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Modelling languages are important in the process of software development. The suitability of a modelling language for a project depends on its applicability to the target domain. Here, domain-specific languages have an advantage over more general modelling languages. On the other hand, modelling languages like the Unified Modeling Language can be used in a wide range of domains, which supports the reuse of development knowledge between projects. This thesis treats the syntactical and semantical harmonisation of modelling languages and their combined use, and the handling of complexity of modelling languages by providing language subsets - called language profiles - with tailor-made formal semantics definitions, generated by a profile tool. We focus on the widely-used modelling languages SDL and UML, and formal semantics definitions specified using Abstract State Machines.
In the theoretical part of this thesis, the difference of the solutions of the elastic and the elastoplastic boundary value problem is analysed, both for linear kinematic and combined linear kinematic and isotropic hardening material. We consider both models in their quasistatic, rate-independent formulation with linearised geometry. The main result of the thesis is, that the differences of the physical obervables (the stresses, strains and displacements) can be expressed as composition of some linear operators and play operators with respect to the exterior forces. Explicit homotopies between both solutions are presented. The main analytical devices are Lipschitz estimates for the stop and the play operator. We present some generalisations of the standard estimates. They allow different input functions, different initial memories and different scalar products. Thereby, the underlying time involving function spaces are the Sobolov spaces of first order with arbitrary integrability exponent between one and infinity. The main results can easily be generalised for the class of continuous functions with bounded total variation. In the practical part of this work, a method to correct the elastic stress tensor over a long time interval at some chosen points of the body is presented and analysed. In contrast to widespread uniaxial corrections (Neuber or ESED), our method takes multiaxiality phenomena like cyclic hardening/softening, ratchetting and non-masing behaviour into account using Jiang's model of elastoplasticity. It can be easily adapted to other constitutive elastoplastic material laws. The theory for our correction model is developped for linear kinematic hardening material, for which error estimated are derived. Our numerical algorithm is very fast and designed for the case that the elastic stress is piecewise linear. The results for the stresses can be significantly improved with Seeger's empirical strain constraint. For the improved model, a simple predictor-correcor algorithm for smooth input loading is established.
The present work deals with the (global and local) modeling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth’s surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions.
Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work an algorithm for the identification of material parameters for large strain viscoelasticity is presented. Thereby, data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. Representative numerical examples are referred to measured data for different polyurethanes. In order to show the general applicability of the identification method for multiple tests, in the last part of this work the parameter identification for small strain plasticity is presented. Thereby three similar test programs on three specimen of the aluminum alloy AlSi9Cu3 are analyzed, and the parameter sets for the respective individual identifications, and for the combination of all tests in one identification, is compared.
Embedded systems have become ubiquitous in everyday life, and especially in the automotive industry. New applications challenge their design by introducing a new class of problems that are based on a detailed analysis of the environmental situation. Situation analysis systems rely on models and algorithms of the domain of computational geometry. The basic model is usually an Euclidean plane, which contains polygons to represent the objects of the environment. Usual implementations of computational geometry algorithms cannot be directly used for safety-critical systems. First, a strict analysis of their correctness is indispensable and second, nonfunctional requirements with respect to the limited resources must be considered. This thesis proposes a layered approach to a polygon-processing system. On top of rational numbers, a geometry kernel is formalised at first. Subsequently, geometric primitives form a second layer of abstraction that is used for plane sweep and polygon algorithms. These layers do not only divide the whole system into manageable parts but make it possible to model problems and reason about them at the appropriate level of abstraction. This structure is used for the verification as well as the implementation of the developed polygon-processing library.
In this thesis, the quasi-static Biot poroelasticity system in bounded multilayered domains in one and three dimensions is studied. In more detail, in the one-dimensional case, a finite volume discretization for the Biot system with discontinuous coefficients is derived. The discretization results in a difference scheme with harmonic averaging of the coefficients. Detailed theoretical analysis of the obtained discrete model is performed. Error estimates, which establish convergence rates for both primary as well as flux unknowns are derived. Besides, modified and more accurate discretizations, which can be applied when the interface position coincides with a grid node, are obtained. These discretizations yield second order convergence of the fluxes of the problem. Finally, the solver for the solution of the produced system of linear equations is developed and extensively tested. A number of numerical experiments, which confirm the theoretical considerations are performed. In the three-dimensional case, the finite volume discretization of the system involves construction of special interpolating polynomials in the dual volumes. These polynomials are derived so that they satisfy the same continuity conditions across the interface, as the original system of PDEs. This technique allows to obtain such a difference scheme, which provides accurate computation of the primary as well as of the flux unknowns, including the points adjacent to the interface. Numerical experiments, based on the obtained discretization, show second order convergence for auxiliary problems with known analytical solutions. A multigrid solver, which incorporates the features of the discrete model, is developed in order to solve efficiently the linear system, produced by the finite volume discretization of the three-dimensional problem. The crucial point is to derive problem-dependent restriction and prolongation operators. Such operators are a well-known remedy for the scalar PDEs with discontinuous coefficients. Here, these operators are derived for the system of PDEs, taking into account interdependence of different unknowns within the system. In the derivation, the interpolating polynomials from the finite volume discretization are employed again, linking thus the discretization and the solution processes. The developed multigrid solver is tested on several model problems. Numerical experiments show that, due to the proper problem-dependent intergrid transfer, the multigrid solver is robust with respect to the discontinuities of the coefficients of the system. In the end, the poroelasticity system with discontinuous coefficients is used to model a real problem. The Biot model, describing this problem, is treated numerically, i.e., discretized by the developed finite volume techniques and then solved by the constructed multigrid solver. Physical characteristics of the process, such as displacement of the skeleton, pressure of the fluid, components of the stress tensor, are calculated and then presented at certain cross-sections.
Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell. Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell.
In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.
The main aim of this work was to obtain an approximate solution of the seismic traveltime tomography problems with the help of splines based on reproducing kernel Sobolev spaces. In order to be able to apply the spline approximation concept to surface wave as well as to body wave tomography problems, the spherical spline approximation concept was extended for the case where the domain of the function to be approximated is an arbitrary compact set in R^n and a finite number of discontinuity points is allowed. We present applications of such spline method to seismic surface wave as well as body wave tomography, and discuss the theoretical and numerical aspects of such applications. Moreover, we run numerous numerical tests that justify the theoretical considerations.
The present thesis deals with multi-user mobile radio systems, and more specifically, the downlinks (DL) of such systems. As a key demand on future mobile radio systems, they should enable highest possible spectrum and energy efficiency. It is well known that, in principle, the utilization of multi-antennas in the form of MIMO systems, offers considerable potential to meet this demand. Concerning the energy issue, the DL is more critical than the uplink. This is due to the growing importance of wireless Internet applications, in which the DL data rates and, consequently, the radiated DL energies tend to be substantially higher than the corresponding uplink quantities. In this thesis, precoding schemes for MIMO multi-user mobile radio DLs are considered, where, in order to keep the complexity of the mobile terminals as low as possible, the rationale receiver orientation (RO) is adopted, with the main focus to further reduce the required transmit energy in such systems. Unfortunately, besides the mentioned low receiver complexity, conventional RO schemes, such as Transmit Zero Forcing (TxZF), do not offer any transmit energy reductions as compared to conventional transmitter oriented schemes. Therefore, the main goal of this thesis is the design and analysis of precoding schemes in which such transmit energy reductions become feasible - under virtually maintaining the low receiver complexity - by means of replacing the conventional unique mappings by the selectable representations of the data. Concerning the channel access scheme, Orthogonal Frequency Division Multiplex (OFDM) is presently being favored as the most promising candidate in the standardization process of the enhanced 3G and forthcoming 4G systems, because it allows a very flexible resource allocation and low receiver complexity. Receiver oriented MIMO OFDM multi-user downlink transmission, in which channel equalization is already performed in the transmitter of the access point, further contributes to low receiver complexity in the mobile terminals. For these reasons, OFDM is adopted in the target system of the considered receiver oriented precoding schemes. In the precoding schemes considered the knowledge of channel state information (CSI) in the access point in the form of the channel matrix is essential. Independently of the applied duplexing schemes FDD or TDD, the provision of this information to the access point is always erroneous. However, it is shown that the impact of such deviations not only scales with the variance of the channel estimation errors, but also with the required transmit energies. Accordingly, the reduced transmit energies of the precoding schemes with selectable data representation also have the advantage of a reduced sensitivity to imperfect knowledge of CSI. In fact, these two advantages are coupled with each other.