<p>Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the <em>thickness function</em> of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the <em>shape amplitude</em>, the Fourier transform of the <em>shape function</em> defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L₃ edge of the three Fe atoms in its basis.</p>

Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the thickness function of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the shape amplitude, the Fourier transform of the shape function defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L3 edge of the three Fe atoms in its basis.

The steady state response of thin-walled members subjected to harmonic forces is investigated in the present study. The governing differential equations of motion and associated boundary conditions are derived from the Hamilton variational principle. The harmonic form of the applied forces is exploited to eliminate the need to discretize the problem in the time domain, resulting in computational efficiency. The formulation is based on a generalization of the Timoshenko-Vlasov beam theory and accounts for warping effects, shear deformation effects due to bending and non-uniform warping, translational and rotary inertial effects and captures flexural-torsional coupling arising in asymmetric cross-sections. Six of the resulting seven field equations are observed to be fully coupled for asymmetric cross-sections while the equation of longitudinal motion is observed to be uncoupled. Separate closed form solutions are provided for the cases of (i) doubly symmetric cross sections, (ii) monosymmetric cross-sections, and (iii) asymmetric cross-sections. The closed-form solutions are provided for cantilever and simply-supported boundary conditions. A family of shape functions is then developed based on the exact solution of the homogeneous field equations and then used to formulate a series of super-convergent finite beam elements. The resulting two-noded beam elements are shown to successfully capture the static and dynamic responses of thin-walled members. The finite elements developed involve no special discretization errors normally encountered in other finite element formulations and provide results in excellent agreement with those based on other established finite elements with a minimal number of degrees of freedom. The formulation is also capable to predict the natural frequencies and mode-shapes of the structural members. Comparisons with non-shear deformable beam solutions demonstrate the importance of shear deformation effects within short-span members subjected to harmonic loads with higher exciting frequencies. Comparisons with shell element solution results demonstrate that distortional effects are more pronounced in cantilevers with short spans. A generalized stress extraction scheme from the finite element formulation is then developed. Also, a generalization of the analysis procedure to accommodate multiple loads with distinct exciting frequencies is established. The study is concluded with design examples which illustrate the applicability of the formulation, in conjunction with established principles of fatigue design, in determining the fatigue life of steel members subjected to multiple harmonic forces.

The steady state response of thin-walled members subjected to harmonic forces is investigated in the present study. The governing differential equations of motion and associated boundary conditions are derived from the Hamilton variational principle. The harmonic form of the applied forces is exploited to eliminate the need to discretize the problem in the time domain, resulting in computational efficiency. The formulation is based on a generalization of the Timoshenko-Vlasov beam theory and accounts for warping effects, shear deformation effects due to bending and non-uniform warping, translational and rotary inertial effects and captures flexural-torsional coupling arising in asymmetric cross-sections. Six of the resulting seven field equations are observed to be fully coupled for asymmetric cross-sections while the equation of longitudinal motion is observed to be uncoupled. Separate closed form solutions are provided for the cases of (i) doubly symmetric cross sections, (ii) monosymmetric cross-sections, and (iii) asymmetric cross-sections. The closed-form solutions are provided for cantilever and simply-supported boundary conditions. A family of shape functions is then developed based on the exact solution of the homogeneous field equations and then used to formulate a series of super-convergent finite beam elements. The resulting two-noded beam elements are shown to successfully capture the static and dynamic responses of thin-walled members. The finite elements developed involve no special discretization errors normally encountered in other finite element formulations and provide results in excellent agreement with those based on other established finite elements with a minimal number of degrees of freedom. The formulation is also capable to predict the natural frequencies and mode-shapes of the structural members. Comparisons with non-shear deformable beam solutions demonstrate the importance of shear deformation effects within short-span members subjected to harmonic loads with higher exciting frequencies. Comparisons with shell element solution results demonstrate that distortional effects are more pronounced in cantilevers with short spans. A generalized stress extraction scheme from the finite element formulation is then developed. Also, a generalization of the analysis procedure to accommodate multiple loads with distinct exciting frequencies is established. The study is concluded with design examples which illustrate the applicability of the formulation, in conjunction with established principles of fatigue design, in determining the fatigue life of steel members subjected to multiple harmonic forces.

Geometrical parameterisation has an important role in the aircraft design process due to its impact on the computational efficiency and accuracy in evaluating different configurations. In the early design stages, an aircraft geometrical model is normally described parametrically with a small number of design parameters which allows fast computation. However, this provides only a course approximation which is generally limited to conventional configurations, where the models have already been validated. An efficient parameterisation method is therefore required to allow rapid synthesis and analysis of novel configurations. Within this context, the main objectives of this research are: 1) Develop an economical geometrical parameterisation method which captures sufficient detail suitable for aerodynamic analysis and optimisation in early design stage, and2) Close the gap between conceptual and preliminary design stages by bringing more detailed information earlier in the design process. Research efforts were initially focused on the parameterisation of two-dimensional curves by evaluating five widely-cited methods for airfoil against five desirable properties. Several metrics have been proposed to measure these properties, based on airfoil fitting tests. The comparison suggested that the Class-Shape Functions Transformation (CST) method is most suitable and therefore was chosen as the two-dimensional curve generation method. A set of blending functions have been introduced and combined with the two-dimensional curves to generate a three-dimensional surface. These surfaces form wing or body sections which are assembled together through a proposed joining algorithm. An object-oriented structure for aircraft components has also been proposed. This allows modelling of the main aircraft surfaces which contain sufficient level of accuracy while utilising a parsimonious number of intuitive design parameters.

The steady state response of thin-walled members subjected to harmonic forces is investigated in the present study. The governing differential equations of motion and associated boundary conditions are derived from the Hamilton variational principle. The harmonic form of the applied forces is exploited to eliminate the need to discretize the problem in the time domain, resulting in computational efficiency. The formulation is based on a generalization of the Timoshenko-Vlasov beam theory and accounts for warping effects, shear deformation effects due to bending and non-uniform warping, translational and rotary inertial effects and captures flexural-torsional coupling arising in asymmetric cross-sections. Six of the resulting seven field equations are observed to be fully coupled for asymmetric cross-sections while the equation of longitudinal motion is observed to be uncoupled. Separate closed form solutions are provided for the cases of (i) doubly symmetric cross sections, (ii) monosymmetric cross-sections, and (iii) asymmetric cross-sections. The closed-form solutions are provided for cantilever and simply-supported boundary conditions. A family of shape functions is then developed based on the exact solution of the homogeneous field equations and then used to formulate a series of super-convergent finite beam elements. The resulting two-noded beam elements are shown to successfully capture the static and dynamic responses of thin-walled members. The finite elements developed involve no special discretization errors normally encountered in other finite element formulations and provide results in excellent agreement with those based on other established finite elements with a minimal number of degrees of freedom. The formulation is also capable to predict the natural frequencies and mode-shapes of the structural members. Comparisons with non-shear deformable beam solutions demonstrate the importance of shear deformation effects within short-span members subjected to harmonic loads with higher exciting frequencies. Comparisons with shell element solution results demonstrate that distortional effects are more pronounced in cantilevers with short spans. A generalized stress extraction scheme from the finite element formulation is then developed. Also, a generalization of the analysis procedure to accommodate multiple loads with distinct exciting frequencies is established. The study is concluded with design examples which illustrate the applicability of the formulation, in conjunction with established principles of fatigue design, in determining the fatigue life of steel members subjected to multiple harmonic forces.

Geometrical parameterisation has an important role in the aircraft design process due to its impact on the computational efficiency and accuracy in evaluating different configurations. In the early design stages, an aircraft geometrical model is normally described parametrically with a small number of design parameters which allows fast computation. However, this provides only a course approximation which is generally limited to conventional configurations, where the models have already been validated. An efficient parameterisation method is therefore required to allow rapid synthesis and analysis of novel configurations. Within this context, the main objectives of this research are: 1) Develop an economical geometrical parameterisation method which captures sufficient detail suitable for aerodynamic analysis and optimisation in early design stage, and2) Close the gap between conceptual and preliminary design stages by bringing more detailed information earlier in the design process. Research efforts were initially focused on the parameterisation of two-dimensional curves by evaluating five widely-cited methods for airfoil against five desirable properties. Several metrics have been proposed to measure these properties, based on airfoil fitting tests. The comparison suggested that the Class-Shape Functions Transformation (CST) method is most suitable and therefore was chosen as the two-dimensional curve generation method. A set of blending functions have been introduced and combined with the two-dimensional curves to generate a three-dimensional surface. These surfaces form wing or body sections which are assembled together through a proposed joining algorithm. An object-oriented structure for aircraft components has also been proposed. This allows modelling of the main aircraft surfaces which contain sufficient level of accuracy while utilising a parsimonious number of intuitive design parameters ... [cont.].

No description available.

Zwangserregtes Kupplungsrupfen ist ein Schwingungsphänomen, dessen Ursache in einer periodischen Modulation der Anpresskraft im Reibkontakt sowie des Drehmoments der Kupplung liegt. Diese periodische Modulation wird im Wesentlichen durch geometrische Abweichungen von der vorgesehenen Gestalt verursacht. Nach wie vor spielt es bei der Entwicklung von Kraftfahrzeugkupplungen eine große Rolle da die davon verursachten longitudinal Schwingungen des Fahrzeugs zu deutlichen Komforteinbußen der Fahrzeuginsassen führen. Obwohl bereits einige Einflussfaktoren des zwangserregten Kupplungsrupfens qualitativ bekannt sind, gibt es noch nicht für alle Einflussfaktoren geeignete, detaillierte Erklärungsmodelle, die Kupplungsentwicklern beim Verständnis der Wirkzusammenhänge von zwangserregtem Kupplungsrupfen unterstützen. Dies liegt unter anderem an den starken Wechselwirkungen, die über verschiedene Systemebenen auftreten und bisher kaum modelliert wurden. Daher werden in diesem Beitrag Gestalt-Funktion-Zusammenhänge auf zwangserregtes Kupplungsrupfen durch geometrische Abweichungen mithilfe des sogenannten C&C²-Ansatzes nach Albers und Matthiessen näher untersucht. Ein bereits vorhandenes Modell wird dabei um geeignete Granularitäten und Perspektiven erweitert und die Wirkzusammenhänge werden zu unterschiedlichen Zeitpunkten als sogenannte Sequenzmodelle dargestellt. In einem iterativen Prozess werden sowohl Hypothesen als auch Modelle entwickelt und es werden experimentelle Untersuchungen abgeleitet. Ausgewählte Einflussfaktoren werden hierzu in Form von Variationen an einem Prüfstand untersucht, um die Hypothesen zu verifizieren oder zu falsifizieren, und es werden erste quantitative Ergebnisse gewonnen. Dies ermöglicht die Erklärung von Ursachen für zwangserregtes Kupplungsrupfen die durch bisherige Erklärungsmodelle noch nicht hinreichend genau beschrieben werden, was durch die zum Teil großen Dynamiken der Wirkzusammenhänge begründet ist.

Le but de cette thèse est de développer une méthode numérique simple, robuste, efficace et précise pour résoudre des problèmes d'ingénierie de grande taille à partir de la méthode Taylor Meshless (TMM) et fournir de nouvelles idées principales de TMM est d'utiliser comme fonctions de forme des polynômes d'ordre élevé qui sont des solutions approchées de l'EDP. Ainsi la discrétisation ne concerne que la frontière. Les coefficients de ces fonctions de forme sont obtenus en discrétisant les conditions aux limites par des procédures de collocation associées à la méthode des moindres carrés. TMM est alors une véritable méthode sans maillage sans processus d'intégration, les conditions aux limites étant obtenues par collocation. Les principales contributions de cette thèse sont les suivantes: 1) Basé sur TMM, un algorithme général et efficace a été développé pour résoudre des EDP elliptiques tridimensionnelles; 2) Trois techniques de couplage pour des résolutions par morceaux ont été discutées dans des cas de problèmes à grande échelle: la méthode de collocation par les moindres carrés et deux méthodes de couplage basées sur les multiplicateurs de Lagrange; 3) Une méthode numérique générale pour résoudre les EDP non-linéaires a été proposée en combinant la méthode de Newton, la TMM et la technique de différentiation automatique. 4) Pour résoudre des problèmes avec un bord non régulier, des solutions singulières satisfaisant l'équation de contrôle sont introduites comme des fonctions de forme complémentaires, ce qui fournit une base théorique pour la résolution de problèmes singuliers / Based on Taylor Meshless Method (TMM), the aim of this thesis is to develop a simple, robust, efficient and accurate numerical method which is capable of solving large scale engineering problems and to provide a new idea for the follow-up study on meshless methods. To this end, the influence of the key factors in TMM has been studied by solving three-dimensional and non-linear Partial Differential Equations (PDEs). The main idea of TMM is to use high order polynomials as shape functions which are approximated solutions of the PDE and the discretization concerns only the boundary. To solve the unknown coefficients, boundary conditions are accounted by collocation procedures associated with least-square method. TMM that needs only boundary collocation without integration process, is a true meshless method. The main contributions of this thesis are as following: 1) Based on TMM, a general and efficient algorithm has been developed for solving three-dimensional PDEs; 2) Three coupling techniques in piecewise resolutions have been discussed and tested in cases of large-scale problems, including least-square collocation method and two coupling methods based on Lagrange multipliers; 3) A general numerical method for solving non-linear PDEs has been proposed by combining Newton Method, TMM and Automatic Differentiation technique; 4) To apply TMM for solving problems with singularities, the singular solutions satisfying the control equation are introduced as complementary shape functions, which provides a theoretical basis for solving singular problems