In the present work, the process chain in tube production by roll forming of the steel 34MnB5 was examined in more detail. The process chain consisting of the steps (i) roll forming, (ii) HFI welding, and then (iii) straightening and final calibration was mapped using the finite element method. In addition to the pipe geometry, the residual stress distribution was considered as an essential target value for the assessment of the performance of the tubes under service conditions. The objective of the project is to describe the manufacturing process and thus the processing induced residual stress distributions as realistically as possible. For a more detailed characterization of the process and above all for the validation of the numerical simulations, experimental residual stress analyses were carried out for the final state of the tubes using complementary analysis methods. The contour method was used to determine the 2D-distribution of residual stresses across the transverse and longitudinal sections of the manufactured pipes. These measurements were supplemented by local residual stress analyses using the incremental hole drilling method and X-ray residual stress analyses. The work thus pursues both a methodical approach to the analysis of the internal stresses induced by the process using complementary methods and also a manufacturing approach to the analysis and evaluation of the production chain. In particular for the axial components of the residual stresses, it can be shown that experimentally determined residual stresses correlate well with the numerically calculated values. The contour method is excellently suited to monitor the uneven distribution of the internal stresses over the pipe cross-section. The results of the simulation show that the overall residual stress distribution that is determined using the contour method mainly results from the plastic strains introduced by the roll forming process. X-ray and hole drilling analyses are shown to be more suitable for measuring locally present residual stresses at defined positions on the outer tube surface. In this way it can be shown that the simulation approach described provides an accurate model of the process.

In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor fields are investigated and a decomposition formula is described. It is pointed out that the decomposition formula is of importance for the spectral analysis of the gravitational tensor in (spaceborne) gradiometry. Tensor spherical harmonics are introduced as eigenfunctions of a tensorial analogue to the Beltrami operator and discussed in detail. Based on these preliminaries, a spline interpolation process is described and error estimates are presented. Furthermore, some relations between the spline basis functions and the theory of radial basis functions are developed.

This paper presents a fully coupled three-dimensional finite element model for the simulation of a tube manufacturing process consisting of roll forming and high-frequency induction welding. The multiphysics model is based on the dual mesh method. Thus, the electromagnetic field, the temperature field, the elasto-plastic deformation of the weld bead, and the phase transformations within the material can be simulated for a moving tube without remeshing. A comparison with measurements shows that the geometry of the welded tube and the weld bead, the force on the squeeze rolls, the temperature along the band edges, and the hardness distribution within the heat-affected zone can be simulated realistically.

If we are interested in gaining a deeper understanding of a signal (signature) on the sphere, it is advantageous to study its space and frequency contributions.

In what follows, we discuss function systems occurring in Cartesian and spherical potential theory to handle problems, e.g., in geosciences, prospection, and exploration.

In what follows we discuss first order differential equations concerned with geoscientifically relevant applications, namely gravitational deflections of the vertical and geostrophic ocean flow.

Thus, potential theory on the sphere $$\Omega \, \subset \,R3$$ with respect to $$\Delta *$$ shows some aspects different from potential theory in Euclidean space R3.

Our considerations in the following chapters will be exclusively undertaken with respect to two-dimensional spheres embedded in the Euclidean space $${\mathbb{R}}^{3}$$ .

In this chapter we start with some notation in the three-dimensional Euclidean space ℝ3. The most important differential operators in ℝ3 to be needed throughout the work are listed. We give the representation of the gradient and the Laplace operator and split them into their radial and angular parts.

This paper presents an experimental electro-thermo-mechanical simulation of high-frequency induction (HFI) welding to investigate the effect of temperature and contact normal stress on the weld seam quality. Therefore welding experiments at different temperatures and contact pressures are performed using flat specimens of 34MnB5 steel sheet. In order to characterize the weld seam strength of the welded specimens, tensile and bending tests are performed. To obtain a relative weld seam strength, the bending specimens were additionally hardened prior to testing. With the hardened specimens, it can be shown that the weld seam strength increases with increasing temperature and contact normal stress until a kind of plateau is formed where the weld seam strength remains almost constant. In addition to mechanical testing, the influence of the investigated process parameters on the weld seam microstructure is studied metallographically using light optical microscopy, scanning electron microscopy, EBSD and hardness measurements. It is shown that the weld seam strength is related to the amount of oxides in the bonding line.

This chapter characterizes the components of the Earth’s magnetic field, but only to the extent needed for the book. An insight into the constituents of crustal geomagnetic field research is given.

This chapter studies graphical demonstrations of locally supported Haar mollifier decorrelation for special test examples, namely the Marmousi-model and an area of the Bavarian Molasse Basin.

This chapter discusses inverse magnetometry as an ill-posed problem in dipole reflected nomenclature. It is mentioned that all criteria of Hadamard’s classification (existence, uniqueness, and stability) are violated for terrestrial data. Consequently, inverse magnetometry is considered to be “too ill-posed” in order to use regularization techniques other than mollifier regularization.

This chapter reviews results of potential theory as far as they are significant for the understanding of dipole potential based magnetometry. The various questions and problems of dipole-oriented magnetometry are made scientifically available.

The simulation of a thin film on a small scale surface that covers only part of the domain must incorporate the contact angle force acting on the border between wetted and dry parts of the surface. A method to reconstruct this contact line and interpolate the resulting force while using smoothed particle hydrodynamics as discretization method is derived, using only geometrical properties to calculate all needed parameters. The method is applied to several test cases to prove its applicability to the simulation of thin films. (C) 2020 Elsevier Ltd. All rights reserved.

The shallow water equations are discretized using the smoothed particle hydrodynamics (SPH) method. This combination is applied to the simulation of a small scale thin fluid film on partially wetted and curved surfaces. The simulation incorporates all relevant forces, including surface tension and the contact angle force at the separating line between dry and wet regions. The resulting rivulet flow is validated using theoretical findings and measurements carried out elsewhere. (C) 2019 Elsevier B.V. All rights reserved.

Dieser Beitrag stellt eine geodätisch relevante Sammlung von besonders wertvollem Material in den diversen Approximationsgebieten dar, die mit Kugelfunktionen, Splines und Wavelets involviert sind, und zwar in einem konsistenten und vereinheitlichtem Gefüge. Das Ziel der Arbeit besteht darin vorzugsweise Geodäten zu überzeugen, dass sphärisch orientierte Approximation ein reiches mathematisches Füllhorn bereitstellt, welches viel für eine breite Palette von Anwendungen zu bieten hat. Geomathematisch spiegelt es sowohl die approximative Erdfigur als auch die typische Satellitengeometrie eines tief fliegenden Erdorbiters wider. Unser wesentliches Interesse liegt in den Charakteristiken der Rekonstruktion und Dekomposition der verschiedenen Datentypen auf Sphären und der natürlich in der geodätischen Praxis auftretenden mannigfaltigen Observablen. Ein weiteres Anliegen ist, eine Zusatzbibliothek für Interessenten in lokal sowie global geprägter sphärischer Approximationstheorie verfügbar zu machen.

Satellite Gravitational Gradiometry (SGG) is an observational technique of globally establishing the fine structure and the characteristics of the external Earth's gravitational field. The "Gravity field and steady-state Ocean Circulation Explorer" GOCE (2009–2013) was the first satellite of ESA's satellite programme intended to realize the principle of SGG and to deliver useful SGG-data sets. In fact, GOCE was capable to provide suitable data material of homogeneous quality and high data density. Mathematically, SGG demands the determination of the gravitational potential in the exterior of the Earth including its surface from given data of the gravitational Hesse tensor along the satellite orbit. For purposes of modeling we are led to invert the "upward continuation"-operator resulting from the Abel–Poisson integral formula of potential theory. This approach requires the solution of a tensorial Fredholm integral equation of the first kind relating the desired Earth's gravitational potential to the measured orbital gravitational gradient acceleration. The integral equation constitutes an exponentially ill-posed problem of the theory of inverse problems, which inevitably needs two regularization processes, namely "downward continuation" and (weak or strong) "error regularization" in the case of noisy data. This contribution deals with two different SGG-multiscale regularization methods, one in space domain and the other in frequency domain. Both procedures provide the gravitational potential as derived from tensorial SGG-data along the satellite orbit on the real Earth's surface as required from the view point of geodesy.

The smoothed particle hydrodynamic (SPH) method is applied to the simulation of a small scale thin fluid film. The major influence of surface tension effects in small scales leads to the need of a method capable of accurately modeling third order derivatives. Previous results show that there are circumstances where SPH is not consistent, resulting in difficulties to calculate higher order derivatives. In order to resolve this, the SPH method is extended using the finite particle method which allows to consistently calculate derivatives up to a chosen order. The model is validated by comparing the stationary simulation of a small drop to the analytical solution.