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Um die in der Automatisierung zunehmenden Anforderungen an Vorschubachsen hinsichtlich Dynamik, Präzision und Wartungsaufwand bei niedriger Bauhöhe und kleiner werdendem Bauvolumen gerecht zu werden, kommen immer mehr Synchron-Linearmotoren in Zahnspulentechnik mit Permanentmagneterregung in Werkzeugmaschinen zum Einsatz. Als hauptsächlicher Vorteil gegenüber der rotierenden Antriebslösung mit Getriebeübersetzung und Kugelrollspindel wird die direkte Kraftübertragung ohne Bewegungswandler genannt. Der Übergang vom konventionellen linearen Antriebssystem zum Direktantriebssystem eröffnet dem Werkzeugmaschinenherstellern und den Industrieanwendungen eine Vielzahl neuer Möglichkeiten durch beeindruckende Verfahrgeschwindigkeit und hohes Beschleunigungsvermögen sowie Positionier- und Wiederholgenauigkeit und bietet darüber hinaus die Chance zu einer weiteren Produktivitäts- und Qualitätssteigerung. Um alle dieser Vorteile ausnutzen zu können, muss der Antrieb zuerst hinsichtlich der für Linearmotoren typisch Kraftwelligkeit optimiert werden. Die Suche nach wirtschaftlichen und praxistauglichen Gegenmaßnahmen ist ein aktuelles Forschungsthema in der Antriebstechnik. In der vorliegenden Arbeit werden die Kraftschwankungen infolge Nutung, Endeffekt und elektrischer Durchflutung in PM-Synchron-Linearmotor rechnerisch und messtechnisch untersucht. Ursachen und Eigenschaften der Kraftwelligkeit werden beschrieben und Einflussparameter aufgezeigt. Es besteht die Möglichkeit, die Kraftwelligkeit durch bestimmte Maßnahmen zu beeinflussen, z. B. mit Hilfe des Kraftwelligkeitsausgleichs bestehend aus ferromagnetischem Material oder durch gegenseitigen Ausgleich mehrerer zusammengekoppelter Primärteile. Wie die Untersuchungen gezeigt haben, ist eine Abstimmung der Einflussparameter auf analytischem Weg kaum möglich, in der Praxis führt das auf eine experimentell-iterative Optimierung mit FEM-Unterstützung. Die gute Übereinstimmung zwischen Messung und Simulation bietet einen klaren Hinweis, dass die hier vorgestellten Maßnahmen als geeignet angesehen werden können, sie ermöglichen eine Kraftwelligkeitsreduzierung von ursprünglichen 3-5% bis auf 1%, wobei eine leichte Herabsetzung der Kraftdichte in Kauf genommen werden muss. Beim Maschinenentwurf muss rechtzeitig ermittelt werden, welches Kompensationsverfahren günstig ist bezüglich der vorgesehenen Anwendungen.
This paper presents a method for approximating spherical functions from discrete data of a block-wise grid structure. The essential ingredients of the approach are scaling and wavelet functions within a biorthogonalisation process generated by locally supported zonal kernel functions. In consequence, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators become attackable. A multiresolution analysis is formulated enabling a fast wavelet transform similar to the algorithms known from one-dimensional Euclidean theory.
A translation contract is a binary predicate corrTransl(S,T) for source programs S and target programs T. It precisely specifies when T is considered to be a correct translation of S. A certifying compiler generates --in addittion to the target T-- a proof for corrTransl(S,T). Certifying compilers are important for the development of safety critical systems to establish the behavioral equivalence of high-level programs with their compiled assembler code. In this paper, we report on a certifying compiler, its proof techniques, and the underlying formal framework developed within the proof assistent Isabelle/HOL. The compiler uses a tiny C-like language as input, has an optimization phase, and generates MIPS code. The underlying translation contract is based on a trace semantics. We investigate design alternatives and discuss our experiences.
Durch vorangegangene Arbeiten wurden transgene Kartoffelpflanzen erzeugt, die eine verringerte Aktivität des plastidären ATP/ADP Transporters aufweisen (NTT-antisense). Die Knollen dieser Pflanzen zeigen nicht nur veränderte Gehalte an Primärmetaboliten sondern auch eine erhöhte Pathogen-Resistenz, zum Beispiel gegen den bakteriellen Krankheitserreger Erwinia carotovora ssp. atroseptica (Eca). In diesem Zusammenhang deuten neuere Veröffentlichungen auf eine Bedeutung von Transportproteinen für Wirt-Pathogen Wechselwirkungen hin. Im Zuge dieser Arbeit konnte durch die Herstellung eines Systems zur gezielten Erzeugung von Eca „K.O.“-Mutanten die Bedeutung von ausgewählten Sequenzen, welche für Transportproteine kodieren, analysiert werden. Hierbei zeigte sich, dass im Bezug auf die Virulenz von Eca, sowohl der Prolin- als auch der d-Galaktonattransport nur von untergeordneter Bedeutung ist. In weiteren Untersuchungen wurde allerdings der Karbonsäuremetabolismus und -transport von Eca als zentrales Element in der Entfaltung maximaler bakterieller Virulenz erkannt. Hierbei wurde das Cit1-Protein als hoch-affiner Citrattransporter, welcher über die bakterielle pmf energetisiert wird, identifiziert. Dieses Protein ist für ein Wachstum von Eca auf Citrat als einziger Kohlenstoffquelle notwendig und essentiell zur Etablierung einer vollständigen Pathogenese auf Kartoffelknollenscheibchen. So weisen Eca cit1 „K.O.“-Mutanten im Vergleich zu Wildtyp Zellen nicht nur eine geringere pektolytische Aktivität und Gewebemazeration, sondern auch ein reduziertes in planta Wachstum, auf. Des Weiteren wurde ermittelt, dass sich NTT-antisense Gewebe nicht nur durch eine erhöhte Pathogen-Resistenz auszeichnet, sondern auch erniedrigte Citratgehalte aufweist. Analog führte eine artifizielle Erhöhung des Citratgehaltes durch Infiltration von Knollengewebe zu einer deutlich erhöhten Gewebemazeration durch Eca sowie einer verringerten Akkumulation von Abwehrrelevanten pflanzlichen Gentranskripten (PR-Gene). Weitere untersuchte Eca-Mutanten belegten, dass im gemeinsamen Wirken mit anderen enzymatischen Komponenten, Citrat ein ambivalentes Molekül für pflanzliche Resistenz und bakterielle Virulenz ist. Weiterhin konnte gezeigt werden, dass Transportproteine nicht nur für die Virulenz von Eca, sondern auch für phytopathogene Pilze wie Magnaporthe grisea, von Bedeutung sind. So konnte durch die Kooperation mit der AG Thines (IBWF) das Genprodukt eines bei Pathogenese induzierten Genes (rig2), biochemisch charakterisiert werden. Hierbei wurde mittels Komplementation einer Hefemutante (22∆8AA) nachgewiesen, dass es sich bei diesem Protein um einen Prolin-Transporter handelt. Diese Arbeit zeigt, dass Transportproteine als ein wichtiges Element in Wirt-Pathogen Beziehungen wirken können und eine Charakterisierung solcher Proteine zum Verständnis dieser Wechselwirkungen unerlässlich ist.
In this article, we consider the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity, with linear Hooke’s law in the elastic regime for both problems and with the linear kinematic hardening law for the plastic regime in the latter problem. We derive expressions and estimates for the difference of the solutions of both models, i.e. for the stresses, the strains and the displacements. To this end, we use the stop and play operators of nonlinear functional analysis. Further, we give an explicit example of a homotopy between the solutions of both problems.
In this thesis we present the implementation of libraries center.lib and perron.lib for the non-commutative extension Plural of the Computer Algebra System Singular. The library center.lib was designed for the computation of elements of the centralizer of a set of elements and the center of a non-commutative polynomial algebra. It also provides solutions to related problems. The library perron.lib contains a procedure for the computation of relations between a set of pairwise commuting polynomials. The thesis comprises the theory behind the libraries, aspects of the implementation and some applications of the developed algorithms. Moreover, we provide extensive benchmarks for the computation of elements of the center. Some of our examples were never computed before.
In contrast to the spatial motion setting, the material motion setting of continuum mechanics is concerned with the response to variations of material placements of particles with respect to the ambient material. The material motion point of view is thus extremely prominent when dealing with defect mechanics to which it has originally been introduced by Eshelby more than half a century ago. Its primary unknown, the material deformation map is governed by the material motion balance of momentum, i.e. the balance of material forces on the material manifold in the sense of Eshelby. Material (configurational) forces are concerned with the response to variations of material placements of 'physical particles' with respect to the ambient material. Opposed to that, the common spatial (mechanical) forces in the sense of Newton are considered as the response to variations of spatial placements of 'physical particles' with respect to the ambient space. Material forces as advocated by Maugin are especially suited for the assessment of general defects as inhomogeneities, interfaces, dislocations and cracks, where the material forces are directly related to the classical J-Integral in fracture mechanics, see also Gross & Seelig. Another classical example of a material - or rather configurational - force is emblematized by the celebrated Peach-Koehler force, see e.g. the discussion in Steinmann. The present work is mainly divided in four parts. In the first part we will introduce the basic notions of the mechanics and numerics of material forces for a quasi-static conservative mechanical system. In this case the internal potential energy density per unit volume characterizes a hyperelastic material behaviour. In the first numerical example we discuss the reliability of the material force method to calculate the vectorial J-integral of a crack in a Ramberg-Osgood type material under mode I loading and superimposed T-stresses. Secondly, we study the direction of the single material force acting as the driving force of a kinked crack in a geometrically nonlinear hyperelastic Neo-Hooke material. In the second part we focus on material forces in the case of geometrically nonlinear thermo-hyperelastic material behaviour. Therefore we adapt the theory and numerics to a transient coupled problem, and elaborate the format of the Eshelby stress tensor as well as the internal material volume forces induced by the gradient of the temperature field. We study numerically the material forces in a bimaterial bar under tension load and the time dependent evolution of material forces in a cracked specimen. The third part discusses the material force method in the case of geometrically nonlinear isotropic continuum damage. The basic equations are similar to those of the thermo-hyperelastic problem but we introduce an alternative numerical scheme, namely an active set search algorithm, to calculate the damage field as an additional degree of freedom. With this at hand, it is an easy task to obtain the gradient of the damage field which induces the internal material volume forces. Numeric examples in this part are a specimen with an elliptic hole with different semi-axis, a center cracked specimen and a cracked disc under pure mode I loading. In the fourth part of this work we elaborate the format of the Eshelby stress tensor and the internal material volume forces for geometrically nonlinear multiplicative elasto-plasticity. Concerning the numerical implementation we restrict ourselves to the case of geometrically linear single slip crystal plasticity and compare here two different numerical methods to calculate the gradient of the internal variable which enters the format of the internal material volume forces. The two numerical methods are firstly, a node point based approach, where the internal variable is addressed as an additional degree of freedom, and secondly, a standard approach where the internal variable is only available at the integration points level. Here a least square projection scheme is enforced to calculate the necessary gradients of this internal variable. As numerical examples we discuss a specimen with an elliptic inclusion and an elliptic hole respectively and, in addition, a crack under pure mode I loading in a material with different slip angles. Here we focus on the comparison of the two different methods to calculate the gradient of the internal variable. As a second class of numerical problems we elaborate and implement a geometrically linear von Mises plasticity with isotropic hardening. Here the necessary gradients of the internal variables are calculated by the already mentioned projection scheme. The results of a crack in a material with different hardening behaviour under various additional T-stresses are given.
Discontinuities can appear in different fields of mechanics. Some examples where discontinuities arise are more obvious such as the formation of cracks. Other sources of discontinuities are less apparent such as interfaces between different materials. Furthermore continuous fields with steep gradients can also be considered as discontinuous fields. This work aims at the inclusion of arbitrary discontinuities within the finite element method. Although the finite element method is the most sophisticated numerical tool in modern engineering, the inclusion of discontinuities is still a challenging task. Traditionally within finite the framework of FE methods discontinuities are modeled explicitely by the construction of the mesh. Thus, when a fixed mesh is used, the position of the discontinuity is prescribed by the location of interelement boundaries and not by the physical situation. The simulation of crack growth requires a frequent adaption of the mesh and that can be a difficult and computationally expensive task. Thus a more flexible numerical approach is needed which leads to the mesh-independent representation of the discontinuity. A challenging field where the accurate description of discontinuities is of vital importance is the modeling of failure in engineering materials. The load capacity of a structure is limited by the material strength. If the load limit is exceeded failure zones arise and increase. Representative examples of failure mechanisms are are cracks in brittle materials or shear bands in metals or soils. Failure processes are often accompanied by a strain softening material behaviour (decreasing load carrying capacity with increasing strain at a material point). It is known that the inclusion of strain softening material behaviour within a continuum description requires regularization techniques to preserve the well- posedness of the governing equations. One possibility is the consideration of non-local or gradient terms in the constitutive equations but these approaches require a sufficiently fine discretization in the localization zone, which leads to a high numerical effort. If the extent of the failure zone and the failure process to the point of the development of discrete cracks is considered it seems reasonable to include strong discontinuities. In the framework of fracture mechanics the inclusion of displacement jumps is intuitively comprehensible. However, the modeling of localized failure processes demands the consideration of inelastic material behaviour. Cohesive zone models represent an approach which is especially suited for the incorporation within the finite element framework. It is supposed that cohesive tractions are transmitted between the discontinuity surfaces. These tractions are constitutively prescribed by a phenomenological traction separation law and thus allow for the modeling of different inelastic mechanisms, like micro-crack evolution, initiation of voids, plastic flow or crack bridging. The incorporation of a displacement discontinuity in combination with a cohesive traction separation law leads to a sound model to describe failure processes and crack propagation. Another area where the existence of discontinuities is not as obvious is the occurence of material interfaces, inclusions or holes. The accurate modeling of such internal interfaces is important to predict the mechanical behaviour of components. The present discontinuity is of different nature: the displacement field is continuous but there is a jump in the strains, which is denoted by the expression weak discontinuity. Usually in FE methods material interfaces are taken into account by the mesh construction. But if the structure exhibits multiple inclusions of complex geometry it can be advantageous if the interface does not have to be meshed. And when we look at at problems where the interface moves with time, e. g. phase transformation, the mesh-independent modeling of the weak discontinuities naturally holds major advantages. The greatest challenge in the modeling of discontinuities is their incorporation into numerical methods. The focus of the present work is the development, analysis and application of a finite element approach to model mesh-independent discontinuities. The method shall be robust and flexible to be applicable to both, strong and weak discontinuities.
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Congress Report 2006.11-12
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Congress Report 2006.PersReg
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Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases of knapsack problems) and linear assignment problems. We also extend already known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for different variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated problem instances.