Bifurcation of Rings Under Concentrated Centrally Directed Loads

1973 ◽  
Vol 40 (2) ◽  
pp. 553-558 ◽  
Author(s):  
E. D. Albano ◽  
P. Seide
Keyword(s):  
Average Pressure ◽  
Uniform Pressure ◽  
Circular Rings ◽  
The Stability

The stability of the large symmetrical deformations of circular rings under equal and equally spaced centrally directed loads is examined. It is found that for 5 or more loads the critical average pressure (the load divided by the distance between loads) does not differ significantly from the result for uniform pressure. The results for 2, 3, and 4 centrally directed or normal loads are identical.

Bifurcation of Circular Rings Under Normal Concentrated Loads

1973 ◽  
Vol 40 (1) ◽  
pp. 233-238 ◽  
Author(s):  
P. Seide ◽  
E. D. Albano
Keyword(s):  
Bifurcation Point ◽  
Circular Ring ◽  
Average Pressure ◽  
Uniform Pressure ◽  
Concentrated Loads ◽  
Finite Distortion ◽  
Circular Rings ◽  
Concentrated Forces

The deformation in bending of a circular ring loaded in its plane by concentrated forces is studied. The ring is assumed to be an elastica. The loads are of equal magnitudes and are equally spaced about the ring. Values of loading at which bifurcation of the symmetrical finite distortion shape occurs are determined for forces which remain normal to the ring. It is found that no bifurcation point exists for a ring under three loads. Buckling of a ring under two loads can occur only when the prebuckling configuration is an extremely distorted one. If the number of loads is five or greater, the critical average pressure does not differ greatly from the result for the ring under uniform pressure.

On Finite Bending of Pressurized Tubes

1959 ◽  
Vol 26 (3) ◽  
pp. 386-392
Author(s):  
Eric Reissner
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Linear Problem ◽  
Bending Moments ◽  
Pure Bending ◽  
Stability Parameters ◽  
Essential Step ◽  
Circular Rings ◽  
The Stability ◽  
Finite Bending

Abstract A unified treatment is presented of two well-known problems which have until now been considered separately. The two problems are: (a) the linear problem of pure bending of curved tubes, and (b) the nonlinear problem of pure bending of straight tubes. In both problems the effect of uniform internal pressure is included. The essential step in the present analysis is the treatment of the flattening of the cross sections of the tube by means of a theory of finite bending of circular rings. The general results of the paper are used to obtain improved values for the stability parameters in the problem of flattening instability of originally straight tubes acted upon by end bending moments, and also to obtain results on the effect of slight original curvature of the beam axis in the problem of flattening instability.

A Uniform Pressure Apparatus for Micro/Nanoimprint Lithography Equipment

2009 ◽  
Vol 3 (1) ◽  
pp. 84-88 ◽  
Author(s):  
Jian-Shian Lin ◽  
◽  
Chieh-Lung Lai ◽  
Ya-Chun Tu ◽  
Cheng-Hua Wu ◽  
...  
Keyword(s):  
External Force ◽  
Nanoimprint Lithography ◽  
Production Cost ◽  
Critical Issue ◽  
Light Diffraction ◽  
Average Pressure ◽  
Uniform Pressure

Nanoimprint lithography (NIL) has overcome the limitation of light diffraction. It is capable of printing features less than 10nm in size with high lithographic resolution, high manufacturing speed, and low production cost. The uniformity of pressure, however, remains a critical issue. To improve the uniformity of pressure, we developed a flexible uniform pressure component based on Pascal's Law. When external force is applied to this component, uniform pressure is delivered to the mold and substrate. Average pressure over the embossed area using our improved nanoimprint equipment deviates by only 3.15%.

One-Way Buckling of Circular Rings Confined Within a Rigid Boundary

1995 ◽  
Vol 117 (2) ◽  
pp. 162-169 ◽  
Author(s):  
C. Sun ◽  
W. J. D. Shaw ◽  
A. M. Vinogradov
Keyword(s):  
Critical Condition ◽  
Experimental Approach ◽  
Equilibrium Analysis ◽  
Initial Deflection ◽  
Rigid Boundary ◽  
Geometric Imperfections ◽  
Circular Rings ◽  
Initial Geometric Imperfections ◽  
The Stability ◽  
Theoretical Results

The stability of a ring confined by a rigid boundary, subjected to circumferential end loads, is investigated both theoretically and experimentally. The effect of initial geometric imperfections on the buckling load is determined by assuming an initial deflection configuration as a simple sine form and the critical condition was derived from equilibrium analysis. An experimental approach was designed to verify the analytical results. Comparison with other theoretical results are also made.

scholarly journals Self-gravitating warped disks around nuclear black holes

2006 ◽  
Vol 2 (S238) ◽  
pp. 467-468
Author(s):  
Ayse Ulubay-Siddiki ◽  
Ortwin Gerhard ◽  
Magda Arnaboldi
Keyword(s):  
Black Hole ◽  
Time Integration ◽  
Galactic Nuclei ◽  
Limited Range ◽  
Black Hole Mass ◽  
Central Black Hole ◽  
Equilibrium Configurations ◽  
Circular Rings ◽  
The Stability ◽  
Self Gravity

AbstractMany galactic nuclei contain disks of gas and possibly stars surrounding a supermassive black hole. These disks may play a key role in the evolution of galactic centers. Here we address the problem of finding stable warped equilibrium configurations for such disks, considering the attraction by the black hole and the disk self-gravity as the only acting forces. We model these disks as a collection of concentric, circular rings.We find the equilibria of such systems of rings, and determine how they scale with the ring parameters and the mass of the central black hole. We show that in some cases these disk equilibria may be highly warped. We then analyze the stability of these disks, using both direct time integration and linear stability analysis. This shows that the warped disks are stable for a range of disk-to-black hole mass ratios, when the rings extend over a limited range of radii.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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