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- Finite-Elemente-Methode (4)
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Briefly, the two basic questions that this research is supposed to answer are:
1. Howmuch fiber is needed and how fibers should be distributed through a fiber reinforced composite (FRC) structure in order to obtain the optimal and reliable structural response?
2. How do uncertainties influence the optimization results and reliability of the structure?
Giving answer to the above questions a double stage sequential optimization algorithm for finding the optimal content of short fiber reinforcements and their distribution in the composite structure, considering uncertain design parameters, is presented. In the first stage, the optimal amount of short fibers in a FRC structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. Presented model considers material, structural and modeling uncertainties. In the second stage, the fiber distribution optimization (with the aim to further increase in structural reliability) is performed by defining a fiber distribution function through a Non-Uniform Rational BSpline (NURBS) surface. The advantages of using the NURBS surface as a fiber distribution function include: using the same data set for the optimization and analysis; high convergence rate due to the smoothness of the NURBS; mesh independency of the optimal layout; no need for any post processing technique and its non-heuristic nature. The output of stage 1 (the optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is the Reliability Index (b ) of the structure with the optimal fiber content and distribution.
First order reliability method (in order to approximate the limit state function) as well as different material models including Rule of Mixtures, Mori-Tanaka, energy-based approach and stochastic multi-scales are implemented in different examples. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. The methodology is successfully implemented for interfacial shear stress optimization in sandwich beams and also for optimization of the internal cooling channels in a ceramic matrix composite.
Finally, after some changes and modifications by combining Isogeometric Analysis, level set and point wise density mapping techniques, the computational framework is extended for topology optimization of piezoelectric / flexoelectric materials.
Synergistic Framework for Analysis and Model Assessment in Bridge Aerodynamics and Aeroelasticity
(2020)
Wind-induced vibrations often represent a major design criterion for long-span bridges. This work deals with the assessment and development of models for aerodynamic and aeroelastic analyses of long-span bridges.
Computational Fluid Dynamics (CFD) and semi-analytical aerodynamic models are employed to compute the bridge response due to both turbulent and laminar free-stream. For the assessment of these models, a comparative methodology is developed that consists of two steps, a qualitative and a quantitative one. The first, qualitative, step involves an extension
of an existing approach based on Category Theory and its application to the field of bridge aerodynamics. Initially, the approach is extended to consider model comparability and completeness. Then, the complexity of the CFD and twelve semi-analytical models are evaluated based on their mathematical constructions, yielding a diagrammatic representation of model quality.
In the second, quantitative, step of the comparative methodology, the discrepancy of a system response quantity for time-dependent aerodynamic models is quantified using comparison metrics for time-histories. Nine metrics are established on a uniform basis to quantify the discrepancies in local and global signal features that are of interest in bridge aerodynamics. These signal features involve quantities such as phase, time-varying frequency and magnitude content, probability density, non-stationarity, and nonlinearity.
The two-dimensional (2D) Vortex Particle Method is used for the discretization of the Navier-Stokes equations including a Pseudo-three dimensional (Pseudo-3D) extension within an existing CFD solver. The Pseudo-3D Vortex Method considers the 3D structural behavior for aeroelastic analyses by positioning 2D fluid strips along a line-like structure. A novel turbulent Pseudo-3D Vortex Method is developed by combining the laminar Pseudo-3D VPM and a previously developed 2D method for the generation of free-stream turbulence. Using analytical derivations, it is shown that the fluid velocity correlation is maintained between the CFD strips.
Furthermore, a new method is presented for the determination of the complex aerodynamic admittance under deterministic sinusoidal gusts using the Vortex Particle Method. The sinusoidal gusts are simulated by modeling the wakes of flapping airfoils in the CFD domain with inflow vortex particles. Positioning a section downstream yields sinusoidal forces that are used for determining all six components of the complex aerodynamic admittance. A closed-form analytical relation is derived, based on an existing analytical model. With this relation, the inflow particles’ strength can be related with the target gust amplitudes a priori.
The developed methodologies are combined in a synergistic framework, which is applied to both fundamental examples and practical case studies. Where possible, the results are verified and validated. The outcome of this work is intended to shed some light on the complex wind–bridge interaction and suggest appropriate modeling strategies for an enhanced design.
The Variability of the Void Ratio of Sand and its Effect on Settlement and Infinite Slope Stability
(2018)
The uncertainty of a soil property can significantly affect the physical behavior of soil, so as to influence geotechnical practice. The uncertainty can be expressed by its stochastic parameters, including the mean, the standard deviation, and the spatial correlation length. These stochastic parameters are regarded as constant value in most of the former studies. The main aim of this thesis is to prove whether they are depth-dependent, and to evaluate the effect of this depth-dependent character on both the settlement and the infinite slope stability during rainwater infiltration.
A stochastic one-dimensional settlement simulation is carried out using random finite element method with the von Wolffersdorff hypoplastic model, so as to evaluate the effect of stress level on the stochastic parameters of void ratio related parameters of sand. It is found that these stochastic parameters are both stress-dependent and depth-dependent.
The non-stationary random field, considering the depth-dependent character of these stochastic parameters, can be generated through the distortion of the stationary random field.
The one-dimensional settlement analysis is carried out to evaluation the effect of the depth-dependent character of the stochastic parameters of void ratio on the strain. It is found that the depth-dependent character has low effect on the strain.
The deterministic analysis of infinite slope stability during rainwater infiltration is simulated.
The transient seepage is carried out using finite difference method, while the steady state seepage is simulated using the analytical solution. The saturated hydraulic conductivity (ks) is taken as the only variable. The results show that the depth-dependent ks has a significant influence on the stability of the slope when the negative flux is high. Without considering the depth-dependent character, can overestimate the factor of safety of the slope. A slope can fail if the depth-dependent character is considered, while it is stable if the depth-dependent character is neglected. The failure time of the slope with a greater depth-dependent ks is earlier during transient infiltration.
Meanwhile, the stochastic infinite slope stability analysis during infiltration, is also carried out to highlight the effect of the depth-dependent character of the stochastic parameters of ks. The results show that: the probability of failure is significantly increased if the depth-dependent character of mean is considered, while, it is moderately reduced if the depth-dependent character of the standard deviation is accounted. If the depth-dependent character of both the mean and standard deviation of ks is considered, the depth-dependent mean value plays a dominant influence on the results. Furthermore, the depth-dependent character of the spatial correlation length can slightly reduce the probability of failure.
Die Zonenmethode nach Hertz ist ein vereinfachtes Verfahren zur Heißbemessung von Stahlbetonbauteilen. Um eine händische Bemessung zu ermöglichen, werden daher verschiedene Annahmen und Vereinfachungen getroffen. Insbesondere werden die thermischen Dehnungen vernachlässigt und das mechanische Verhalten durch einen verkleinerten Querschnitt mit konstanten Stoffeigenschaften beschrieben.
Ziel der vorliegenden Arbeit ist, dieses vereinfachte Verfahren in ein nichtlineares Verfahren zur Heißbemessung von Stahlbetondruckgliedern bei Brandbeanspruchung durch die Einheits-Temperaturzeitkurve zu überführen. Dazu werden die wesentlichen Annahmen der Zonenmethode überprüft und ein Vorschlag zur Weiterentwicklung vorgestellt. Dieser beruht im Wesentlichen auf der Modellierung der druckbeanspruchten Bewehrung. Diese weiterentwickelte Zonenmethode wird durch die Nachrechnung von Laborversuchen validiert und das Sicherheitsniveau durch eine vollprobabilistische Analyse und den Vergleich mit dem allgemeinen Verfahren bestimmt.