This dissertation presents an approach to use blade tip timing measurements with finite element analysis to predict the fatigue life of a low pressure steam turbine last stage blade under high backpressure and low flow conditions. Material fatigue properties were determined through the extended universal material law for FV566 material, along with different temper scenarios. A finite element model of a blade with damping pins was developed, using the principle of cyclic symmetry for a perfectly tuned model. Pre-stress modal analysis was conducted, incorporating damping via friction and plasticity for initial 20% overspeed test. The finite element model was verified by two experimental tests: the first being a blade impact test and the second a telemetry strain gauge test in a balance pit. Fatigue life analysis was conducted under the assumption that non-synchronous vibration is experienced by the blade and that only one mode is dominant in the vibration. The results from the fatigue analysis corresponded to the location of the cracks experienced on the blades. The results show twelve orders of magnitude lower life at low load, high backpressure conditions, compared to high load high pressure conditions. The research was further extended to check the same vibratory response on the first three modes, up to their tenth nodal diameters. This was done to analyse fatigue life in a case that a different mode was excited. / Dissertation (MEng)--University of Pretoria, 2020. / Eskom Rotek Industries / Mechanical and Aeronautical Engineering / MEng / Unrestricted

The thesis is concerned with theoretical and practical aspects of the hp- adaptive finite element method for solving elliptic and electromagnetic prob- lems described by partial differential equations in three spatial dimensions. Besides the standard element refinements, the hp-adaptivity allows indepen- dent adaptation of degrees of the polynomial approximation as well. This leads to exponentially fast convergence even for problems with singularities. The efficiency of the hp-adaptivity is enhanced even more by the ability of the algorithm to work with meshes with arbitrary-level hanging nodes. This generality, however, leads to great complexity of the implementation. There- fore, the thesis concentrates on the mathematical analysis of algorithms that have led to successful implementation of the method. In addition, the the- sis discusses the numerical integration in 3D and the implementation of the method itself. Finally, numerical results obtained by this new implemen- tation are presented. They confirm advantages of hp-adaptivity on meshes with arbitrary-level hanging nodes. 1

Les équations de Navier-Stokes linéarisées sont utilisées dans l’industrie aéronautique pour l’optimisation de forme aérodynamique, l’aéroélasticité et l’aéroacoustique. Deux axes ont été suivis pour accélérer et rendre plus robuste la résolution de ces équations. Le premier est l’amélioration de la méthode itérative de résolution de systèmes linéaires utilisée, et le deuxième la formulation du schéma numérique conduisant à ce système linéaire. Dans cette première partie, l’extension de l’algorithme GMRES avec déflation spectrale à des systèmes à plusieurs seconds membres a été testée sur des cas tests industriels. L’amélioration du préconditionnement de la méthode GMRES par l’utilisation d'une méthode de Schwarz additive avec préconditionneur ILU(k) a permis une accélération du temps de résolution allant jusqu’à un facteur dix, ainsi que la convergence de cas jusqu’alors impossibles à résoudre. La deuxième partie présente d’abord un travail sur la stabilisation SUPG du schéma élément fini utilisé. La forme proposée de la matrice de stabilisation, dite complète, a donné des résultats encourageants en non-linéaire qui ne se sont pas transposés en linéarisé. Une étude sur les conditions aux limites de Dirichlet clôt cette partie. Une méthode algébrique d’imposition de conditions non homogènes sur des variables non triviales du calcul, qui a permis l’application industrielle à l’aéroacoustique, y est détaillée. De plus, la preuve est apportée que le caractère transparent d’une condition de Dirichlet homogène sur toutes les variables s’explique par le schéma SUPG. / The linearized Navier-Stokes equations are solved at Dassault Aviation within numerical simulations for aerodynamic shape optimisation, flutter calculations and aeroacoustics. In order to improve the robustness and efficiency of the Navier-Stokes solver, this thesis followed two complementary paths. The first is work on the iterative methods used to solve linear systems, and the second is the improvement of the numerical scheme underlying these linear systems. In the first part, the extension to multiple right-hand sides of the GMRES algorithm with spectral deflation was tested on industrial test cases. The use of the ILU(k) preconditioner within an additive Schwarz method led to a reduction of the time needed to solve the systems with GMRES by a factor ten. It also enabled the convergence of some numerically very difficult cases which could not be solved by the software available before this thesis. The second part of the manuscript begins with work on the SUPG method used to stabilise the finite element scheme. A new way of computing the stabilisation matrix gave promising results on non-linear cases, which were however not observed for linear cases. A study on Dirichlet boundary conditions concludes this part. An algebraic method to impose non homogeneous Dirichlet boundary conditions on non-trivial variables is introduced. It enables the use, in an industrial context, of linearized Navier-Stokes for aeroacoustics. Moreover, the transparent behaviour of a homogeneous Dirichlet boundary conditions on all variables is proved to be due to the SUPG stabilisation.

This master’s thesis deals with the strength analysisby frame lift cage with lift capacity of 675 kg used the Finite Element Method (FEM). Furtheris performed the calculation of the guideanchoring instituted for this steel structure and the strength analysis of the used guides according to norm ČSN EN 81-1. The thesis also includes the drawing of the frame lift cage.

No description available.

No description available.

Physically assembled gels are widely applicable in the food industry, biomedical devices, drug delivery, and soft robotics due to their tunable mechanical properties and thermoreversibility. The mechanical responses of these gels originate from their microstructure. Therefore, factors affecting the gel microstructure like polymer molecular weight, solvent quality, and polymer concentration play a significant role in determining their mechanical behavior. Gel microstructure also changes during the deformations resulting in a deviation from the structure-property relationship established for the low deformations. During large deformations, other factors like stress relaxation, poroelasticity, and polymer chain entanglement contribute significantly to the gel response. This complexity extends to the understanding of their failure behavior that occurs at large deformations. The low strain mechanical behavior of gels is governed by load-bearing chain density. They are often represented with non-linear elastic models, which ignore the contribution from viscous dissipation, polymer entanglements, surface tension, and bond dissociation. In addition, the available theoretical models cannot capture the experimental conditions like boundary confinement, therefore, numerical simulations are useful to test the developed model by comparing with experimental observations. With this objective, the present dissertation is focused on understanding the failure of physically assembled gels that consists of an ABA-type triblock copolymer dissolved in a B-block (midblock) selective solvent. Here, gelation occurs as a result of relative difference in the solubility of A-blocks (endblocks) and B-blocks (midblocks) with solvent. The thermo-mechanical characterization of these gels was performed using rheology, cavitation rheology, and DSC. A custom-built experimental set-up was developed to conduct large deformation experiments like tensile tests, creep failure experiments, and fracture experiments with a predefined crack. To characterize the gel microstructure, small-angle x-ray/neutron techniques were used. A change in the gel microstructure during deformation was also captured. The microstructure of gels was tuned by varying temperature, polymer volume fraction, midblock length, and by addition of midblock homopolymer. Finite element simulations have been used to understand the effect of boundary confinement, surface tension, and viscous dissipation. The present work provides a better understanding of failure behavior in physically assembled gels through the polymer dynamics at nano-scale level.

[pt] Este trabalho tem por objetivo apresentar um sistema integrado para otimização de forma de estruturas planas que tenham comportamento elasto-plástico. A metodologia implementada propõe uma alternativa à forma conservadora com que tradicionalmente as estruturas têm sido otimizadas, ou seja, admitindo-se que as mesmas possuam comportamento linear elástico. O sistema computacional é denominado integrado pois reúne diversos módulos distintos para o tratamento do problema, como modelagem geométrica, geração de malhas de elementos finitos, análise não-linear da resposta da estrutura, análise de sensibilidade,programação matemática e otimização de estruturas. A geometria do contorno da estrutura plana é definida por meio de curvas (paramétricas)B-splines cúbicas. Estas, por sua vez, são determinadas em função de um conjunto de pontos de interpolação (pontos-chave) e condições de contorno em seus vértices extremos. A correta definição da geometria da estrutura é responsável pelo sucesso do processo de otimização. A resposta da estrutura às solicitações do carregamento externo é avaliada pelo método dos elementos finitos. Para isso, é necessário que o domínio da estrutura seja discretizado. No presente trabalho foi empregado um gerador automático de malhas não estruturadas de elementos finitos isoparamétricos. A configuração de equilíbrio da estrutura é obtida através de um procedimento iterativo/incremental envolvendo o método de Newton-Raphson. Localmente, o equilíbrio é satisfeito pela aplicação de um algoritmo implícito de integração de tensões nos pontos que violarem o critério de plastificação do material. A matriz tangente de rigidez é atualizada a cada iteração da análise e é obtida de forma consistente com o algoritmo de integração das tensões, preservando as características de convergência quadrática assintótica inerentes ao método de Newton- Raphson. No procedimento iterativo de otimização é empregado um algoritmo de programac¸ ão quadrática recursiva que requer a avaliação dos gradientes da função-objetivo e restrições. Para tal, foi implementado um método semi-analítico para a determinação das sensibilidades da resposta estrutural envolvidas nas expressôes dos gradientes citados. O método leva em consideração os efeitos da plastificação ocorrida durante o carregamento da estrutura e é dito -exato- por apresentar imprecisões apenas nos casos em que a magnitude da perturbação da variável é muito pequena, não podendo ser representada corretamente pelo hardware. Os exemplos analisados mostram que a consideração do comportamento elastoplástico da estrutura na otimização de sua forma leva a configurações mais eficientes do que aquelas obtidas admitindo-se a relação linear elástica entre deformações e tensões. / [en] The main goal of this work is to present an integrated system for the optimization of plane structures with elastoplastic behavior. The methodology proposes an alternative for the conservative way in which structures traditionally have been optimized, i.e., that they present linear elastic behavior. The computational system is said to be integrated because it congregates distinct modules for the solution of the problem, such as geometric modelling, finite element mesh generation, non-linear structural response analysis, sensitivity analysis, mathematical programming and optimization of structures. The geometry of the plane structure`s boundary is defined by cubic (parametric) B-splines curves. Those, in turn, are determined by a set of interpolation points (key points) and boundary constraints at their ends. The correct definition of the structure`s geometry is responsible for the success of the optimization process.The structural response to the applied loading is evaluated by the finite element method. For that, the domain of the structure must be discretized. In the present work, an automatic unstructured mesh generator of isoparametric finite elements has been used. The equilibrium layout of the structure is obtained by an iterative/incremental procedure using the standard Newton-Raphson method. Locally, the equilibrium is satisfied by applying an implicit stress return mapping algorithm at points which violate the yield criterion of the material. The tangent stiffness matrix is updated at each analysis iteration and it is obtained in a way which is consistent with the return mapping algorithm, so that the asymptotic quadratic rate of convergence of the Newton-Raphson method is preserved. The use of a quadratic recursive programming algorithm in the optimization procedure involves the gradient evaluation of the objective function and constraints. For that, a semi-analytical method for the calculation of the response sensitivities, which appear in the gradient expressions, has been implemented. The technique takes into account the plastic effects which take place during the loading of the structure and is considered - exact- up to round-off errors, which occurs when the magnitude of the perturbation is so small that the hardware cannot accurately represent it.The examples presented demonstrate that the consideration of the elastoplastic behavior of the material during the optimization process leads to structural layouts which are more efficient than of those obtained under the assumption of linear elastic relationship between strains and stresses. / [es] Este trabajo tiene por objetivo presentar un sistema integrado para otimización de forma de extructuras planas que tengan comportamiento elástico-plástico. LA metodología implementada propone una alternativa a la forma conservadora con que tradicionalmente las extructuras han sido optimizadas, o sea, admitiendo que las poseen um comportamiento lineal-elástico. EL sistema computacional se denomina integrado pues reúne diversos módulos para el tratamiento del problema, como modelage geométrica, generación de mallas de elementos finitos, análisis no lineal de la respuesta de la extructura, análisis de sensibilidad,programación matemática y otimización de extructuras. LA geometría del contorno de la extructura plana es definida por medio de curvas (paramétricas)B splines cúbicas. Estas, por su vez, son determinadas en función de un conjunto de puntos de interpolación (puntos claves) y condiciones de contorno en sus vértices extremos. La definición correta de la geometría de la extructura es responsable por el éxito del proceso de otimización. La respuesta de la extructura a las solicitudes de carga externa se evalúa por el método de los elementos finitos. Para esto, es necesario que el dominio de la extructura sea discretizado. En este trabajo se utiliza un generador automático de mallas no extructuradas de elementos finitos isoparamétricos. La configuración de equilíbrio de la extructura se obtiene a través de un procedimiento iterativo/incremental que envuelve el método de Newton Raphson. Localmente, el equilíbrio es satisfecho por la aplicación de un algoritmo implícito de integración de tensiones en los puntos que violen el critério de plastificación del material. La matriz tangente de rigidez se actualiza a cada iteración del análisis y se obtiene de forma consistente con el algoritmo de integración de las tensiones, preservando las características de convergencia cuadrática asintótica inherentes al método de Newton Raphson. En el procedimiento iterativo de otimización se utiliza un algoritmo de programación cuadrática recursiva que requiere la evaluación de los gradientes de la función objetivo y restricciones. Para tal, se implementó un método semi analítico para la determinación de las sensibilidades de la respuesta extructural envolvidas en las expresóes de los gradientes citados. EL método lleva en consideración el hecho de que la plastificación que ocurre durante la carga de la extructura y se dice exacta por presentar imprecisiones apenas en los casos en que la magnitud de la perturbación de la variable es muy pequeña, no puede ser representada correctamente por el hardware. Los ejemplos analizados muestran que la consideración del comportamiento elástico-plástico de la extructura en la otimización de su forma lleva la configuraciones más eficientes de que aquellas obtenidas admitiendo la relación lineal elástica entre deformaciones y tensiones.

No description available.

The applications of Li-ion batteries in the electronics and vehicle industry is increasing at a very rapid pace. This is primarily due to superior properties such as high specific energy storage and power as well as wider operation temperature ranges. Additional potential for improved properties is connected to capacity losses with time and the thereby resulting limitations of lifetime of batteries. The lifetime of a battery is strongly related to the mechanical and chemical degradation of the active material of electrodes during repeated electrochemical reactions at charging and discharging. To identify this phenomenon from a mechanical perspective, the mechanical properties of the electrode active layers should be characterized. Additionally, with the aid of mechanical properties, realistic electro-chemo-mechanical models should be developed to comprehend the mechanisms causing capacity fade. In the first part of this thesis, macroscopic material properties of the active layers of Li-ion battery electrodes were measured with a unique bending test technique. Contrary to methods previously used; it is capable to overcome the challenges that were encountered in other traditional testing techniques. In papers 1 and 2 this bending test technique (U-shaped bending test), is used to characterize the elastic and viscoelastic behavior of NMC cathodic and graphite anodic active layers, respectively. By using single-sided thin electrode specimens in U-shape bending tests, it was possible to distinguish tensile and compressive elastic and viscoelastic behavior of the electrode active materials. The tensile Young’s moduli of cathodic and anodic active layers are found as 0.73 GPa and 1 GPa, respectively. On the other hand, the compressive Young’s moduli show a stiffening behavior at increasing strains. Stiffnesses between 1.3 GPa and 2.8 GPa for the cathodic active layer, and between 1 GPa and 3.8 GPa for the anodic active layer were recorded. This compressive behavior of the electrode active layers is expected as a result of the porous nature of the materials. In addition, the viscoelastic behavior of the electrode active layers is expressed through Prony series. It was observed that the behavior can be described by a short term (minutes) and a long term (hours, days) relaxation. In paper 3, a statistical representative volume element is introduced to predict the elastic properties of a dry cathodic electrode active layer. A porous cathodic electrode active layer that is composed of NMC active particles and polymeric binder material with conductive carbon additives is modeled as a face-centered-cubic structure. Several particle-binder and particle-particle interaction conditions are repeated 50 times with random orientations. Based on the statistics for each interaction case, Young’s modulus is estimated. The results show a good agreement with the experimental findings from Paper 1. Furthermore, particle-particle and particle-binder contact force distributions are calculated for 3% of particle swelling. The characteristics of the force distributions are correlated with the typical material failures in the active layer such as particle cracking and binder debonding. The statistical data obtained here are also used to improve an analytical model that was previously derived to estimate the elastic properties of active porous layers. The analytical model, complemented by the statistical results, showed an excellent agreement with the finite element simulations. / <p>QC 230124</p>