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Sparse grids can be used to discretize elliptic differential equations of second order on a d‐dimensional cube. Using the Ritz‐Galerkin discretization, one obtains a linear equation system with 𝒪 (N (log N)d−1) unknowns. The corresponding discretization error is 𝒪 (N−1 (log N)d−1) in the H1‐norm. A major difficulty in using this sparse grid discretization is the complexity of the related stiffness...
This contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity‐ (and capillarity‐)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump...
Coated fabric membranes have been widely used in construction of light‐weight structures. The material behavior of textile membranes is highly nonlinear and anisotropic which may not be sufficiently represented by commonly used linear elastic orthotropic models. This contribution presents a formulation of a suitable nonlinear anisotropic polyconvex energy function for textile membranes in the geometrically...
Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models when there are discontinuities, such as cracks, present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study, we focus on the dispersion properties of a one‐dimensional state‐based linearized peridynamics model...
The improvement of the dynamic behaviour of an elastic rotor which is supported by journal bearings represents an ongoing field of research, whereby various modifications of the corresponding bearings and their geometry have been proposed in literature. In order to suppress or at least to decrease unwanted oscillations due to negative effects of instability phenomena of the ’oil‐whirl’‐ and/or ’oil‐whip’‐type,...
High‐frequency vibrations have been shown to smooth the effective characteristics of dry friction and may be used in order to quench undesired phenomena such as friction induced vibrations. As the agreement between classical modelling and related experimental results appears to be insufficient, the effect of contact compliance on vibrational smoothing of dry friction has been discussed. Recently,...
The assembly of bolted joints is often based on the assumption that the joint has been assembled as the design guidelines prescribe. However, during the tightening process, errors can occur, some of which can be affiliated with friction‐induced vibrations. In order to improve the automated tightening process and reduce the influence of friction‐induced vibrations, an additional high frequency torque...
Shaft seals shall prevent the leakage of oil and the intrusion of dirt particles in rotating machineries. A loss of contact between shaft and seal results in leakage. In order to ensure the functionality of the sealing system, the followability of the seal needs to be ensured. To analyze this problem, a model of a Polytetrafluorethylen (PTFE) shaft seal is coupled with an unbalanced rotor. PTFE has...
Solving an engineering problem starts with the description of the problem in mathematical formulas and the identification of parameters. The generated model is then used to simulate the behavior of the underlying system. However, most systems are not static. They change over time. Thus, the model needs to be adapted to these activities otherwise the predictions are wrong.
A data driven modeling method...
A global forming model for the special and unconventional forming process called “Die‐Less‐Hydroforming” that can be used for the inflation of arbitrary double‐layered or multi‐layered seal‐welded blanks was already presented by the authors in recent publications. While looking on the modeling of the specific seal‐weld in this global model, as a special modeling step the elements at the edges of the...
In the analysis of plate and shell bending problems using an isogeometric Reissner‐Mindlin approach, transversal shear locking effects may occur especially for thin structures. One possibility to overcome locking effects is to increase the polynomial order of the NURBS basis functions. However, there are certain examples where this method shows some deficiencies, like oscillations. For low polynomial...
We apply a multipreconditioned domain decomposition method based on Finite Element Tearing and Interconnecting to linear structural dynamics with highly heterogeneous material properties. A recently published method to build and select the multiple directions is presented and applied. We hint at possible problems when localized phenomena are considered and present a new simple measure that extends...
Open‐cell metal foams are a new class of cellular materials with structural features resembling those of lightweight load‐bearing materials such as cancellous bones and wood. Their high stiffness‐to‐weight ratio coupled with their typical long, flat stress‐strain response make them ideal candidates as cost‐effective shock energy absorbers in crashworthiness, impact loading and blast mitigation strategies...
The present work focuses on spectral analysis of the streamwise velocity fluctuations obtained, utilizing the Cottbus Large Pipe (CoLaPipe) test facility for R+ ≤ 3500, where R+ is the Reynolds number based on the wall friction velocity, uτ, and the pipe radius, R. Measurements of the streamwise spectra have been conducted using a single hot‐wire probe. Few runs have been also performed using Particle...
Classical molecular dynamics (MD) simulations are performed to study the stress‐strain behaviour of armorphous silica glass (a‐SiO2) at small time and length scales. Various amorphous states are generated by quenching molten SiO2 using a two‐body and a three‐body interaction potential. This quenching process is carried out for different cooling rates. The structural properties of a‐SiO2 are validated...
Wafers are usually coated by using spin‐coating, where centrifugal forces are used to spread a droplet on the rotating wafer. This flow is unstable to the fingering instability, where several segments of the wetting front spread faster than the average, resulting in several fingers. The liquid flows via the existing fingers while the area in between does not get coated. A precise experimental investigation...
The objective of this investigation is the development of a reliable methodology allowing the accurate prediction of compressor surge. In this context a centrifugal compressor used in a commercial application with five main and five splitter blades, installed in regular passenger vehicles, is numerically analyzed. For this purpose a CFD analysis is conducted. The steady‐state and unsteady secondary...
Consider planar, incompressible laminar high Reynolds number (Re) flow between two parallel plates: fluid is removed through the permeable upper wall in order to generate adverse pressure gradient conditions in mean flow direction. As a consequence of relatively weak suction, the boundary layer at the impermeable lower wall is forced to separate locally. The corresponding reverse flow region (separation...
In this contribution three mixed least‐squares finite element methods (LSFEMs) for the incompressible Navier‐Stokes equations are investigated with respect to accuracy and efficiency. The well‐known stress‐velocity‐pressure formulation is the basis for two further div‐grad least‐squares formulations in terms of stresses and velocities (SV). Advantage of the SV formulations is a system with a smaller...
This paper focuses on experimental investigations for lubricated contacts with partially filled gaps. The measurements are performed on two different scales. A pin‐on‐disc test bench represents the microscopic scale whereas a novel test bench with asperities in the range of centimeters corresponds to a rather macroscopic scale. The results are compared and conclusions towards the tribological properties...
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