Further Consideration of the Thick-Plate Problem With Axially Symmetric Loading

1962 ◽  
Vol 29 (1) ◽  
pp. 91-98 ◽  
Author(s):  
C. W. Nelson
Keyword(s):  
Approximate Method ◽  
Numerical Evaluation ◽  
Thick Plate ◽  
Hankel Transform ◽  
Integral Approach ◽  
Axially Symmetric ◽  
Transform Method ◽  
Thick Plates ◽  
Symmetric Loading ◽  
Special Case

The Fourier-Bessel integral approach was first applied to thick-plate problems of elasticity by Lamb and later by Dougall. Still later, the method, now known as the Hankel transform method, was applied to several cases of the thick-plate problem by Sneddon who, apparently, was the first to obtain numerical results for the stresses in thick plates by this method. Sneddon devised an approximate method for evaluating the integrals; i.e., inverting the transforms, which he encountered. The main contribution of the present paper consists in the more precise numerical evaluation of the integrals involved for a special case previously considered by Sneddon, but for values of parameters outside the range studied by Sneddon. In particular, it is hoped that the formulation of integration procedures presented will be found useful in other thick-plate problems.

Stresses in a Thick Plate With Axially Symmetric Loading

1965 ◽  
Vol 32 (2) ◽  
pp. 458-459 ◽  
Author(s):  
T. J. Lardner
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Numerical Integration ◽  
Elastic Plate ◽  
Thick Plate ◽  
Axially Symmetric ◽  
Pressure Loading ◽  
Normal Stress Distribution ◽  
Symmetric Loading

The problem of the thick elastic plate with a symmetric circular pressure loading is considered. The normal stress distribution on the midplane and for two positions off the midplane is obtained by a numerical integration of the solutions. A comparison of the stress distribution on the midplane is made with previous results.

On the Reconstruction of NQR Nutation Spectra in Solids with Powder Geometry

1994 ◽  
Vol 49 (1-2) ◽  
pp. 35-41 ◽  
Author(s):  
H. Robert ◽  
D. Pusiol ◽  
E. Rommel ◽  
R. Kimmich
Keyword(s):  
Single Crystals ◽  
Maximum Entropy Method ◽  
Hankel Transform ◽  
Entropy Method ◽  
Reconstruction Method ◽  
Zero Field ◽  
Axially Symmetric ◽  
Transform Method ◽  
The Fourier Transform

Abstract In single crystals the NQR nutation frequency depends on the relative orientation of the coil and the quadrupole axes. In powders the nutation lineshape is a superposition of spectra from the randomly oriented single crystals, so that powder patterns appear in such experiments if the recon­struction is performed by the Fourier transform method. In this paper an alternative reconstruction method of nutation spectra is suggested making use of the Hankel Transform. In this way the nutation spectra are simplified. Singularities arising with experiments for the determination of the asymmetry parameter η can easily be resolved. In the particular case of an axially symmetric quadrupolar tensor and a homogeneous radiofrequency field one can reduce the powder pattern to a single line without heterogeneous broadening with respect to orientation. Further improvement o f the nutation spectra can be achieved by taking advantage of the maximum entropy method, which strongly reduces apodisation and noise problems. Applications of the new data manipulation techniques to N Q R imaging methods published elsewhere and 2D zero-field N Q R spectroscopy are reported.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

The Adjustment of Incomplete Direction Observations

1965 ◽  
Vol 19 (5) ◽  
pp. 462-471
Author(s):  
G. G. Bennett
Keyword(s):  
Iterative Method ◽  
Approximate Method ◽  
Theoretical Justification ◽  
Special Case

An iterative method for the solution of the problem of adjusting incomplete direction observations has been known and practised for many years, apparently without theoretical justification. The method is shown to be theoretically sound and convergent in all cases. In fact, the approximate method may be classed as a general case, which includes the special case of the adjustment of complete direction observations.

scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

The Refined Theory of One-Dimensional Quasi-Crystals in Thick Plate Structures

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Thick Plate ◽  
Ad Hoc ◽  
Plate Theory ◽  
Pure Shear ◽  
Refined Theory ◽  
Plate Structures ◽  
Thick Plates ◽  
Refined Plate Theory ◽  
One Dimensional ◽  
Quasi Crystals

For one-dimensional quasi-crystals, the refined theory of thick plates is explicitly established from the general solution of quasi-crystals and the Luré method without employing ad hoc stress or deformation assumptions. For a homogeneous plate, the exact equations and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined plate theory. In an illustrative example, explicit expressions of analytical solutions are obtained for torsion of a rectangular quasi-crystal plate.

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