Masterstudiengang Computational Engineering
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This thesis covers the application and evaluation of new methods to describe laminate stiffness and strength. It has been shown that the trace of laminate stiffness is a rotation-invariant quantity and exactly describes the stiffness potential of a material. Together with an invariant strength criterion, the unit circle criterion, this makes the trace-based sizing approach for the design of composite structures possible. The use of so-called double-double [±Φ/ ±Ψ] sublaminates allows a continuous field of possible fiber angles and an efficient method for optimizing laminate properties. Using homogenized asymmetric stacking sequences makes the trace-based sizing approach possible and simplifies manufacturing rules. A metamodel for grid reinforced structure has been derived using artificial neural networks. The metamodel shows good predictive quality for the weight response of those grid/skin structures and provides a fast tool for a weight estimation of a fail-safe design. The unit circle criterion appers to be quite conservative for shallow fiber angles and non-conservative for steeper fiber. The traditional [0/ ± 45/90] laminate of an aerospace wing could be replaced by a [±Φ/ ±Ψ] sublaminate with significant reduction of the weight of over 10%. The commercial softwares Abaqus, Matlab and optiSLang are used. A laminate search algorithm for the best fiber angles shows good agreement with the nonlinear programming algorithms. Computational effort can be drastically reduced with the former. Thermomechanically induced warping or spring-in appear to be a challenge when using asymmetric stacking sequences. A hull of a race car has been optimized with the software OptiStruct. A weight of 2.86 kg for the composite is achieved while meeting several design constraints.
Ziel der vorliegenden Arbeit ist die strukturmechanische Analyse des historischen Flugzeugflügels der Nr. 21 von Gustav Weißkopf sowie des Nachbaus Nr. 21B, um strukturelle Eigenschaften der Flügelkonstruktion bewerten und damit ein Indiz bzw. Gegenindiz für die Flugfähigkeit der Nr. 21 liefern zu können, sowie einen Einstieg in die Themenstellung der simulatorischen Bewertung der Nr. 21 zu schaffen. Hierfür wird ein Modell erstellt, um die Machbarkeit der Simulationen mit numerischen Lösungsverfahren, sowie Fragen der Modellierung bewerten zu können. Auf der Basis einer Lastabschätzung für die verschiedenen Flugzustände, sowie einer berechneten Druckverteilung über den Flügel mit der allgemeinen Wirbelgittermethode werden die Spannungen und Verformungen in den Bambusholmen und in den Spannseilen des Flügels für die Belastungen im Flug ermittelt und bewertet. Einen wichtigen strukturellen Teil der Konstruktion stellt der Prozess der Vorspannung des Flügels über die Spannseile dar, welcher gesondert betrachtet und der Einfluss auf die Festigkeit im Flug beleuchtet wird. Des Weiteren werden verschiedene geometrische, formliche und lastverstärkende Variationen durchgeführt und bezüglich ihrer Flugtauglichkeit sowie der strukturellen Verbesserung diskutiert und dahingehend bewertet, dass ein Flug aus festigkeitstechnischen Gesichtspunkten möglich gewesen ist. Als Simulationsprogramm für die Validierung vorausgegangener strukturmechanischer Untersuchungen mit der Finiten-Elemente-Methode wurde ANSYS verwendet.
In modern lightweight engineering, often fibre reinforced plastics such as carbon fibre reinforced plastic or glass fibre reinforced plastic is the go to solution. The failure of those so-called composite materials cannot be predicted with simple means used for metallic materials but use specialised failure criterion, which can predict the failure of the material. Within this thesis, I compare criteria which are provided by literature to get a better understanding of the pros and cons and the potential for lightweight design with these criteria.
This work should determine whether a criterion has an advantage over the other criteria in terms of calculatory effort, conservatism or potential for lightweight design.
To assess this question, I take three different approaches which are of increasing complexity. The first approach is a simple comparison based on plots of the different failure envelopes. This gives a first qualitative feeling and potentials of the different criterion. The second is a simple analytic approach to calculate the strength values for different specimen geometries (notched and unnotched), with the use of the classic laminate theory. With this, it is possible to compare the found results with values taken from literature and do first quantitative comparisons. The last consideration is an optimisation of the laminate lay-up for the different geometries using all the described criteria.
Those considerations do not lead to a clear best criteria. All the criteria have their own advantages and downsides. Never the less I can conclude that some criteria have an advantage in terms of simplicity but lose some of their potential for lightweight structure because of the inherent conservatism implemented in them.
In 2013 the Heat Method was presented as an alternative to the Fast Marching Method to compute geodesic distances in 2D and 3D. The Heat Method has a potential to be very fast, because its numerical solution cuts down to solving linear systems of equations, which can be parallelized. This work analyzes the suitability of the Heat Method for geodesic distance computation in pedestrian dynamics simulation. The thesis reveals several limitations of the Heat Method on 2D domains, which are of general interest. This is done by presenting numerical experiments using unstructured triangle meshes as spatial discretization. In the experiments linear numerical convergence is lost in the L2-Norm when the boundary is not smooth. It is also demonstrated that the method is sensitive to round-off errors. The latter finding is also true for closed 3D surfaces. The limitations of the Heat Method found in this study are not discussed in the original publication paper (2013). The findings of this work serve as additional information for users who consider using the Heat Method for geodesic distance computation instead of the Fast Marching Method.
Uncertainty Quantification in Microscopic Crowd Simulation Based on Polynomial Chaos Expansions
(2020)
Microscopic crowd simulation, for example performed with the optimal steps model, can support the planning process of mass events if the model parameters are chosen correctly. The exact values of these parameters are often unknown, so the input suffers from uncertainties that can affect the output. To assure that the right conclusions are drawn from a simulation, modellers can employ forward uncertainty quantification methods. However, applying such methods to the optimal steps model is rather uncommon. Therefore, this thesis addresses the question which approach is suitable for estimating the uncertainty and sensitivity of the model output. It focuses on polynomial chaos expansions, which allow to derive statistical moments and Sobol’ sensitivity indices for uncertainty and sensitivity analyses, respectively. The polynomial chaos expansion combined with the point collocation method and the pseudo-spectral approach is applied to a corridor scenario and the results are compared to Monte Carlo simulations. Thus, it can be shown that the point collocation method is efficient because it yields accurate results while the computational effort is low. Based on that, the method is transferred to a large scale scenario, a parade through a city center. The outcomes are interpreted to demonstrate that they are relevant to reality.