A Polar Coordinate Integration Scheme with a Hierarchical Correction Procedure to Improve Numerical Accuracy

1988 ◽  
pp. 215-222 ◽  
Author(s):  
Makoto Koizumi ◽  
Motoaki Utamura
Keyword(s):  
Integration Scheme ◽  
Correction Procedure ◽  
Numerical Accuracy ◽  
Polar Coordinate

scholarly journals Elastoplasticité anisotrope non normale en grandes déformations avec endommagement

2007 ◽  
pp. 913-940
Author(s):  
Houssem Badreddine ◽  
Khémaïs Saanouni ◽  
Abdelwaheb Dogui ◽  
M. Amen Gahbich
Keyword(s):  
Thin Sheet ◽  
Constitutive Models ◽  
Plasticity Theory ◽  
Integration Scheme ◽  
Correction Procedure ◽  
Elastoplastic Model ◽  
Classical Dynamic ◽  
Strongly Coupled ◽  
Plastic Correction ◽  
Bulging Test

This work is devoted to the numerical integration of an elastoplastic model strongly coupled with ductile damage and formulated in finite deformation. This model with mixed nonlinear work hardening (kinematic and isotropic) is based on a non associative and non normal plasticity theory. The integration is based on the elastic prediction – plastic correction procedure. The proposed constitutive models as well as the associated integration scheme are implemented into ABAQUS/Explicit thanks to VUMAT subroutine. The global resolution is done using the classical Dynamic Explicit (DE) strategy with ABAQUS/Explicit F.E. code. Application is made to the prediction of rupture in anisotropic thin sheet subjected to a hydro bulging test with circular and elliptic matrices. A conparison between the numerical and experimental results shows the capacity of such a modeling to reproduce the anisotropic thin sheet rupture.

Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts
Keyword(s):  
Resonant Absorption ◽  
Numerical Code ◽  
Mhd Waves ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Element Discretization ◽  
Flux Tubes ◽  
Magnetohydrodynamic Waves ◽  
Viscosity Coefficients ◽  
Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

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

Bence-albee after 25 years: A new superior α-factor correction procedure for the quantitative analysis of oxides and silicates

1992 ◽  
Vol 50 (2) ◽  
pp. 1744-1745
Author(s):  
John T. Armstrong
Keyword(s):  
Quantitative Analysis ◽  
Electron Microprobe ◽  
Binary Systems ◽  
Correction Procedure ◽  
Geological Samples ◽  
The Past ◽  
Large Matrix ◽  
Computational Speed ◽  
Microprobe Data ◽  
Geological Sciences

One of the most cited papers in the geological sciences has been that of Albee and Bence on the use of empirical " α -factors" to correct quantitative electron microprobe data. During the past 25 years this method has remained the most commonly used correction for geological samples, despite the facts that few investigators have actually determined empirical α-factors, but instead employ tables of calculated α-factors using one of the conventional "ZAF" correction programs; a number of investigators have shown that the assumption that an α-factor is constant in binary systems where there are large matrix corrections is incorrect (e.g, 2-3); and the procedure’s desirability in terms of program size and computational speed is much less important today because of developments in computing capabilities. The question thus exists whether it is time to honorably retire the Bence-Albee procedure and turn to more modern, robust correction methods. This paper proposes that, although it is perhaps time to retire the original Bence-Albee procedure, it should be replaced by a similar method based on compositiondependent polynomial α-factor expressions.

Reconstruction of complex shaped crack from ECT signals based on a fast forward solver using an advanced multi-media element

2020 ◽  
Vol 64 (1-4) ◽  
pp. 621-629
Author(s):  
Yingsong Zhao ◽  
Cherdpong Jomdecha ◽  
Shejuan Xie ◽  
Zhenmao Chen ◽  
Pan Qi ◽  
...  
Keyword(s):  
Coefficient Matrix ◽  
Crack Edge ◽  
Numerical Accuracy ◽  
Gauss Point ◽  
Current Testing ◽  
Efficient Simulation ◽  
Shaped Crack ◽  
Multi Media ◽  
Profile Reconstruction ◽  
Crack Profile

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.

Numerical Study of the Combined Free-Forced Convection and Mass Transfer Flow Past a Vertical Porous Plate in a Porous Medium with Heat Generation and Thermal Diffusion

2006 ◽  
Vol 11 (4) ◽  
pp. 331-343 ◽  
Author(s):  
M. S. Alam ◽  
M. M. Rahman ◽  
M. A. Samad
Keyword(s):  
Mass Transfer ◽  
Flow Field ◽  
Differential Equations ◽  
Forced Convection ◽  
Heat Generation ◽  
Numerical Study ◽  
Porous Plate ◽  
Integration Scheme ◽  
Suction Parameter ◽  
Transfer Flow

The problem of combined free-forced convection and mass transfer flow over a vertical porous flat plate, in presence of heat generation and thermaldiffusion, is studied numerically. The non-linear partial differential equations and their boundary conditions, describing the problem under consideration, are transformed into a system of ordinary differential equations by using usual similarity transformations. This system is solved numerically by applying Nachtsheim-Swigert shooting iteration technique together with Runge-Kutta sixth order integration scheme. The effects of suction parameter, heat generation parameter and Soret number are examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The analysis of the obtained results showed that the flow field is significantly influenced by these parameters.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

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