Richards Grzhibovskis

Analysis of the deep rolling process on turbine blades using the FEM/BEM-coupling

Highly stressed components of aircraft engines, like turbine blades, have to satisfy stringent requirements regarding durability and reliability. The induction of compressive stresses and strain hardening in their surface layer has proven as a promising method to significantly increase their fatigue resistance. The required surface layer properties can be achieved by deep rolling. The determination of optimal process parameters still requires elaborate experimental set-up and subsequent time- and cost-extensive measurements. In previous works the application of the Finite Element Method (FEM) was proposed as an effective and cost reducing alternative to predict the surface layer state for given process parameters. However, FEM requires very fine mesh in the surface layer to resolve the high stress gradients with sufficient accuracy. The hereby caused high time and memory requirements render an efficient simulation of complete turbine components as impossible. In this article a solution is offered by coupling the FEM with the Boundary Elements Method (BEM). It enables the computing of large scale models at low computational cost and high result accuracy. Different approaches of the FEM/BEM-coupling for the simulation of deep rolling are examined with regard to their stability and required computing time.

Fast numerical method for the Boltzmann equation on non-uniform grids

We introduce a new fast numerical method for computing discontinuous solutions to the Boltzmann equation and illustrate it by numerical examples. A combination of adaptive grids for approximation of the distribution function and an approximate fast Fourier transform on non-uniform grids for computing smooth terms in the Boltzmann collision integral is used.

A convolution thresholding scheme for the Willmore flow

A convolution thresholding scheme fro geometric Willmore flows is suggested and the consistency is proved.

Entropy Inequalities for Evaporation/Condensation Problem in Rarefied Gas Dynamics

The present paper is devoted mainly to the half space problem for stationary Boltzmann-type equations. Using only conservation laws and the Boltzmann H-theorem we derive an inequality for unknown constant fluxes of mass, energy, and momentum. This inequality is expressed in terms of three parameters (pressure p, temperature T and the Mach number M) of the asymptotic Maxwellian at infinity. Geometrically the inequality describes a “physical” domain with positive entropy production in the 3-d space of the parameters. The domain appears to be qualitatively different for evaporation and condensation problems. We show that for given M, the curve p=p(M), T=T(M) of maximal entropy production practically coincides with the experimental evaporation curve obtained by Sone et al. on the basis of numerical solutions of BGK equation. Similar consideration for the condensation problem is also in qualitative agreement with known numerical results.

A Convolution-Thresholding Approximation of Generalized Curvature Flows

We construct a convolution-thresholding approximation scheme for the geometric surface evolution in the case when the velocity of the surface at each point is a given function of the mean curvature. Conditions for the monotonicity of the scheme are found and the convergence of the approximations to the corresponding viscosity solution is proved. We also discuss some aspects of the numerical implementation of such schemes and present several numerical results.

Time-Efficient and Precise FEM/BEM Simulation of a Cold Forging Process Verified by Tool Load Determination

Developing green processes establishes new possibilities for cold forging industry. Current technological developments require automotive parts with less mass, but higher material-efficiency. To achieve these goals, high-strength steels and complex geometries are used. The rising process forces lead to increased tool loads and subsequently elastic tool deformation resulting in early tool failure or dimensional deviations. A numerical determination of tool loads during process enables their reduction by a load-dependent design of the tool geometry. Aim of this work is a time-efficient and precise determination of tool loads considering the complete tool system using the example of a lateral extrusion process. By domain decomposition into Finite Element Method (FEM) and Boundary Element Method (BEM) domains and subsequently an integrated FEM/BEM simulation, a significant computation time reduction towards a conventional FEM model is achieved. Experiments of the examined lateral extrusion process provide data for the verification of the investigated process simulation models. In order to be able to validate the simulated elastic tool deformations, strain gauges are installed on the die insert and allow an experimental measurement of the elastic radial die strains. Additionally the simulated process force development and the final workpiece geometry of the simulation models are compared with experimental results.

Mechanics of lipid bilayer junctions affecting the size of a connecting lipid nanotube

In this study we report a physical analysis of the membrane mechanics affecting the size of the highly curved region of a lipid nanotube (LNT) that is either connected between a lipid bilayer vesicle and the tip of a glass microinjection pipette (tube-only) or between a lipid bilayer vesicle and a vesicle that is attached to the tip of a glass microinjection pipette (two-vesicle). For the tube-only configuration (TOC), a micropipette is used to pull a LNT into the interior of a surface-immobilized vesicle, where the length of the tube L is determined by the distance of the micropipette to the vesicle wall. For the two-vesicle configuration (TVC), a small vesicle is inflated at the tip of the micropipette tip and the length of the tube L is in this case determined by the distance between the two interconnected vesicles. An electrochemical method monitoring diffusion of electroactive molecules through the nanotube has been used to determine the radius of the nanotube R as a function of nanotube length L for the two configurations. The data show that the LNT connected in the TVC constricts to a smaller radius in comparison to the tube-only mode and that tube radius shrinks at shorter tube lengths. To explain these electrochemical data, we developed a theoretical model taking into account the free energy of the membrane regions of the vesicles, the LNT and the high curvature junctions. In particular, this model allows us to estimate the surface tension coefficients from R(L) measurements.

Shape of red blood cells in contact with artificial surfaces

The phenomenon of physical contact between red blood cells and artificial surfaces is considered. A fully three-dimensional mathematical model of a bilayer membrane in contact with an artificial surface is presented. Numerical results for the different geometries and adhesion intensities are found to be in agreement with experimentally observed geometries obtained by means of digital holographic microscopy.