scholarly journals Discussion: “Further Consideration of the Thick-Plate Problem With Axially Symmetric Loading” (Nelson, C. W., 1962, ASME J. Appl. Mech., 29, pp. 91–98)

1963 ◽  
Vol 30 (1) ◽  
pp. 156-157
Author(s):  
Chih-Bing Ling
Keyword(s):  
Thick Plate ◽  
Axially Symmetric ◽  
Symmetric Loading

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.

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.

scholarly journals The elastoplastic problem of the half-space with a hole subjected to axially symmetric loading

2005 ◽  
Vol 27 (4) ◽  
pp. 245-255
Author(s):  
Vu Do Long
Keyword(s):  
Half Space ◽  
Deformation Process ◽  
Elastoplastic Deformation ◽  
Solution Method ◽  
Elastoplastic Problem ◽  
The Body ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Symmetric Loading ◽  
Theory Solution

The elastoplastic problem of the half-space with a hole subjected to axially symmetric loading considered in this paper is based on the elastoplastic deformation process theory. Solution of this problem is carried out by using the modified elastic solution method and the finite element method. Some results of numerical calculation are presented here to give the picture of plastic domains enlarging in the body and the obtained displacements on the free boundary of the half-space.

Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks I. Cracks in an infinite solid and a thick plate

1962 ◽  
Vol 266 (1326) ◽  
pp. 359-386 ◽  
Keyword(s):  
Integral Equations ◽  
Interior Point ◽  
Thick Plate ◽  
Elastic Solid ◽  
Point Force ◽  
Fredholm Integral Equations ◽  
Stress Distributions ◽  
Axially Symmetric ◽  
Single Crack ◽  
Elastic Solids

Some axially symmetric stress distributions in an infinite elastic solid and in a thick plate containing penny-shaped cracks are considered. It is shown that, by use of a representation for the displacement in an infinite elastic solid containing a single crack, representations for the displacements in an infinite solid containing two or more cracks and in a thick plate containing a single crack can be constructed and used to reduce the problems of determining the stresses in these solids to the solutions of Fredholm integral equations of the second kind. Various stress distributions investigated include those due to the opening of a crack in an infinite solid by a point force acting at an interior point of the solid and the opening of cracks in an infinite solid and a thick plate under the action of constant pressures over the cracks.

A Digital Computer Program for the General Axially Symmetric Thin-Shell Problem

1962 ◽  
Vol 29 (4) ◽  
pp. 655-661 ◽  
Author(s):  
W. K. Sepetoski ◽  
C. E. Pearson ◽  
I. W. Dingwell ◽  
A. W. Adkins
Keyword(s):  
Computer Program ◽  
Thin Shell ◽  
Thin Shells ◽  
Axially Symmetric ◽  
Shells Of Revolution ◽  
Computational Accuracy ◽  
Symmetric Loading ◽  
Shell Geometry ◽  
General Computer Program ◽  
General Computer

This paper describes the development of a general computer program to handle arbitrary thin shells of revolution subject to radially symmetric loading or temperature variation. An elimination method is used to solve the set of difference equations obtained from the basic differential equations; a feature of the method is that “edge effect” difficulties that can arise with conventional differential-equation routines are avoided. The program is quite flexible and permits discontinuities in shell geometry or loading. The results of applying the program to several classical problems of known solution are given. These results permit the examination of computational accuracy for varying boundary conditions and mesh sizes. Finally, some program solutions of unconventional problems are presented.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

Unstable axially symmetric mhd flow between rotating boundaries

2001 ◽  
Vol 7 (2s) ◽  
pp. 19-25
Author(s):  
A.A. Loginov ◽  
◽  
Yu.I. Samoilenko ◽  
V.A. Tkachenko ◽  
◽  
...  
Keyword(s):  
Mhd Flow ◽  
Axially Symmetric
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