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Shell Models (shell + models)

Distribution by Scientific Domains

Chemistry	33%

Selected Abstracts

Aspects of the modelling of the radial distribution function for small nanoparticles

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2007
Vladimir I. Korsunskiy
An approach to modelling radial distribution functions (RDFs) of nanoparticle samples over a wide range of interatomic distances is presented. Two different types of contribution to the model RDF are calculated. The first explicitly reflects the structure of the nanoparticle parts with more or less crystalline atomic structure. It can be calculated precisely and contains comparatively sharp peaks, which are produced by the set of discrete interatomic distances. The second includes RDF contributions from distances between weakly correlated atoms positioned within different nanoparticles or within different parts of a nanoparticle model. The calculation is performed using the approximation of a uniform distribution of atoms and utilizes the ideas of the characteristic functions of the particle shape known in small-angle scattering theory. This second RDF contribution is represented by slowly varying functions of interatomic distance r. The relative magnitude of this essential part of the model RDF increases with increasing r compared with the part that represents the ordered structure. The method is applied to test several spherical and core/shell models of semiconductor nanoparticles stabilized with organic ligands. The experimental RDFs of ZnSe and CdSe/ZnS nanoparticle samples were obtained by high-energy X-ray diffraction at beamline BW5, HASYLAB, DESY. The ZnSe nanoparticles have a spherical core with approximately 26,Å diameter and zincblende structure. The RDF of the CdSe/ZnS nanoparticle sample shows resolved peaks of the first- and the second-neighbour distances characteristic for CdSe (2.62 and 4.27,Å) and for ZnS (2.33 and 3.86,Å) and for the first time clearly confirms the presence of CdSe and ZnS nanophases in such objects. The diameters of the CdSe and ZnS spherical cores are estimated as 27 and 15,Å. CdSe and ZnS are present in the sample for the most part as independent nanoparticles. A smaller amount of ZnS forms an irregularly shaped shell around the CdSe cores, which consists of small independently oriented ZnS particles. [source]

Consistent coupling of beam and shell models for thermo-elastic analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004
K. S. Chavan
Abstract In this paper, the finite element formulation of a transition element for consistent coupling between shell and beam finite element models of thin-walled beam-like structures in thermo-elastic problems is presented. Thin-walled beam-like structures modelled only with beam elements cannot be used to study local stress concentrations or to provide local mechanical or thermal boundary conditions. For this purpose, the structure has to be modelled using shell elements. However, computations using shell elements are a lot more expensive as compared to beam elements. The finite element model can be more efficient when the shell elements are used only in regions where the local effects are to be studied or local boundary conditions have to be provided. The remaining part of the structure can be modelled with beam elements. To couple these two models (i.e. shell and beam models) at transitional cross-sections, transition elements are derived here for thermo-elastic problems. The formulation encloses large displacement and rotational behaviour, which is important in case of thin-walled beam-like structures. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A general high-order finite element formulation for shells at large strains and finite rotations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003
Y. Ba
Abstract For hyperelastic shells with finite rotations and large strains a p -finite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general three-dimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent stiffness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking effects. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On the classical shell model underlying bilinear degenerated shell finite elements: general shell geometry

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2002
Mika Malinen
Abstract We study the shell models arising in the numerical modelling of shells by geometrically incompatible finite elements. We build a connection from the so-called bilinear degenerated 3D FEM to the classical 2D shell theory of Reissner,Naghdi type showing how nearly equivalent finite element formulations can be constructed within the classical framework. The connection found here facilitates the mathematical error analysis of the bilinear elements based on the degenerated 3D approach. In particular, the connection reveals the ,secrets' that relate to the treatment of locking effects within this formulation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the classical shell model underlying bilinear degenerated shell finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2001
Mika MalinenArticle first published online: 2 AUG 200
Abstract We study the shell models arising in the numerical modelling of shells by bilinear degenerated shell finite elements. The numerical model of a cylindrical shell obtained by using flat shell elements is given an equivalent formulation based on a classical two-dimensional shell model. We use the connection between the models to explain how a parametric error amplification difficulty or locking is avoided by some elements. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Debye,Waller factors of compounds with the caesium chloride structure

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2000
H. X. Gao
The lattice dynamics of five compounds with the caesium chloride structure have been investigated using shell models. Debye,Waller factors for these compounds are calculated over the temperature range from 1 to 1000,K and the results are presented analytically in a polynomial form. When experimental results are available, the calculated results are compared to the experimentally measured Debye,Waller factors and typically the discrepancies between these factors are less than 10%. [source]