scholarly journals Direct determination of shape functions for isoparametric elements with arbitrary node configuration

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Julian Hoth ◽  
Wojciech Kowalczyk
Keyword(s):  
Shape Function ◽  
Direct Determination ◽  
Correction Procedure ◽  
Shape Functions ◽  
Isoparametric Element ◽  
Lagrange Polynomial ◽  
Regular Node ◽  
Element Type ◽  
Single Formula

AbstractShape functions have been derived to describe different forms of elements, notably triangles and rectangles in 2-D, and tetrahedrons, cuboids, and triangular prisms in 3-D. There are generalised solutions for some regular node configurations, and hierarchical correction algorithms help with more difficult node distributions. But to this point there is no single formula or set of formulae that allows the direct determination of shape functions for any node configuration without restrictions. This paper shows how a general set of formulae can be derived which is applicable to any isoparametric element type with arbitrary node configuration. This formulation is in such a form that it is clear and concise. The approach is based on the Lagrange polynomial considering up to three Cartesian and four volume coordinates. Additionally, the correction procedure that is inherent in the formulation to guarantee an appropriate evaluation of the generalised shape functions and to fulfil all four isoparametric shape function criteria is discussed. The proof of validity illustrates the correctness of the method.

scholarly journals Learned Peak Shape Functions for Powder Diffraction Data

1988 ◽  
Vol 41 (2) ◽  
pp. 229 ◽  
Author(s):  
A Hepp ◽  
Ch Baerlocher
Keyword(s):  
Crystal Structure ◽  
Powder Diffraction ◽  
Shape Function ◽  
Linear Interpolation ◽  
Peak Shape ◽  
Powder Diffraction Data ◽  
Shape Functions ◽  
Inflection Points ◽  
Asymmetry Function

An algorithm is described for the determination of an experimental (learned) peak shape function, which has been used succesfully in crystal structure refinements from powder data. The function gives an optimal fit to almost any peak shape since it is not based on an analytical expression. It is determined from a single peak in a pattern by first fitting this peak with the proposed algorithm which ensures that the function is smooth and has only one maximum and two inflection points. The learned function is then normalised and decomposed into a symmetric and an asymmetric part. These are stored in tabulated form, permitting linear interpolation. As with an analytical function, a FWHM and asymmetry function describing the 26 dependence of the peak shape can be applied.

On the Analysis of Raman Spectra by Curve Resolution

1977 ◽  
Vol 31 (5) ◽  
pp. 451-455 ◽  
Author(s):  
Peter Gans ◽  
J. Bernard Gill
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Liquid Ammonia ◽  
Shape Function ◽  
Shape Functions ◽  
Large Uncertainty ◽  
Empirical Parameter ◽  
Curve Resolution ◽  
Lorentzian Shape

Raman spectra obtained during studies of solution equilibria are subjected to analysis using a combination of a small, manually controlled, digital minicomputer and a large digital computer. The shape-function of the bands is regarded as an empirical parameter, and the majority of bands are found to have Lorentzian shape. Simultaneous determination of shape-function and curved baseline is shown to be unsatisfactory. The possibility that components of a multiplet have different shape-functions is considered, and a probable example of such a case is given. Finally, it is shown that the ν3 region of the Raman spectrum of sodium nitrate in liquid ammonia probably contains three component bands, but uncertainty regarding shape-function introduces large uncertainty into the areas and positions of the bands.

Lateral resolution of the electron microbeam analysis

1978 ◽  
Vol 36 (1) ◽  
pp. 542-543
Author(s):  
H.J. Dudek
Keyword(s):  
Quantitative Analysis ◽  
Depth Resolution ◽  
Lateral Resolution ◽  
Cylindrical Particle ◽  
Correction Procedure ◽  
X Ray ◽  
Element Concentrations ◽  
Microbeam Analysis ◽  
The Matrix

The chemical inhomogenities in modern materials such as fibers, phases and inclusions, often have diameters in the region of one micrometer. Using electron microbeam analysis for the determination of the element concentrations one has to know the smallest possible diameter of such regions for a given accuracy of the quantitative analysis.In th is paper the correction procedure for the quantitative electron microbeam analysis is extended to a spacial problem to determine the smallest possible measurements of a cylindrical particle P of high D (depth resolution) and diameter L (lateral resolution) embeded in a matrix M and which has to be analysed quantitative with the accuracy q. The mathematical accounts lead to the following form of the characteristic x-ray intens ity of the element i of a particle P embeded in the matrix M in relation to the intensity of a standard S

The Direct Determination of I131 in Heterogeneous Fecal Specimens

1961 ◽  
Vol 41 (4) ◽  
pp. 380-384 ◽  
Author(s):  
Arthur F. Dratz ◽  
James C. Coberly
Keyword(s):  
Direct Determination

A New Method for Direct Determination of the Recoilless Fraction with Application to Magnetic Nanoparticles

2002 ◽  
Vol 721 ◽  
Author(s):  
Monica Sorescu
Keyword(s):  
Room Temperature ◽  
Average Particle Size ◽  
Direct Determination ◽  
Average Particle ◽  
Lattice Method ◽  
Recoilless Fraction ◽  
Single Room ◽  
Magnetite Particles ◽  
Physical Mixtures

AbstractWe propose a two-lattice method for direct determination of the recoilless fraction using a single room-temperature transmission Mössbauer measurement. The method is first demonstrated for the case of iron and metallic glass two-foil system and is next generalized for the case of physical mixtures of two powders. We further apply this method to determine the recoilless fraction of hematite and magnetite particles. Finally, we provide direct measurement of the recoilless fraction in nanohematite and nanomagnetite with an average particle size of 19 nm.

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