The Stresses in a Flat Curved Bar Resulting From Concentrated Tangential Boundary Loads

1954 ◽  
Vol 21 (2) ◽  
pp. 151-159
Author(s):  
Ning-Gau Wu ◽  
C. W. Nelson
Keyword(s):  
Plane Stress ◽  
Integral Method ◽  
Radial Direction ◽  
Fourier Integral ◽  
Concentric Circles

Abstract The Fourier integral method is applied to plane-stress problems of a curved bar bounded by two concentric circles and loaded by concentrated tangential boundary loads. The solutions presented may be combined with results given in previous papers (1, 2) dealing with radial boundary loads so as to obtain the stresses in a curved bar loaded by any combination of concentrated boundary loads inclined at any angle to the radial direction.

A Fourier Integral Solution for the Plane-Stress Problem of a Circular Ring With Concentrated Radial Loads

1951 ◽  
Vol 18 (2) ◽  
pp. 173-182
Author(s):  
Carl W. Nelson
Keyword(s):  
Plane Stress ◽  
Integral Method ◽  
Fourier Integral ◽  
Circular Ring ◽  
Outer Radius ◽  
Integral Solution ◽  
Concentrated Loads ◽  
Stress Problem ◽  
Plane Stress Problem ◽  
Circular Rings

Abstract A Fourier integral solution for the stresses in a straight bar of uniform cross section loaded by various combinations of loads applied normally to the edges of the bar was published by L. N. G. Filon in 1903 (3). Solutions for the stresses in circular rings, loaded on one or both boundaries by radial loads, have been limited to Fourier-series solutions for closed circular rings (1, 12, 13, 14, 15), except that solutions in closed form have been obtained for the limiting cases which occur either when the inner radius becomes very small or when the outer radius becomes very large. This paper presents a Fourier integral solution for the plane-stress problem of a curved bar bounded by two concentric circles and loaded by radial loads on the circular boundaries. It treats only the particular case of a curved bar in equilibrium under the action of two equal and opposite radial forces, one on each boundary. However, the method can be extended so as to deal with other combinations of loads. Sufficient numerical results are given to show that the Fourier integral method permits the calculation of numerical values of the stresses in the particular case considered. It is the purpose of this paper to show that the Fourier integral method can be used successfully in what is probably the simplest problem of concentrated loads acting on a curved bar and to furnish a background of material for use in less simple problems such as bending of curved bars due to concentrated loads.

The Stresses in a Flat Curved Bar Due to Concentrated Radial Loads

1952 ◽  
Vol 19 (4) ◽  
pp. 529-536
Author(s):  
C. W. Nelson ◽  
C. J. Ancker ◽  
Ning-Gau Wu
Keyword(s):  
Integral Method ◽  
Loading Condition ◽  
Fourier Integral ◽  
Integral Solution ◽  
Machine Design ◽  
Design Problems ◽  
Plane Stress Problem ◽  
Elasticity Problems ◽  
Radial Forces ◽  
Concentric Circles

Abstract This paper presents a Fourier integral solution for the plane-stress problem of a curved bar bounded by two concentric circles and loaded by any combination of radial loads on the circular boundaries. It is an extension of an earlier investigation (1) which dealt with only the particular case of a curved bar in equilibrium under the action of two equal and opposite radial forces, one on each boundary. Numerical results are given for one of two basic cases from which the stresses for any combination of concentrated radial loads may be obtained by superposition. An example is included to show how superposition may be used to obtain the stresses for a loading condition which may occur frequently in practical machine-design problems. It is believed that the procedures developed in this paper will be useful in the solution of other elasticity problems by the Fourier integral method.

Transient Response of a Rigid Spherical Inclusion in an Elastic Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 637-642 ◽  
Author(s):  
C. C. Mow
Keyword(s):  
Exact Solution ◽  
Elastic Medium ◽  
Transient Response ◽  
Integral Method ◽  
Spherical Inclusion ◽  
Time History ◽  
Fourier Integral ◽  
Incident Pulse ◽  
History Of

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.

Finite Twisting and Expansion of a Hole in a Rigid/Plastic Plate

1963 ◽  
Vol 30 (4) ◽  
pp. 605-612 ◽  
Author(s):  
R. P. Nordgren ◽  
P. M. Naghdi
Keyword(s):  
Plane Stress ◽  
Work Hardening ◽  
Infinite Plate ◽  
Yield Function ◽  
The State ◽  
Numerical Results ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Combined Action ◽  
Concentric Circles

This paper is concerned with the finite twisting and expansion of an annular rigid/plastic plate in the state of plane stress. The plate, bounded by two concentric circles one of which may extend to infinity, is subjected in its plane to the combined action of pressure on the inner boundary and a couple due to circumferential shear. A detailed solution which includes the effect of isotropic work hardening is obtained with the use of Tresca’s yield function and its associated flow rules and the corresponding solution with the use of Mises’ yield function and its associated flow rules is also discussed. Numerical results are given which illustrate the influence of twisting on the expansion of a hole in an infinite plate.

scholarly journals XI. The electrification of two parallel circular discs

1924 ◽  
Vol 224 (616-625) ◽  
pp. 303-369 ◽  
Keyword(s):  
Exact Solution ◽  
Integral Method ◽  
Electrical Potential ◽  
Fourier Integral ◽  
Infinite Plane ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
The Earth

The only problem relating to two electrified circular discs, placed parallel to each other, for which an exact solution has been obtained hitherto, is the classical one of Nobili’s rings. This was solved by Riemann,* by an application of the Bessel-Fourier integral method. In this problem the discs are circular electrodes fixed to two infinite conducting planes, which are themselves connected together by the earth or by a wire at infinity. If the axis of z is that of the two co-axial discs, and perpendicular to the infinite plane conducting sheets, the electrical potential V satisfies Laplace’s equation at all points between the plates, and the further conditions (1) ∂V/∂ z = 0, z = ± a , p > p 1 (2) ∂v/∂ z = A/√(r 1 2 —r 2 ), z = ± a , p < p 1 where A is a constant, 2 a is the distance between the plates, bisected by the origin, p 1 is the radius of either disc, and p is the distance of any point from the axis of z . In fact ( z , p ) are the two cylindrical polar co-ordinates on which V can alone depend.

The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes

1953 ◽  
Vol 20 (1) ◽  
pp. 82-86
Author(s):  
H. D. Conway
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Integral Method ◽  
Fourier Integral ◽  
Straight Edge ◽  
Variable Method ◽  
Stress Distributions ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Method Of Solution

Abstract Using a Fourier integral method, the solution is obtained to an isotropic half plane subjected to a concentrated load acting at some distance from the straight edge. This problem was discussed previously by Melan, using a complex variable method of solution. The Fourier integral method is then extended to solve the corresponding problems of the orthotropic half plane.

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