Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Design and Finite Element Analysis of Hybrid Stepper Motor for Spacecraft Applications

This paper presents the design and analysis of a 400-step hybrid stepper motor for spacecraft applications. The design of the hybrid stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. In this paper, a detailed account of the results of two-dimensional finite-element (FE) analysis conducted with different tooth shapes such as square and trapezoidal, is presented. The use of % more corresponding increase in detent torque and distorted static torque profile. For the requirements of maximum torque density, less-detent torque, and better positional accuracy and smooth static torque profile, different pitch slotting with equal tooth width has to be provided. From the various FE models subjected to analysis trapezoidal teeth configuration with unequal tooth pitch on the stator and rotor is found to be the best configuration and is selected for fabrication. The designed motor is fabricated and the experimental results is compared with the FE results

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Calculations of the polycentric linear molecule H^2+_3 with the finite element method

A fully numerical two-dimensional solution of the Schrödinger equation is presented for the linear polyatomic molecule H^2+_3 using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the 1\sigma and 2\sigma orbitals is of the order of 10^-7 au.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N_2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.

Spin-polarized Hartree-Fock-Slater calculations in atoms and diatomic molecules with the finite element method

We present spin-polarized Hartree-Fock-Slater calculations performed with the highly accurate numerical finite element method for the atoms N and 0 and the diatomic radical OH as examples.

H_2 solved by the finite element method

We report on the solution of the Hartree-Fock equations for the ground state of the H_2 molecule using the finite element method. Both the Hartree-Fock and the Poisson equations are solved with this method to an accuracy of 10^-8 using only 26 x 11 grid points in two dimensions. A 41 x 16 grid gives a new Hartree-Fock benchmark to ten-figure accuracy.

Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

A finite state model for on-line analytical processing in triadic contexts

About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the basic ideas of OLAP, and show how they may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.