In micro-structure theory, the equations of motion have their foundations in the relation tension / deformation. Microstructure analysis is focused on the science of preparing, interpreting and studying microstructures in engineering materials to understand the behavior and performance of materials. There is a need to evaluate the methods of manufacturing metallic materials for use in the metal industry, including the aerospace industry, the automotive industry, and parts of the construction industry. From a project point of view, the control of vibrations in micro-structures plays a key role. In this work, a bar of the Euler-Bernoulli type with conditions of the crimping-free type. The aim is to analyze the effects of vibrations in in the crimped end of the frame. For control purposes, a field magnetic field at the free end and the distance from the magnetic field source to the control parameter. It is shown that this control design introduces boundary conditions not linear in the formulation of the equations of motion of the structure. The deformation field, in turn, describes the curvature, which can be obtained through the displacement field in a first and second order nonlinear relationship. Assuming small displacements in the deflection angle, the moment / curvature relationship can be described by means of the second-order derivative of the displacement field. This model allows the analysis of the terms of shear forces and momentum that are present in the theory. Like this using the variational principle, the equations of motion are obtained, which allows to determine the field of displacement. The finite element method is used to discretize the equations of motion. Due to the complexity of equations involved the finite difference method is employed to model the nonlinear problem.

ABSTRACT Proposing technological innovations in the investigation of the structure and behaviour of wood is important to optimize its use. The assimilation of methods diffused in other areas, such as particle image velocimetry (PIV), can allow a rich range of information for different aspects. The aim of this study was to estimate the Young’s modulus using the PIV technique, independently of the wood density. The Young modulus value was obtained by universal testing machine, transversal vibration and PIV technique. Cedrela spp. and Eucalyptus cloeziana wood specimens were analyzed and their Young modulus were compared and correlated. The PIV technique presented mean Young’s modulus values statistically equal to those of the universal testing machine. The standard error of prediction from PIV approach was 0.46 and 0.97 GPa for Young’s modulus estimates for Cedrela spp. and Eucalyptus cloeziana wood, respectively.

The test data of metals, brittle materials and polymers in high, medium and low strain-rate range were summarized. It was found that the dynamic strength or yield stress of these materials was not sensitive to strain-rate in the low and high strain-rate range (corresponding to weak sensitivity area and saturated zone). But in the medium strain-rate range (strong sensitivity area), the dynamic strength or yield stress of these materials was extremely sensitive to strain-rate. The strain-rate effect function in classic Johnson-Cook constitutive model could not describe these phenomena in the range of low to high strain-rate. Therefore, the strain-rate effect function in classic Johnson-Cook constitutive model has been modified to a strain-rate effect expression which is suitable for different materials. This new model can better describe the phenomena of the weak sensitivity area, strong sensitivity area and saturated zone. With this model, the fitted curves are in good agreement with the test data, and the parameters are different for different materials. Finally, the fitting parameters are given.

PIV (particle image velocimetry) has been spreading in studies that use the movement of particles to monitor the displacement of an object or the flow of a fluid by means of velocity vectors using optical techniques and second order statistics. PIV is also known as laser speckle velocimetry when associated with speckle patterns. This technique has been used in works involving fluids, in general, building a map of velocity vectors representing the flow under analysis. This paper presents an approach by using PIV associated to speckle patterns for deformation measurements in a cantilever beam (ASTM A36 steel), one of the most common examples used in civil engineering, without the introduction of external particles. Results showed that the difference between PIV associated to speckle patterns and the analytic displacement values is increased along the beam length for a load of 1.96 N as an evidence of sensitivity of the proposed measurement method. This indicates that PIV is also capable for detecting displacement fields associated with laser speckle patterns in solid mechanics generating a map of deformation as an additional option for non-destructive tests.

A otimização topológica de peças vem se tornando uma realidade no dia a dia de empresas que as fabricam. Com o advento da impressão 3D, inicialmente para materiais poliméricos e para metálicos, a construção de peças otimamente projetadas tem se intensificado. Devido ao uso racional e eficiente das resistências dos materiais, as peças podem apresentar comportamentos que exigem performance destes materiais. A análise não-linear geométrica permite levar em conta efeitos importantes da deformação da peça, principalmente quando feita em materiais poliméricos (p.e., PLA) e de forma esbelta, com maior precisão para deformações, deslocamentos e tensões mais reais. O presente trabalho propõe a implementação de uma formulação para otimização topológica não-linear geométrica de materiais utilizando uma metodologia BESO (Bi-directional Evolutionary Structural Optimization). São avaliados resultados para casos benchmark da literatura em comparação com os resultados do código implementado. Obteve-se com a implementação resultados similares aos encontrados na literatura e topologias finais muito semelhantes.

Com o avanço dos recursos computacionais, o uso da ferramenta de otimização topológica vem se tornando uma constante no dia a dia do projeto de estruturas, peças e equipamentos. Entretanto, manter o nível de segurança nestes projetos otimizados passa a ser uma necessidade, visto que a estrutura final está otimamente projetada. Apenas em situações bem específicas, o projeto pode ser baseado e assegurado para apenas um caso de carregamento, sendo comum a existência de carregamentos dinâmicos e de múltiplas possibilidades de solicitação ao longo da vida útil da peça. Neste trabalho, é desenvolvido um código para otimização topológica com a inclusão de múltiplos casos de carregamento, com o objetivo de manter a segurança da peça otimamente projetada. O código é baseado na metodologia BESO. Exemplos numéricos da literatura são utilizados para validar o algoritmo desenvolvido demonstrando a importância da inclusão do efeito destes carregamentos na topologia final da peça.

A low-cost and simple magnetic particle tracer method was adapted to characterize the hydrodynamic behavior of an internal- and an external-loop airlift reactor (ALR). The residence time distribution of three magnetic particles differing in diameter (5.5, 11.0 and 21.2mm) and with a density very close to that of water was measured in individual reactor sections. The measured data were analyzed and used to determine the velocity of the liquid phase. Validation of the experimental results for liquid velocity was done by means of the data obtained by an independent reference method. Furthermore, analysis of the differences found in the settling velocity of the particle in single-liquid and gas-liquid phases was carried out, using a simplified 3D momentum transfer model. The model considering particle-bubble interaction forces resulting from changes in the liquid velocity field due to bubble motion was able to predict satisfactorily the increase in the particle settling velocity in the homogeneous bubbly regime. The effective drag coefficient in two-phase flow was found to be directly dependent on particle Reynolds number to the power of - 2 but independent of gas flow-rate for all particle diameters studied. Based on the experimental and theoretical investigations, the valid exact formulation of the effective buoyancy force necessary for the calculation of the correct particle settling velocity in two-phase flow was done. In addition, recommendations concerning the use of flow-following particles in internal-loop ALRs for liquid velocity measurements are presented.