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Nach Stand von Wissenschaft und Technik werden Komponenten hinsichtlich ihrer Eigenschaften, wie Lebensdauer oder Energieeffizienz, optimiert. Allerdings können selbst hervorragende Komponenten zu ineffizienten oder instabilen Systemen führen, wenn ihr Zusammenspiel nur unzureichend berücksichtigt wird. Eine Systembetrachtung schafft ein größeres Optimierungspotential - dem erhöhten Potential steht jedoch auch ein erhöhter Komplexitätsgrad gegenüber. Die vorliegende Arbeit ist im Rahmen des Sonderforschungsbereichs 805 entstanden, dessen Ziel die Beherrschung von Unsicherheit in Systemen des Maschinenbaus ist. Die Arbeit zeigt anhand eines realen Systems aus dem Bereich der Hydraulik, wie Unsicherheit in der Entwicklungsphase beherrscht werden kann. Hierbei ist neu, dass die durch den späteren Betrieb zu erwartende Systemdegradation eines jeden möglichen Systemvorschlags antizipiert werden kann. Dadurch können Betriebs- und Wartungskosten vorausgesagt und minimiert werden und durch eine optimale Betriebs- und Wartungsstrategie die Verfügbarkeit des Systems garantiert werden. Wesentliche Fragen bei der optimalen Auslegung des betrachteten hydrostatischen Getriebes sind dessen physikalische Modellierung, die Darstellung des Optimierungsproblems als gemischt-ganzzahliges lineares Programm, und dessen algorithmische Behandlung zur Lösungsfindung. Hierzu werden Heuristiken zum schnelleren Auffinden sinnvoller Systemtopologien vorgestellt und mittels mathematischer Dekomposition eine Bewertung des dynamischen Verschleiß- und Wartungsverlaufs möglicher Systemvorschläge vorgenommen. Die Arbeit stellt die Optimierung technischer Systeme an der Schnittstelle von Mathematik, Informatik und Ingenieurwesen sowohl gründlich als auch anschaulich und nachvollziehbar dar.
Finding a good system topology with more than a handful of components is a
highly non-trivial task. The system needs to be able to fulfil all expected load cases, but at the
same time the components should interact in an energy-efficient way. An example for a system
design problem is the layout of the drinking water supply of a residential building. It may be
reasonable to choose a design of spatially distributed pumps which are connected by pipes in at
least two dimensions. This leads to a large variety of possible system topologies. To solve such
problems in a reasonable time frame, the nonlinear technical characteristics must be modelled
as simple as possible, while still achieving a sufficiently good representation of reality. The
aim of this paper is to compare the speed and reliability of a selection of leading mathematical
programming solvers on a set of varying model formulations. This gives us empirical evidence
on what combinations of model formulations and solver packages are the means of choice with the current state of the art.
The behaviour of infilled reinforced concrete frames under horizontal load has been widely investigated, both experimentally and numerically. Since experimental tests represent large investments, numerical simulations offer an efficient approach for a more comprehensive analysis. When RC frames with masonry infill walls are subjected to horizontal loading, their behaviour is highly non-linear after a certain limit, which makes their analysis quite difficult. The non-linear behaviour results from the complex inelastic material properties of the concrete, infill wall and conditions at the wall-frame interface. In order to investigate this non-linear behaviour in detail, a finite element model using a micro modelling approach is developed, which is able to predict the complex non-linear behaviour resulting from the different materials and their interaction. Concrete and bricks are represented by a non-linear material model, while each reinforcement bar is represented as an individual part installed in the concrete part and behaving elasto-plastically. Each brick is modelled individually and connected taking into account the non-linearity of a brick mortar interface. The same approach is followed using two finite element software packages and the results are compared with the experimental results. The numerical models show a good agreement with the experiments in predicting the overall behaviour, but also very good matching for strength capacity and drift. The results emphasize the quality and the valuable contribution of the numerical models for use in parametric studies, which are needed for the derivation of design recommendations for infilled frame structures.
Eine seismische Anregung verursacht in einem Flüssigkeitstank einen kombinierten Spannungszustand, was zu einem Stabilitätsversagen der häufig sehr dünnwandigen Konstruktionen führen kann. Für die Durchführung von Stabilitätsnachweisen stehen verschiedene Verfahren zur Verfügung. Üblicherweise werden aus Gründen der Einfachheit spannungsbasierte Verfahren angewendet. Diese sind für Einheitslastfälle experimentell abgesichert, wobei eine Übertragung auf kombinierte Spannungszustände wie im Erdbebenfall nur begrenzt möglich ist. Alternativ kann ein globales, numerisches Konzept, das LBA/MNA-Verfahren, angewendet werden. Das Verfahren kombiniert eine materiell nichtlineare Berechnung (MNA) mit einer linearen Beulanalyse (LBA) und erfasst die Interaktion verschiedener gleichzeitig auftretender Beanspruchungen implizit im Nachweis. Dieser Beitrag demonstriert die Anwendung der Verfahren am Beispiel verschiedener Tankgeometrien mit Höhe/Radius-Verhältnissen zwischen 1 ≤ H/R ≤ 2 und Radius/Tankwand-Verhältnissen zwischen 500 ≤ R/t ≤ 1000 und diskutiert zusätzlich die Defizite der spannungsbasierten Nachweisverfahren.
Elastomers are exceptional materials owing to their ability to undergo large deformations before failure. However, due to their very low stiffness, they are not always suitable for industrial applications. Addition of filler particles provides reinforcing effects and thus enhances the material properties that render them more versatile for applications like tyres etc. However, deformation behavior of filled polymers is accompanied by several nonlinear effects like Mullins and Payne effect. To this day, the physical and chemical changes resulting in such nonlinear effect remain an active area of research. In this work, we develop a heterogeneous (or multiphase) constitutive model at the mesoscale explicitly considering filler particle aggregates, elastomeric matrix and their mechanical interaction through an approximate interface layer. The developed constitutive model is used to demonstrate cluster breakage, also, as one of the possible sources for Mullins effect observed in non-crystallizing filled elastomers.
Rubber materials filled with reinforcing fillers display nonlinear rheological behavior at small strain amplitudes below γ0 < 0.1. Nevertheless, rheological data are analyzed mostly in terms of linear parameters, such as shear moduli (G′, G″), which loose their physical meaning in the nonlinear regime. In this work styrene butadiene rubber filled with carbon black (CB) under large amplitude oscillatory shear (LAOS) is analyzed in terms of the nonlinear parameter I3/1. Three different CB grades are used and the filler load is varied between 0 and 70 phr. It is found that I3/1(φ) is most sensitive to changes of the total accessible filler surface area at low strain amplitudes (γ0 = 0.32). The addition of up to 70 phr CB leads to an increase of I3/1(φ) by a factor of more than ten. The influence of the measurement temperature on I3/1 is pronounced for CB levels above the percolation threshold.
We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.