Buckling and Post-buckling of Circular Rings: Some Differential Geometry Issues

2021 ◽  
Author(s):  
Federico Guarracino ◽  
Ida Mascolo
Keyword(s):  
Differential Geometry ◽  
Post Buckling ◽  
Circular Rings

Influence of loading behavior on the post buckling of circular rings

AIAA Journal ◽  
1976 ◽  
Vol 14 (2) ◽  
pp. 266-267 ◽  
Author(s):  
M. S. El Naschie ◽  
Amr El Nashai
Keyword(s):  
Post Buckling ◽  
Circular Rings

Behavior of Thin Elastic Circular Rings With Large Deformations Under Nonuniform Loads

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
E. Azzuni ◽  
S. Guzey
Keyword(s):  
Large Deformations ◽  
Normal Pressure ◽  
Numerical Approach ◽  
Circular Ring ◽  
Order Ordinary Differential Equation ◽  
Pressure Profiles ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Circular Rings ◽  
Small Deformations

Thin elastic circular rings under uniform pressure have been extensively studied by many researchers. Both the deflection and buckling behavior of rings were considered in these studies, but most have focused on the small deformations analysis approach. Even though the use of the small deformations assumption helps find the deflections of the ring prior to reaching the buckling load, it does not accurately capture the behavior of the ring after buckling. The in-plane large deformations analysis of thin elastic circular rings under nonuniform pressure explored in this paper expands on previous work and investigates varying pressure profiles. The pressure profiles studied here can be described by p=p01+qcosnθ. The large deformations assumption allows for the investigating of buckling loads as well as post-buckling behavior. Nonuniform normal pressure acting on a thin elastic circular ring results in a behavior that is described by a second-order ordinary differential equation (ODE) of the Duffing type, which is solved here through a numerical approach.

Applicable Differential Geometry

1987 ◽  
Author(s):  
M. Crampin ◽  
F. A. E. Pirani
Keyword(s):  
Differential Geometry

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

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