An efficient mass lumping scheme for isogeometric analysis based on approximate dual basis functions

In this contribution, we propose a new mass lumping scheme for explicit dynamics in isogeometric analysis (IGA). To this end, an element formulation based on the idea of dual functionals is developed. Non-Uniform Rational B-splines (NURBS) are applied as shape functions and their corresponding dual basis functions are applied as test functions in the variational form, where two kinds of dual basis functions are compared. The first type are approximate dual basis functions (AD) with varying degree of reproduction, resulting in banded and diagonally-dominant mass matrices. Dual basis functions derived from the inversion of the Gram matrix (IG) are the second type and already yield diagonal mass matrices. We will show that it is possible to apply the dual scheme as a transformation of the resulting system of equations based on NURBS for both – shape and test functions. Hence, it can be easily implemented into existing IGA routines and it is also promising to retain the accuracy known from similar formulations without mass lumping. Applying additional row-sum lumping to the mass matrices is either not necessary for IG or the caused loss of accuracy is lowered to a reasonable magnitude in the case of AD. Numerical examples show a significantly better approximation of the dynamic behavior for the dual lumping scheme compared to standard NURBS approaches making use of conventional row-sum lumping. In a nutshell, applying IG yields accurate numerical results but fully populated stiffness matrices occur, which are entirely unsuitable for explicit dynamic simulations, while combining AD and row-sum lumping leads to efficient dynamical computations, with respect to effort and accuracy

Investigation of three-body abrasive wear systems with hard particles and liquid as intermediate medium using a customized tribometer

This article discusses dynamic phenomena and the measurement of forces in short-term tests of tribological three-body abrasive wear systems with hard silicon carbide particles. Tribometers enable the measurement of forces, whereby analytical methods are used to determine the forces transmitted in the tribological contact zone on the basis of the forces recorded with a dynamometer that is not directly located in the tribological contact zone. In addition to the theoretical background, this article also deals with a realization of the tribometer, which requires some finely tuned adaptations compared to the ideal tribometer due to tolerances existing in reality. The data basis for the evaluation is a series of experiments with three-body abrasive wear systems with and without liquid, different particle sizes, particle quantities, loads and speeds. In contrast to many other publications, the focus is not only on mean values, but also on the relative spread (i.~e.~the standard deviation per mean value) of occurring forces. In particular, the relative spread shows clear and repeatable trends and thus qualifies as a supporting criterion for the comparison of different force measurements of tribological systems. Furthermore, an alternative to the established procedure of randomized test execution is presented in order to detect (unintentional) temporal changes in the test conditions

Development of a screw extruder for extracting linseed oil from flax

Due to the short shelf life of linseed oil, it makes sense to produce it by pressing linseed directly before consumption. Inorder to gain knowledge about the pressing process, a simulation model using the Discrete Element Method (DEM) was created.For the description of the model basic tests were carried out to determine characteristic parameters of the seeds such as modulus of elasticity, coefficients of friction, particle size and bulk density. Subsequently an oil press has been designed and a prototypewas produced. Experiments in which linseed, rapeseed and hemp has been processed under different test conditions have shownmoderate functionality. As a result the mass flow in the entry section of the prototype was adjusted. Within this modification amodular structure was realized in order to enable further adaptations and tests with less effort

Attraktivitätsfaktoren der Fakultät für Wirtschaftswissenschaft (FWW) und der Otto-von-Guericke-Universität Magdeburg (OvGU): Eine empirische Untersuchung im Raum Magdeburg

Die hier skizzierte empirische Untersuchung wurde im Rahmen eines Projektseminars des Lehrstuhls für Unternehmensführung und Organisation an der FWW in der Zeit vom 10.10.2023 bis zum 20.03.2024 von insgesamt 24 Studierenden entwickelt und ausgewertet. Dabei entstanden Projektberichte im Gesamtumfang von ca. 600 Seiten. Der vorliegende Bericht fasst diese selektiv zusammen und wird durch zusätzliche Analysen seitens des Lehrstuhlteams ergänzt. Die theoretisch fundierte und repräsentative empirische Untersuchung wurde an vier Magdeburger Gymnasien (Abiturjahrgänge) durchgeführt. Auf Basis geeigneter SWOTund Portfolioanalysen werden ausgewählte Strategievorschläge unterbreitet

Influence of cyclic stress wave form on the fatigue behavior of bolts

Bolted joints offer the great advantage of a non-destructive disassembly and can transfer higher loads than otherdetachable connections during operation. Therefore, bolted joints are one of the most commonly used joining methods inmechanical engineering and steel construction. In current guidelines the wave form and frequency of the load are neglected whenestimating the fatigue strength. Even in rainflow counting the influence of load frequency and load wave form is also neglected.Although it is known from unnotched material samples that the wave form and frequency of the load have a measurable influence.In this study, bolts of size M10 are examined at different test frequencies and wave forms in the finite life range. The mean load iskept constant for all different wave forms during the tests. Each test is performed at a constant amplitude. For this purpose, a testsetup was designed to perform fatigue tests with fluctuating axial load. It is shown that a long application time of the load shortensthe fatigue life. In addition, the effective value of the load has an influence on the achievable service life. The greater the effectivevalue of the load, the shorter the fatigue life

An Elastohydrodynamic Lubrication Framework for Hip Prostheses based on Isogeometric Analysis

The hip prosthesis modeling involves complex fluid-structure interaction between lubricant flow and solid deformation, which is a typical elastohydrodynamic lubrication regime. This study introduces a novel numerical framework for addressing such challenges through Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis (IGA). A new form of the Reynolds equation, derived in the parametric space of curved surfaces rather than spherical coordinates, is introduced to streamline discretization within the IGA framework and integration with solid mechanics. Additionally, the momentum balance equation is utilized for calculating solid deformations, providing a more accurate description than the conventional Boussinesq approximation. Furthermore, a developed mass-conserving cavitation formulation is incorporated to depict the formation and volumetric distribution of cavitation bubbles in hip prostheses. These equations are discretized utilizing NURBS basis functions and solved simultaneously via the Newton-Raphson method, enabling efficient strong coupling and rapid convergence. This IGA-based framework also facilitates future integration of nonlinear solid deformation and frictional contact

Numerical and Experimental Considerations of Non-linearities for a Trifilar Pendulum

Moments of inertia of machine-components or whole machines are essential for numerical simulations, especially for Mutli-Body-Simulations. Various measuring techniques exists, which can be rougly divided in techniques using oscillations or accelerations. One possibility to measure indirectly the inertia properties are multifilar pendulums, for example the trifilar pendulum using a platform and three ropes or filars. A lot of literature dealing with the trifilar pendulums exists. We will give a brief overview of the literature with emphasis to non-linearities. Furthermore, we will investigate nonlinear effects and compare them with experimental and numerical results

The onset of electrothermoconvection in a viscoelastic dielectric fluid layer with internal heat source: Navier-Stokes-Voigt model

In the present paper, the combined effect of a vertical alternating current (AC) electric field and a vertical temperature gradient on a horizontal layer of viscoelastic dielectric fluid with internal heat source/heat sink has been investigated using Navier-Stokes–Voigt model. A linear stability analysis employing the normal mode technique is conducted in the present problem for free boundaries, considering cases of heating the fluid layer from below and above separately. The effect of the electric field and internal heat source/heat sink is analysed numerically on the fluid system for stationary convection using the software MATHEMATICA and also predicted graphically

Unscharfe Regelsysteme im Strategischen Management

Im Kontext des Strategischen Managements der Unternehmung sind Bündel abstrakter Maßnahmen zur Steuerung und Führung von und in Systemen zu entwickeln sowie anzuwenden, die erst zu späteren Zeitpunkten konkretisiert und ausdifferenziert werden. Solche Maßnahmenbündel nennen wir Strategien. Strategien müssen logisch fundiert und formuliert werden, es sind also aus wahren Prämissen die richtigen Schlüsse zu ziehen und Fehlschlüsse zu vermeiden. Zu deren Generierung, Evaluierung und Selektion benötigt man Regelsysteme, die entweder univok oder ambiguos konstruiert sein können. Unscharfen Regelsystemen im Strategischen Management ist die vorliegende Arbeit gewidmet.In the context of the strategic management of the company, bundles of abstract measures for the control and management of and in systems are to be developed and applied, which are only concretized and differentiated at later points in time. We call such bundles of measures strategies. Strategies must be logically founded and formulated, i.e. the correct conclusions must be drawn from true premises and false conclusions must be avoided. To generate, evaluate and select them, rule systems are required that can be constructed either univocally or ambiguously.  This paper is dedicated to fuzzy rule systems in strategic management

On Estimating the Growth Rate of Perturbations in Rivlin-Ericksen Ferromagnetic Convection with Magnetic Field Dependent Viscosity

The unique viscoelastic properties and the consideration of MFD (magnetic field dependent) viscosity in the Viscoelastic ferrofluid model render it highly suitable for the accurate modeling of complex biological fluids, such as blood. The present research comprises the study of perturbation growth rate in a case of Rivlin-Ericksen Ferrofluid layer with viscosity depending on a vertically acting magnetic field. The complex growth rate of an arbitrary oscillatory motion with growing amplitude in Rivlin-Ericksen ferromagnetic convection for free-free boundaries has been analytically proven to be located within a semicircle in the right half of the σiσr-plane and (radius)2 = [RM1/Pr(1+2(1+δM3)π2Fν)]. Bounds are also obtained for situation involving rigid boundaries. For stress-free boundaries, the sufficient condition for PES validity is derived as [RM1Pr/π4(1+(1+δM3)π2Fν)] ≤ 1, where R represents the Rayleigh number, Pr is the Prandtl number, Fν characterizes viscoelasticity of Rivlin- Ericksen ferrofluid, M3 > 0 is the measure of the nonlinearity of magnetization and M1 is the magnetic number. The mathematical derivation of these results is presented in detail. Thus the analysis presented here reveals that the oscillations in Rivlin-Ericksen ferromagnetic convection can be regulated or halted by taking into account the viscosity dependent on the magnetic field and the viscoelasticity of the fluid