Elastic stability of thin-walled cylindrical and conical shells under axial compression

AIAA Journal ◽  
1965 ◽  
Vol 3 (3) ◽  
pp. 500-505 ◽  
Author(s):  
V. I. WEINGARTEN ◽  
E. J. MORGAN ◽  
PAUL SEIDE
Keyword(s):  
Axial Compression ◽  
Elastic Stability ◽  
Conical Shells ◽  
Thin Walled

Low Buckling Loads of Axially Compressed Conical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 384-392 ◽  
Author(s):  
M. Baruch ◽  
O. Harari ◽  
J. Singer
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Plane Boundary ◽  
Essential Difference ◽  
Physical Reason ◽  
Buckling Loads ◽  
Conical Shells ◽  
Simple Supports ◽  
Interaction Curves ◽  
The Stability

The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell-type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expression for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the “classical” ones are obtained for all but the stiffest simple supports SS4 (v = u = 0). Except for short shells, the effects do not depend on the length of the shell. The physical reason for the low buckling loads in the SS3 case is explained and the essential difference between cylinder and cone in this case is discussed. Buckling under combined axial compression and external or internal pressure is studied and interaction curves have been calculated for the 4 sets of in-plane boundary conditions.

ELASTIC BUCKLING OF THIN-WALLED CIRCULAR TUBES CONTAINING AN ELASTIC INFILL

2006 ◽  
Vol 06 (04) ◽  
pp. 457-474 ◽  
Author(s):  
M. A. BRADFORD ◽  
A. ROUFEGARINEJAD ◽  
Z. VRCELJ
Keyword(s):  
Axial Compression ◽  
A Priori ◽  
Local Buckling ◽  
Steel Tube ◽  
Transcendental Equation ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Elastic Tubes ◽  
Thin Walled ◽  
Energy Formulation

Circular thin-walled elastic tubes under concentric axial loading usually fail by shell buckling, and in practical design procedures the buckling load can be determined by modifying the local buckling stress to account empirically for the imperfection sensitive response that is typical in Donnell shell theory. While the local buckling stress of a hollow thin-walled tube under concentric axial compression has a solution in closed form, that of a thin-walled circular tube with an elastic infill, which restrains the local buckling mode, has received far less attention. This paper addresses the local buckling of a tubular member subjected to axial compression, and formulates an energy-based technique for determining the local buckling stress as a function of the stiffness of the elastic infill by recourse to a transcendental equation. This simple energy formulation, with one degree of buckling freedom, shows that the elastic local buckling stress increases from 1 to [Formula: see text] times that of a hollow tube as the stiffness of the elastic infill increases from zero to infinity; the latter case being typical of that of a concrete-filled steel tube. The energy formulation is then recast into a multi-degree of freedom matrix stiffness format, in which the function for the buckling mode is a Fourier representation satisfying, a priori, the necessary kinematic condition that the buckling deformation vanishes at the point where it enters the elastic medium. The solution is shown to converge rapidly, and demonstrates that the simple transcendental formulation provides a sufficiently accurate representation of the buckling problem.

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