição global de tensão. Em ambos os problemas as formulações são apresentadas e sua eficiência é discutida através de exemplos numéricos. / This work presents the Topology Optimization Method (TOM) with stress constraint applied to two Engineering problems: the design of mechanical structures subjected to stress constraint and the design of material distribution in structures made of Functionally Graded Materials (FGMs). The TOM is a numerical method capable of synthesizing the basic layout of a mechanical structure accomplishing to a given design requirement, for example the maximum stress in the structure. The FGMs are materials with spatially varying properties, which are obtained through a continuum change of the microstructuremade of two different materials. In this work, the TOM was implemented with Solid Isotropic Microstructure with Penalization (SIMP) material model and the density field was parameterized with the Continuous Approximations of Material Distribution. To obtain the intermediate density stresses, the material model is applied together with a stress localization matrix. The design of mechanical structures through the TOM has two major problems: the singular topology phenomenon, which is characterized by the optimization algorithm impossibility of removing material from certain regions, where the stress overpasses the limiting stress when the density goes to zero, and the large number of constraints, once the stress is a local value that must be constrained everywhere in the structure. To deal with the first problem, it is applied the \"-realaxation concept, and for the second one two approaches are considered: one is to change the local stress constraint into a global stress constraint and the other is to apply the Augmented Lagrangian Method. Both approaches were implemented and applied to the design of plane and axisymmetric structures. In the design of material distribution in structures made of FGMs a material model based on Hashin-Shtrikman bounds is applied. From this model, stresses in each phase are obtained by the stress localization matrix. To deal with the singular topology phenomenon it is proposed a modified von Mises failure criteria index that avoids such problem. A global stress constraint is applied to deal with the large number of constraints. In both problems formulations are presented and their performance are discussed through numerical examples.

O objetivo do presente estudo foi verificar a possibilidade de identificação dos dois limiares metabólicos pelo comportamento da VFC. Para isso, 22 voluntários do gênero masculino [74,5 + 7,99kg, 177,0 + 8cm, 23,86 + 1,69 (índice de massa corporal) e 9,10 % de gordura], habituados à prática do ciclismo, realizaram teste ergométrico em bicicleta estacionária com carga inicial de 120W e incrementos de 30W a cada 3min, até a exaustão. Durante todo o teste foram feitos os registros da freqüência cardíaca (FC) e de sua variabilidade (VFC) e ao final de cada carga foram coletados 25µL de sangue para análise da concentração sangüínea de lactato. Aplicou-se um modelo matemático que ajustou a curva da VFC em três retas e o primeiro e segundo limiar de VFC foram identificados nas intersecções entre as retas. Para identificação do primeiro e segundo limiar de lactato, considerou-se as concentrações fixas de 2,0 e 3,5mM, respectivamente. A análise de variância para medidas repetidas indicou não haver diferenças significativas nas cargas em que os limiares de VFC e de lactato foram encontrados, mostrando que a metodologia proposta pode ser promissora. Entretanto a falta de correlação entre as variáveis indica que novos estudos necessitam ser realizados para confirmação desta possibilidade. / The purpose of this study was to verify the possibility of metabolic thresholds identifications through HRV. For that, 22 male volunteers [74,5 + 7,99kg, 177,0 + 8cm, 23,86 + 1,69 (body mass index) e 9,10 % fat], familiarized to cyclism practice, realized a cycloergometer test with initial load of 120W and 30W increases every 3min., until exhaustion. During all test, it was registered heart rate (HR) and its variability (HRV) and, at the end of each load, it was collected 25mL blood for lactate concentration analysis. It was applied a mathematical model to adjust HRV curve in three straight lines and first and second HRV thresholds were identified in intersections among the lines. For the identification of first and second lactate thresholds, it was considered 2,0 and 3,5mM fixed concentrations, respectively. Variance analysis for repeated measures indicated that there were no significant differences between loads in which HRV and lactate thresholds were found, showing that purposed methodology can be promissor. However, the lack of correlation between variables indicate that new studies must be made to confirm that possibility.

Palms support the largest leaves in the world and have evolved on Earth for over 120 million years. They are often reported to be the only structure left standing post-hurricane. Cross-sectional shapes of cantilevered structures are important design factors affecting torsional and bending performance. Understanding the shape contribution of natural sections such as palm petioles (modified leaf stalks) is more difficult than those for simple 2D shapes because conventional methods of calculating section properties are not well suited to these irregular shapes. The role of internal structure, material properties and external shape of palm petioles in cantilever performance has been investigated and three main contributions to knowledge result from this research. Firstly, 3D mapping, i.e., the size, orientation and position, of vascular bundles in the Trachycarpus fortunei palm petiole reveals the distributions of stress and Young’s modulus values, providing a more detailed understanding of petioles than previous work. Secondly, bulk elastic material properties along the longitudinal axis of the same petiole are then input to a bi-layered model of the same petiole establishing the Young’s modulus of the two layers without mechanically testing them individually and for determining that the outer layer is not lignified. Thirdly, the largest contribution is the introduction of modified shape transformers employing the use of circular envelopes, eliminating error caused by approximating second moment of area with the torsional constant. This leads to a novel Shape Edge Mapping (SEM) technique which deconstructs petiole cross section shape elements and enables the structural contribution of these elements to be calculated, improving the understanding of the petiole section and how it relates to its mechanical function. This thesis makes a valuable addition to the knowledge of palm function and presents novel techniques for non-destructive extraction of natural shape data for abstraction and use in preliminary engineering design.

"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

This master thesis is aimed at the didactic concept of natural communities at village schools with age-mixed-pupil classes. The introductory part summarizes basic facts of the classes, the natural communities such as the forest, meadow, water and its basic characteristics. This part also outlines views of teaching natural science to young pupils by different authors. The second part consists of suggested teaching methods, discussion with hunters and teaching with walks in the countryside. The suggested teaching methods have been thaught at two different age-mixed-pupil classes. Success of the teaching methods has been scrutinized through a test the pupils have worked with two times, before and after the teaching. The final part of the thesis sums up the conditions, process, acquired knowledge and the evaluation of the methods.

Propagation of cracks in functionally graded materials (FGMs) under cyclic loading was investigated via experiments and finite element (FE) analysis. Alumina-epoxy composites with an interpenetrating-network structure and tailored spatial variation in composition were produced via a multi-step infiltration technique. Compressed polyurethane foam was infiltrated with alumina slip. After foam burn-out and sintering, epoxy was infiltrated into the porous alumina body. Non-graded specimens with a range of compositions were produced, and elastic properties and fatigue behaviour were characterised. An increase in crack propagation resistance under cyclic loading was quantified via a novel analytical approach. A simulation platform was developed with the commercial FE package ANSYS. Material gradient was applied via nodal temperature definitions. Stress intensity factors were calculated from nodal displacements near the crack-tip. Deflection criteria were compared and the local symmetry criterion provided the most accurate and efficient predictions. An automated mesh-redefinition algorithm enabled incremental simulation of crack propagation. Effects of gradient and crack-geometry parameters on crack-tip stresses were investigated, along with influences of crack-shape, crack-bridging, residual stresses and plasticity. The model provided predictions and data analysis for experimental specimens. Fatigue cracks in graded specimens deflected due to elastic property mismatch, concordant with FE predictions. In other FGMs, thermal or plastic properties may dominate deflection behaviour. Weaker step-interfaces influenced crack paths in some specimens; otherwise effects of toughness variation and gradient steps on crack path were negligible. Crack shape has an influence, but this is secondary to that of elastic gradient. Cracks in FGM specimens initially experienced increase in fatigue resistance with crack-extension followed by sudden decreases at step-interfaces. Bridging had a notable effect on crack propagation resistance but not on crack path. Similarly, crack paths did not differ between monotonic and cyclic loading, although crack-extension effects did. Recommendations for analysis and optimisation strategies for other FGM systems are given. Experimental characterization of FGMs is important, rather than relying on theoretical models. Opportunities for optimization of graded structures are limited by the properties of the constituent materials and resultant general crack deflection behaviour.

Graded InGaN buffers were employed to relax the strain arising from the lattice and thermal mismatch in GaN/InGaN epilayers grown on sapphire. An enhanced strain relaxation was observed in GaN grown on a stack of five InGaN layers, each 200 nm thick with the In content increased in each layer, and with an intermediate thin GaN layer, 10 nm thick inserted between the InGaN layers, as compared to the conventional two-step growth of GaN epilayer on sapphire. The function of the intermediate layer is to progressively relax the strain and to annihilate the dislocations that build up in the InGaN layer. If the InGaN layers were graded too rapidly, more dislocations will be generated. This increases the probability of the dislocations getting entangled and thereby impeding the motion of the dislocations to relax the strain in the InGaN layer. The optimum growth conditions of the intermediate layer play a major role in promoting the suppression and filling of the V-pits in the GaN cap layer, and were empirically found to be a thin 10 nm GaN grown at 750 0°C and annealed at 1000 0°C. / Singapore-MIT Alliance (SMA)

Graded InGaN buffers are employed to relax the strain arising from the lattice and thermal mismatches between GaN/InGaN epilayers grown on sapphire. The formation of V-pits in linearly graded InGaN/GaN bulk epilayers is illustrated. The V-pits were sampled using Atomic Force Microscopy and Scanning Electron Microscopy to examine their variation from the theoretical geometry shape. We discovered that the size of the V-pit opening in linearly graded InGaN, with and without GaN cap layer, has a Gaussian distribution. As such, we deduce that the V-pits are produced at different rates, as the growth of the InGaN layer progresses. In Stage I, the V-pits form at a slow rate at the beginning and then accelerate in Stage II when a critical thickness is reached before decelerating in Stage III after arriving at a mean size. It is possible to fill the V-pits by growing a GaN cap layer. It turns out that the filling of the V-pits is more effective at lower growth temperature of the GaN cap layer and the size of the V-pits opening, which is continued in to GaN cap layer, is not dependent on the GaN cap layer thickness. Furthermore, graded InGaN/GaN layers display better strain relaxation as compared to conventionally grown bulk GaN. By employing a specially design configuration, the V-pits can be eliminated from the InGaN epilayer. / Singapore-MIT Alliance (SMA)

This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell⁰́₉s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells⁰́₉ interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this thesis we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a universal finite type invariant.